## INTRODUCTION

### Introduction

WIKI

A communications satellite or comsat is an artificial satellite sent to space for the purpose of telecommunications. Modern communications satellites use a variety of orbits including geostationary orbits, Molniya orbits, elliptical orbits and low (polar and non-polar Earth orbits). For fixed (point-to-point) services, communications satellites provide a microwave radio relay technology complementary to that of communication cables. They are also used for mobile applications such as communications to ships, vehicles, planes and hand-held terminals, and for TV and radio broadcasting. The Merriam-Webster dictionary defines a satellite as a celestial body orbiting another of larger size or a manufactured object or vehicle intended to orbit the earth, the moon, or another celestial body.[1] Today's satellite communications can trace their origins all the way back to the Moon. A project named Communication Moon Relay was a telecommunication project carried out by the United States Navy. Its objective was to develo

# Communications satellite

(Redirected from Satellite communications)
An Advanced Extremely High Frequency communications satellite relays secure communications for the United States and other allied countries.

A communications satellite or comsat is an artificial satellite sent to space for the purpose of telecommunications. Modern communications satellites use a variety of orbits including geostationary orbits, Molniya orbits, elliptical orbits and low (polar and non-polar Earth orbits).

For fixed (point-to-point) services, communications satellites provide a microwave radio relay technology complementary to that of communication cables. They are also used for mobile applications such as communications to ships, vehicles, planes and hand-held terminals, and for TV and radio broadcasting.

## History

The Merriam-Webster dictionary defines a satellite as a celestial body orbiting another of larger size or a manufactured object or vehicle intended to orbit the earth, the moon, or another celestial body.[1]

Today's satellite communications can trace their origins all the way back to the Moon. A project named Communication Moon Relay was a telecommunication project carried out by the United States Navy. Its objective was to develop a secure and reliable method of wireless communication by using the Moon as a natural communications satellite.

The first artificial satellite used solely to further advances in global communications was a balloon named Echo 1.[2] Echo 1 was the world's first artificial communications satellite capable of relaying signals to other points on Earth. It soared 1,000 miles (1,609 km) above the planet after its Aug. 12, 1960 launch, yet relied on humanity's oldest flight technology — ballooning. Launched by NASA, Echo 1 was a giant metallic balloon 100 feet (30 meters) across. The world's first inflatable satellite — or "satelloon," as they were informally known — helped lay the foundation of today's satellite communications. The idea behind a communications satellite is simple: Send data up into space and beam it back down to another spot on the globe. Echo 1 accomplished this by essentially serving as an enormous mirror 10 stories tall that could be used to bounce communications signals off of.

The first American satellite to relay communications was Project SCORE in 1958, which used a tape recorder to store and forward voice messages. It was used to send a Christmas greeting to the world from U.S. President Dwight D. Eisenhower. NASA launched the Echo satellite in 1960; the 100-foot (30 m) aluminised PET film balloon served as a passive reflector for radio communications. Courier 1B, built by Philco, also launched in 1960, was the world's first active repeater satellite.

It is commonly believed that the first "satellite" was Sputnik 1. Put into orbit by the Soviet Union on October 4, 1957, it was equipped with an onboard radio-transmitter that worked on two frequencies: 20.005 and 40.002 MHz. Sputnik 1 was launched as a step in the exploration of space and rocket development. While incredibly important it was not placed in orbit for the purpose of sending data from one point on earth to another. Hence, it was not the first "communications" satellite, but it was the first artificial satellite in the steps leading to today's satellite communications.

Telstar was the first active, direct relay communications satellite. Belonging to AT&T as part of a multi-national agreement between AT&T, Bell Telephone Laboratories, NASA, the British General Post Office, and the French National PTT (Post Office) to develop satellite communications, it was launched by NASA from Cape Canaveral on July 10, 1962, the first privately sponsored space launch. Relay 1 was launched on December 13, 1962, and became the first satellite to broadcast across the Pacific on November 22, 1963[3]

An immediate antecedent of the geostationary satellites was Hughes' Syncom 2, launched on July 26, 1963. Syncom 2 revolved around the earth once per day at constant speed, but because it still had north-south motion, special equipment was needed to track it.

### Geostationary orbits

To an observer on the earth, a satellite in a geostationary orbit appears motionless, in a fixed position in the sky. This is because it revolves around the earth at the earth's own angular velocity (360 degrees every 24 hours, in an equatorial orbit).

A geostationary orbit is useful for communications because ground antennas can be aimed at the satellite without their having to track the satellite's motion. This is relatively inexpensive. In applications that require a large number of ground antennas, such as DirectTV distribution, the savings in ground equipment can more than outweigh the cost and complexity of placing a satellite into orbit.

The concept of the geostationary communications satellite was first proposed by Arthur C. Clarke, building on work by Konstantin Tsiolkovsky and on the 1929 work by Herman Poto?nik (writing as Herman Noordung) Das Problem der Befahrung des Weltraums — der Raketen-motor. In October 1945 Clarke published an article titled "Extra-terrestrial Relays" in the British magazine Wireless World.[4] The article described the fundamentals behind the deployment of artificial satellites in geostationary orbits for the purpose of relaying radio signals. Thus, Arthur C. Clarke is often quoted as being the inventor of the communications satellite.[citation needed]

The first geostationary satellite was Syncom 3, launched on August 19, 1964, and used for communication across the Pacific starting with television coverage of the 1964 Summer Olympics. Shortly after Syncom 3, Intelsat I, aka Early Bird, was launched on April 6, 1965 and placed in orbit at 28° west longitude. It was the first geostationary satellite for telecommunications over the Atlantic Ocean.

On November 9, 1972, Canada's first geostationary satellite serving the continent, Anik A1, was launched by Telesat Canada, with the United States following suit with the launch of Westar 1 by Western Union on April 13, 1974.

On May 30, 1974, the first geostationary communications satellite in the world to be three-axis stabilized was launched: the experimental satellite ATS-6 built for NASA

After the launches of the Telstar through Westar 1 satellites, RCA Americom (later GE Americom, now SES) launched Satcom 1 in 1975. It was Satcom 1 that was instrumental in helping early cable TV channels such as WTBS (now TBS Superstation), HBO, CBN (now ABC Family), and The Weather Channel become successful, because these channels distributed their programming to all of the local cable TV headends using the satellite. Additionally, it was the first satellite used by broadcast television networks in the United States, like ABC, NBC, and CBS, to distribute programming to their local affiliate stations. Satcom 1 was widely used because it had twice the communications capacity of the competing Westar 1 in America (24 transponders as opposed to the 12 of Westar 1), resulting in lower transponder-usage costs. Satellites in later decades tended to have even higher transponder numbers.

By 2000, Hughes Space and Communications (now Boeing Satellite Development Center) had built nearly 40 percent of the more than one hundred satellites in service worldwide. Other major satellite manufacturers include Space Systems/Loral, Orbital Sciences Corporation with the STAR Bus series, Indian Space Research Organization, Lockheed Martin (owns the former RCA Astro Electronics/GE Astro Space business), Northrop Grumman, Alcatel Space, now Thales Alenia Space, with the Spacebus series, and Astrium.

### Low-Earth-orbiting satellites

Low Earth orbit in Cyan

A low Earth orbit (LEO) typically is a circular orbit about 200 kilometres (120 mi) above the earth's surface and, correspondingly, a period (time to revolve around the earth) of about 90 minutes. Because of their low altitude, these satellites are only visible from within a radius of roughly 1000 kilometers from the sub-satellite point. In addition, satellites in low earth orbit change their position relative to the ground position quickly. So even for local applications, a large number of satellites are needed if the mission requires uninterrupted connectivity.

Low-Earth-orbiting satellites are less expensive to launch into orbit than geostationary satellites and, due to proximity to the ground, do not require as high signal strength (Recall that signal strength falls off as the square of the distance from the source, so the effect is dramatic). Thus there is a trade off between the number of satellites and their cost. In addition, there are important differences in the onboard and ground equipment needed to support the two types of missions.

A group of satellites working in concert is known as a satellite constellation. Two such constellations, intended to provide satellite phone services, primarily to remote areas, are the Iridium and Globalstar systems. The Iridium system has 66 satellites.

It is also possible to offer discontinuous coverage using a low-Earth-orbit satellite capable of storing data received while passing over one part of Earth and transmitting it later while passing over another part. This will be the case with the CASCADE system of Canada's CASSIOPE communications satellite. Another system using this store and forward method is Orbcomm.

### Molniya satellites

Geostationary satellites must operate above the equator and therefore appear lower on the horizon as the receiver gets the farther from the equator. This will cause problems for extreme northerly latitudes, affecting connectivity and causing multipath (interference caused by signals reflecting off the ground and into the ground antenna). For areas close to the North (and South) Pole, a geostationary satellite may appear below the horizon. Therefore Molniya orbit satellite have been launched, mainly in Russia, to alleviate this problem. The first satellite of the Molniya series was launched on April 23, 1965 and was used for experimental transmission of TV signal from a Moscow uplink station to downlink stations located in Siberia and the Russian Far East, in Norilsk, Khabarovsk, Magadan and Vladivostok. In November 1967 Soviet engineers created a unique system of national TV network of satellite television, called Orbita, that was based on Molniya satellites.

Molniya orbits can be an appealing alternative in such cases. The Molniya orbit is highly inclined, guaranteeing good elevation over selected positions during the northern portion of the orbit. (Elevation is the extent of the satellite's position above the horizon. Thus, a satellite at the horizon has zero elevation and a satellite directly overhead has elevation of 90 degrees).

The Molniya orbit is designed so that the satellite spends the great majority of its time over the far northern latitudes, during which its ground footprint moves only slightly. Its period is one half day, so that the satellite is available for operation over the targeted region for six to nine hours every second revolution. In this way a constellation of three Molniya satellites (plus in-orbit spares) can provide uninterrupted coverage.

## Structure

Communications Satellites are usually composed of the following subsystems:

• Communication Payload, normally composed of transponders, antenna, and switching systems
• Engines used to bring the satellite to its desired orbit
• Station Keeping Tracking and stabilization subsystem used to keep the satellite in the right orbit, with its antennas pointed in the right direction, and its power system pointed towards the sun
• Power subsystem, used to power the Satellite systems, normally composed of solar cells, and batteries that maintain power during solar eclipse
• Command and Control subsystem, which maintains communications with ground control stations. The ground control earth stations monitor the satellite performance and control its functionality during various phases of its life-cycle.

The bandwidth available from a satellite depends upon the number of transponders provided by the satellite. Each service (TV, Voice, Internet, radio) requires a different amount of bandwidth for transmission. This is typically known as link budgeting and a network simulator can be used to arrive at the exact value.

## Applications

### Telephone

An Iridium satellite

The first and historically most important application for communication satellites was in intercontinental long distance telephony. The fixed Public Switched Telephone Network relays telephone calls from land line telephones to an earth station, where they are then transmitted to a geostationary satellite. The downlink follows an analogous path. Improvements in submarine communications cables, through the use of fiber-optics, caused some decline in the use of satellites for fixed telephony in the late 20th century.

Satellite communication are still used in many applications today. Remote islands such as Ascension Island, Saint Helena, Diego Garcia, and Easter Island, where no submarine cables are in service need satellite telephones. There are also regions of some continents and countries where landline telecommunications are rare to nonexistent, for example large regions of South America, Africa, Canada, China, Russia, and Australia. Satellite communications also provide connection to the edges of Antarctica and Greenland. Other land use for satellite phones are rigs at sea, a back up for hospitals, military, and recreation. Ships at sea use often use satellite phones, and planes. [5]

Satellite phones can be accomplished in many different ways. On larger scale often there will be local telephone system in the isolated area with a linked to a telephone system in a main land area. There are services that will patch an radio signal to a telephone system in this example most any type of satellite can be used. Satellite phones connect directly to a constellation of either geostationary or low-earth-orbit satellites. Calls are then forwarded to a satellite teleport connected to the Public Switched Telephone Network .

### Television

As television became the main market, its demand for simultaneous delivery of relatively few signals of large bandwidth to many receivers being a more precise match for the capabilities of geosynchronous comsats. Two satellite types are used for North American television and radio: Direct broadcast satellite (DBS), and Fixed Service Satellite (FSS)

The definitions of FSS and DBS satellites outside of North America, especially in Europe, are a bit more ambiguous. Most satellites used for direct-to-home television in Europe have the same high power output as DBS-class satellites in North America, but use the same linear polarization as FSS-class satellites. Examples of these are the Astra, Eutelsat, and Hotbird spacecraft in orbit over the European continent. Because of this, the terms FSS and DBS are more so used throughout the North American continent, and are uncommon in Europe.

Fixed Service Satellites use the C band, and the lower portions of the Ku bands. They are normally used for broadcast feeds to and from television networks and local affiliate stations (such as program feeds for network and syndicated programming, live shots, and backhauls), as well as being used for distance learning by schools and universities, business television (BTV), Videoconferencing, and general commercial telecommunications. FSS satellites are also used to distribute national cable channels to cable television headends.

Free-to-air satellite TV channels are also usually distributed on FSS satellites in the Ku band. The Intelsat Americas 5, Galaxy 10R and AMC 3 satellites over North America provide a quite large amount of FTA channels on their Ku band transponders.

The American Dish Network DBS service has also recently utilized FSS technology as well for their programming packages requiring their SuperDish antenna, due to Dish Network needing more capacity to carry local television stations per the FCC's "must-carry" regulations, and for more bandwidth to carry HDTV channels.

A direct broadcast satellite is a communications satellite that transmits to small DBS satellite dishes (usually 18 to 24 inches or 45 to 60 cm in diameter). Direct broadcast satellites generally operate in the upper portion of the microwave Ku band. DBS technology is used for DTH-oriented (Direct-To-Home) satellite TV services, such as DirecTV and DISH Network in the United States, Bell TV and Shaw Direct in Canada, Freesat and Sky in the UK, Ireland, and New Zealand and DSTV in South Africa.

Operating at lower frequency and lower power than DBS, FSS satellites require a much larger dish for reception (3 to 8 feet (1 to 2.5m) in diameter for Ku band, and 12 feet (3.6m) or larger for C band). They use linear polarization for each of the transponders' RF input and output (as opposed to circular polarization used by DBS satellites), but this is a minor technical difference that users do not notice. FSS satellite technology was also originally used for DTH satellite TV from the late 1970s to the early 1990s in the United States in the form of TVRO (TeleVision Receive Only) receivers and dishes. It was also used in its Ku band form for the now-defunct Primestar satellite TV service.

Some satellites have been launched that have transponders in the Ka band, such as DirecTV's SPACEWAY-1 satellite, and Anik F2. NASA as well has launched experimental satellites using the Ka band recently.[6]

Some manufacturers have also introduced special antennas for mobile reception of DBS television. Using Global Positioning System (GPS) technology as a reference, these antennas automatically re-aim to the satellite no matter where or how the vehicle (on which the antenna is mounted) is situated. These mobile satellite antennas are popular with some recreational vehicle owners. Such mobile DBS antennas are also used by JetBlue Airways for DirecTV (supplied by LiveTV, a subsidiary of JetBlue), which passengers can view on-board on LCD screens mounted in the seats.

### Digital cinema

Realization and demonstration, on October 29, 2001, of the first digital cinema transmission by satellite in Europe[7] of a feature film by Bernard Pauchon, Alain Lorentz, Raymond Melwig, Philippe Binant.[8]

Satellite radio offers audio services in some countries, notably the United States. Mobile services allow listeners to roam a continent, listening to the same audio programming anywhere.

A satellite radio or subscription radio (SR) is a digital radio signal that is broadcast by a communications satellite, which covers a much wider geographical range than terrestrial radio signals.

Satellite radio offers a meaningful alternative to ground-based radio services in some countries, notably the United States. Mobile services, such as SiriusXM, and Worldspace, allow listeners to roam across an entire continent, listening to the same audio programming anywhere they go. Other services, such as Music Choice or Muzak's satellite-delivered content, require a fixed-location receiver and a dish antenna. In all cases, the antenna must have a clear view to the satellites. In areas where tall buildings, bridges, or even parking garages obscure the signal, repeaters can be placed to make the signal available to listeners.

Initially available for broadcast to stationary TV receivers, by 2004 popular mobile direct broadcast applications made their appearance with the arrival of two satellite radio systems in the United States: Sirius and XM Satellite Radio Holdings. Later they merged to become the conglomerate SiriusXM.

Radio services are usually provided by commercial ventures and are subscription-based. The various services are proprietary signals, requiring specialized hardware for decoding and playback. Providers usually carry a variety of news, weather, sports, and music channels, with the music channels generally being commercial-free.

In areas with a relatively high population density, it is easier and less expensive to reach the bulk of the population with terrestrial broadcasts. Thus in the UK and some other countries, the contemporary evolution of radio services is focused on Digital Audio Broadcasting (DAB) services or HD Radio, rather than satellite radio.

Amateur radio operators have access to the amateur radio satellites that have been designed specifically to carry amateur radio traffic. Most such satellites operate as spaceborne repeaters, and are generally accessed by amateurs equipped with UHF or VHF radio equipment and highly directional antennas such as Yagis or dish antennas. Due to launch costs, most current amateur satellites are launched into fairly low Earth orbits, and are designed to deal with only a limited number of brief contacts at any given time. Some satellites also provide data-forwarding services using the X.25 or similar protocols.

### Internet access

After the 1990s, satellite communication technology has been used as a means to connect to the Internet via broadband data connections. This can be very useful for users who are located in remote areas, and cannot access a broadband connection, or require high availability of services.

### Military

Communications satellites are used for military communications applications, such as Global Command and Control Systems. Examples of military systems that use communication satellites are the MILSTAR, the DSCS, and the FLTSATCOM of the United States, NATO satellites, United Kingdom satellites (for instance Skynet), and satellites of the former Soviet Union. India has launched its first Military Communication satellite GSAT-7, its transpinders operate in UHF, F, C and Ku bands. [9] Many military satellites operate in the X-band, and some also use UHF radio links, while MILSTAR also utilizes Ka band.

X

YOU TUBE

## ORBITAL MECHANICS & LAUNCHERS

### Orbital Mechanics

WIKI

Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and Newton's law of universal gravitation. It is a core discipline within space mission design and control. Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets. Orbital mechanics focuses on spacecraft trajectories, including orbital maneuvers, orbit plane changes, and interplanetary transfers, and is used by mission planners to predict the results of propulsive maneuvers. General relativity is a more exact theory than Newton's laws for calculating orbits, and is sometimes necessary for greater accuracy or in high-gravity situations (such as orbits close to the Sun). Until the rise of space travel in the tw

# Orbital mechanics

A satellite orbiting the earth has a tangential velocity and an inward acceleration.

Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and Newton's law of universal gravitation. It is a core discipline within space mission design and control. Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets. Orbital mechanics focuses on spacecraft trajectories, including orbital maneuvers, orbit plane changes, and interplanetary transfers, and is used by mission planners to predict the results of propulsive maneuvers. General relativity is a more exact theory than Newton's laws for calculating orbits, and is sometimes necessary for greater accuracy or in high-gravity situations (such as orbits close to the Sun).

## History

Until the rise of space travel in the twentieth century, there was little distinction between orbital and celestial mechanics. The fundamental techniques, such as those used to solve the Keplerian problem (determining position as a function of time), are therefore the same in both fields. Furthermore, the history of the fields is almost entirely shared.

Johannes Kepler was the first to successfully model planetary orbits to a high degree of accuracy, publishing his laws in 1605. Isaac Newton published more general laws of celestial motion in his 1687 book, Philosophiæ Naturalis Principia Mathematica.

## Practical techniques

### Rules of thumb

The following rules of thumb are useful for situations approximated by classical mechanics under the standard assumptions of astrodynamics. The specific example discussed is of a satellite orbiting a planet, but the rules of thumb could also apply to other situations, such as orbits of small bodies around a star such as the Sun.

• Kepler's laws of planetary motion, which can be mathematically derived from Newton's laws, hold strictly only in describing the motion of two gravitating bodies, in the absence of non-gravitational forces, or approximately when the gravity of a single massive body like the Sun dominates other effects:
• Orbits are elliptical, with the heavier body at one focus of the ellipse. Special cases of this are circular orbits (a circle being simply an ellipse of zero eccentricity) with the planet at the center, and parabolic orbits (which are ellipses with eccentricity of exactly 1, which is simply an infinitely long ellipse) with the planet at the focus.
• A line drawn from the planet to the satellite sweeps out equal areas in equal times no matter which portion of the orbit is measured.
• The square of a satellite's orbital period is proportional to the cube of its average distance from the planet.
• Without applying thrust (such as firing a rocket engine), the height and shape of the satellite's orbit won't change, and it will maintain the same orientation with respect to the fixed stars.
• A satellite in a low orbit (or low part of an elliptical orbit) moves more quickly with respect to the surface of the planet than a satellite in a higher orbit (or a high part of an elliptical orbit), due to the stronger gravitational attraction closer to the planet.
• If thrust is applied at only one point in the satellite's orbit, it will return to that same point on each subsequent orbit, though the rest of its path will change. Thus to move from one circular orbit to another, at least two brief applications of thrust are needed.
• From a circular orbit, thrust in a direction which slows the satellite down will create an elliptical orbit with a lower periapse (lowest orbital point) at 180 degrees away from the firing point. If thrust is applied to speed the satellite, it will create an elliptical orbit with a higher apoapse 180 degrees away from the firing point.

The consequences of the rules of orbital mechanics are sometimes counter-intuitive. For example, if two spacecraft are in the same circular orbit and wish to dock, unless they are very close, the trailing craft cannot simply fire its engines to go faster. This will change the shape of its orbit, causing it to gain altitude and miss its target. One approach is to actually fire a reverse thrust to slow down, and then fire again to re-circularize the orbit at a lower altitude. Because lower orbits are faster than higher orbits, the trailing craft will begin to catch up. A third firing at the right time will put the trailing craft in an elliptical orbit which will intersect the path of the leading craft, approaching from below.

To the degree that the standard assumptions of astrodynamics do not hold, actual trajectories will vary from those calculated. For example, simple atmospheric drag is another complicating factor for objects in Earth orbit. These rules of thumb are decidedly inaccurate when describing two or more bodies of similar mass, such as a binary star system (see n-body problem). (Celestial mechanics uses more general rules applicable to a wider variety of situations.) The differences between classical mechanics and general relativity can also become important for large objects like planets.

## Laws of astrodynamics

The fundamental laws of astrodynamics are Newton's law of universal gravitation and Newton's laws of motion, while the fundamental mathematical tool is his differential calculus.

Every orbit and trajectory outside atmospheres is in principle reversible, i.e., in the space-time function the time is reversed. The velocities are reversed and the accelerations are the same, including those due to rocket bursts. Thus if a rocket burst is in the direction of the velocity, in the reversed case it is opposite to the velocity. Of course in the case of rocket bursts there is no full reversal of events, both ways the same delta-v is used and the same mass ratio applies.

Standard assumptions in astrodynamics include non-interference from outside bodies, negligible mass for one of the bodies, and negligible other forces (such as from the solar wind, atmospheric drag, etc.). More accurate calculations can be made without these simplifying assumptions, but they are more complicated. The increased accuracy often does not make enough of a difference in the calculation to be worthwhile.

Kepler's laws of planetary motion may be derived from Newton's laws, when it is assumed that the orbiting body is subject only to the gravitational force of the central attractor. When an engine thrust or propulsive force is present, Newton's laws still apply, but Kepler's laws are invalidated. When the thrust stops, the resulting orbit will be different but will once again be described by Kepler's laws. The three laws are:

1. The orbit of every planet is an ellipse with the sun at one of the foci.
2. A line joining a planet and the sun sweeps out equal areas during equal intervals of time.
3. The squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axis of the orbits.

### Escape velocity

The formula for escape velocity is easily derived as follows. The specific energy (energy per unit mass) of any space vehicle is composed of two components, the specific potential energy and the specific kinetic energy. The specific potential energy associated with a planet of mass M is given by

$- \frac{G M}{r} \,$

while the specific kinetic energy of an object is given by

$\frac{v^2}{2} \,$

Since energy is conserved, the total specific orbital energy

$\frac{v^2}{2} - \frac{G M}{r} \,$

does not depend on the distance, $r$, from the center of the central body to the space vehicle in question. Therefore, the object can reach infinite $r$ only if this quantity is nonnegative, which implies

$v\geq\sqrt{\frac{2 G M}{r}}$

The escape velocity from the Earth's surface is about 11 km/s, but that is insufficient to send the body an infinite distance because of the gravitational pull of the Sun. To escape the Solar System from a location at a distance from the Sun equal to the distance Sun–Earth, but not close to the Earth, requires around 42 km/s velocity, but there will be "part credit" for the Earth's orbital velocity for spacecraft launched from Earth, if their further acceleration (due to the propulsion system) carries them in the same direction as Earth travels in its orbit.

Orbits are conic sections, so, naturally, the formulas for the distance of a body for a given angle corresponds to the formula for that curve in polar coordinates, which is:

$r = \frac{ p }{1 + e \cos \theta}$
$\mu= G(m_1+m_2)\,$
$p=h^2/\mu\,$

where ? is called the gravitational parameter, G is the gravitational constant, m1 and m2 are the masses of objects 1 and 2, and h is the specific angular momentum of object 2 with respect to object 1. The parameter ? is known as the true anomaly, p is the semi-latus rectum, while e is the orbital eccentricity, all obtainable from the various forms of the six independent orbital elements.

### Circular orbits

All bounded orbits where the gravity of a central body dominates are elliptical in nature. A special case of this is the circular orbit, which is an ellipse of zero eccentricity. The formula for the velocity of a body in a circular orbit at distance r from the center of gravity of mass M is

$\ v = \sqrt{\frac{GM} {r}\ }$

where $G$ is the gravitational constant, equal to

6.673 84 × 10 ?11 m 3/(kg·s 2)

To properly use this formula, the units must be consistent; for example, M must be in kilograms, and r must be in meters. The answer will be in meters per second.

The quantity GM is often termed the standard gravitational parameter, which has a different value for every planet or moon in the Solar System.

Once the circular orbital velocity is known, the escape velocity is easily found by multiplying by the square root of 2:

$\ v = \sqrt 2\sqrt{\frac {GM} {r}\ } = \sqrt{\frac {2GM} {r}\ }.$

### Elliptical orbits

If 0<e<1, then the denominator of the equation of free orbits varies with the true anomaly ?, but remains positive, never becoming zero. Therefore, the relative position vector remains bounded, having its smallest magnitude at periapsis rp which is given by:

$r_p=\frac{p}{1+e}$

The maximum value r is reached when ? = 180. This point is called the apoapsis, and its radial coordinate, denoted ra, is

$r_a=\frac{p}{1-e}$

Let 2a be the distance measured along the apse line from periapsis P to apoapsis A, as illustrated in the equation below:

$2a=r_p+r_a$

Substituting the equations above, we get:

$a=\frac{p}{1-e^2}$

a is the semimajor axis of the ellipse. Solving for r we get:

$r=\frac{a(1-e^2)}{1+e\cos\theta}$

#### Orbital period

Under standard assumptions the orbital period ($T\,\!$) of a body traveling along an elliptic orbit can be computed as:

$T=2\pi\sqrt{a^3\over{\mu}}$

where:

Conclusions:

• The orbital period is equal to that for a circular orbit with the orbit radius equal to the semi-major axis ($a\,\!$),
• For a given semi-major axis the orbital period does not depend on the eccentricity (See also: Kepler's third law).

#### Velocity

Under standard assumptions the orbital speed ($v\,$) of a body traveling along an elliptic orbit can be computed from the Vis-viva equation as:

$v=\sqrt{\mu\left({2\over{r}}-{1\over{a}}\right)}$

where:

• $\mu\,$ is the standard gravitational parameter,
• $r\,$ is the distance between the orbiting bodies.
• $a\,\!$ is the length of the semi-major axis.

The velocity equation for a hyperbolic trajectory has either + ${1\over{a}}$, or it is the same with the convention that in that case a is negative.

#### Energy

Under standard assumptions, specific orbital energy ($\epsilon\,$) of elliptic orbit is negative and the orbital energy conservation equation (the Vis-viva equation) for this orbit can take the form:

${v^2\over{2}}-{\mu\over{r}}=-{\mu\over{2a}}=\epsilon<0$

where:

• $v\,$ is the speed of the orbiting body,
• $r\,$ is the distance of the orbiting body from the center of mass of the central body,
• $a\,$ is the semi-major axis,
• $\mu\,$ is the standard gravitational parameter.

Conclusions:

• For a given semi-major axis the specific orbital energy is independent of the eccentricity.

Using the virial theorem we find:

• the time-average of the specific potential energy is equal to 2?
• the time-average of r?1 is a?1
• the time-average of the specific kinetic energy is equal to -?

### Parabolic orbits

If the eccentricity equals 1, then the orbit equation becomes:

$r={{h^2}\over{\mu}}{{1}\over{1+\cos\theta}}$

where:

As the true anomaly ? approaches 180°, the denominator approaches zero, so that r tends towards infinity. Hence, the energy of the trajectory for which e=1 is zero, and is given by:

$\epsilon={v^2\over2}-{\mu\over{r}}=0$

where:

• $v\,$ is the speed of the orbiting body.

In other words, the speed anywhere on a parabolic path is:

$v=\sqrt{2\mu\over{r}}$

### Hyperbolic orbits

If e>1, the orbit formula,

$r={{h^2}\over{\mu}}{{1}\over{1+e\cos\theta}}$

describes the geometry of the hyperbolic orbit. The system consists of two symmetric curves. the orbiting body occupies one of them. The other one is its empty mathematical image. Clearly, the denominator of the equation above goes to zero when cos? = -1/e. we denote this value of true anomaly

? ? = cos -1(-1/ e)

since the radial distance approaches infinity as the true anomaly approaches ??. ?? is known as the true anomaly of the asymptote. Observe that ?? lies between 90° and 180°. From the trig identity sin2?+cos2?=1 it follows that:

sin ? ? = (e 2-1) 1/2/e

#### Energy

Under standard assumptions, specific orbital energy ($\epsilon\,$) of a hyperbolic trajectory is greater than zero and the orbital energy conservation equation for this kind of trajectory takes form:

$\epsilon={v^2\over2}-{\mu\over{r}}={\mu\over{-2a}}$

where:

#### Hyperbolic excess velocity

Under standard assumptions the body traveling along hyperbolic trajectory will attain in infinity an orbital velocity called hyperbolic excess velocity ($v_\infty\,\!$) that can be computed as:

$v_\infty=\sqrt{\mu\over{-a}}\,\!$

where:

The hyperbolic excess velocity is related to the specific orbital energy or characteristic energy by

$2\epsilon=C_3=v_{\infty}^2\,\!$

## Calculating trajectories

### Kepler's equation

One approach to calculating orbits (mainly used historically) is to use Kepler's equation:

$M = E - \epsilon \cdot \sin E$.

where M is the mean anomaly, E is the eccentric anomaly, and $\displaystyle \epsilon$ is the eccentricity.

With Kepler's formula, finding the time-of-flight to reach an angle (true anomaly) of $\theta$ from periapsis is broken into two steps:

1. Compute the eccentric anomaly $E$ from true anomaly $\theta$
2. Compute the time-of-flight $t$ from the eccentric anomaly $E$

Finding the eccentric anomaly at a given time (the inverse problem) is more difficult. Kepler's equation is transcendental in $E$, meaning it cannot be solved for $E$ algebraically. Kepler's equation can be solved for $E$ analytically by inversion.

A solution of Kepler's equation, valid for all real values of $\textstyle \epsilon$ is:

$E = \begin{cases} \displaystyle \sum_{n=1}^{\infty} {\frac{M^{\frac{n}{3}}}{n!}} \lim_{\theta \to 0} \left( \frac{\mathrm{d}^{\,n-1}}{\mathrm{d}\theta^{\,n-1}} \left( \frac{\theta}{ \sqrt[3]{\theta - \sin(\theta)} } ^n \right)\right), & \epsilon = 1 \\\displaystyle \sum_{n=1}^{\infty}{ \frac{ M^n }{ n! } }\lim_{\theta \to 0} \left(\frac{\mathrm{d}^{\,n-1}}{\mathrm{d}\theta^{\,n-1}} \left( \frac{ \theta }{ \theta - \epsilon \cdot \sin(\theta)} ^n \right)\right), & \epsilon \ne 1 \end{cases}$

Evaluating this yields:

$E = \begin{cases} \displaystylex + \frac{1}{60} x^3 + \frac{1}{1400}x^5 + \frac{1}{25200}x^7 + \frac{43}{17248000}x^9 + \frac{ 1213}{7207200000 }x^{11} + \frac{151439}{12713500800000 }x^{13} \cdots \ | \ x = ( 6 M )^\frac{1}{3} , & \epsilon = 1 \\\\\displaystyle \frac{1}{1-\epsilon} M - \frac{\epsilon}{( 1-\epsilon)^4 } \frac{M^3}{3!} + \frac{(9 \epsilon^2 + \epsilon)}{(1-\epsilon)^7 } \frac{M^5}{5!} - \frac{(225 \epsilon^3 + 54 \epsilon^2 + \epsilon ) }{(1-\epsilon)^{10} } \frac{M^7}{7!}+ \frac{ (11025\epsilon^4 + 4131 \epsilon^3 + 243 \epsilon^2 + \epsilon ) }{(1-\epsilon)^{13} } \frac{M^9}{9!} \cdots, & \epsilon \ne 1 \end{cases}$

Alternatively, Kepler's Equation can be solved numerically. First one must guess a value of $E$ and solve for time-of-flight; then adjust $E$ as necessary to bring the computed time-of-flight closer to the desired value until the required precision is achieved. Usually, Newton's method is used to achieve relatively fast convergence.

The main difficulty with this approach is that it can take prohibitively long to converge for the extreme elliptical orbits. For near-parabolic orbits, eccentricity $\epsilon$ is nearly 1, and plugging $e = 1$ into the formula for mean anomaly, $E - \sin E$, we find ourselves subtracting two nearly-equal values, and accuracy suffers. For near-circular orbits, it is hard to find the periapsis in the first place (and truly circular orbits have no periapsis at all). Furthermore, the equation was derived on the assumption of an elliptical orbit, and so it does not hold for parabolic or hyperbolic orbits. These difficulties are what led to the development of the universal variable formulation, described below.

### Conic orbits

For simple procedures, such as computing the delta-v for coplanar transfer ellipses, traditional approaches[clarification needed] are fairly effective. Others, such as time-of-flight are far more complicated, especially for near-circular and hyperbolic orbits.

### The patched conic approximation

The Hohmann transfer orbit alone is a poor approximation for interplanetary trajectories because it neglects the planets' own gravity. Planetary gravity dominates the behaviour of the spacecraft in the vicinity of a planet and in most cases Hohmann severely overestimates delta-v, and produces highly inaccurate prescriptions for burn timings.

A relatively simple way to get a first-order approximation of delta-v is based on the 'Patched Conic Approximation' technique. One must choose the one dominant gravitating body in each region of space through which the trajectory will pass, and to model only that body's effects in that region. For instance, on a trajectory from the Earth to Mars, one would begin by considering only the Earth's gravity until the trajectory reaches a distance where the Earth's gravity no longer dominates that of the Sun. The spacecraft would be given escape velocity to send it on its way to interplanetary space. Next, one would consider only the Sun's gravity until the trajectory reaches the neighbourhood of Mars. During this stage, the transfer orbit model is appropriate. Finally, only Mars's gravity is considered during the final portion of the trajectory where Mars's gravity dominates the spacecraft's behaviour. The spacecraft would approach Mars on a hyperbolic orbit, and a final retrograde burn would slow the spacecraft enough to be captured by Mars.

The size of the "neighborhoods" (or spheres of influence) vary with radius $r_{SOI}$:

$r_{SOI} = a_p\left(\frac{m_p}{m_s}\right)^{2/5}$

where $a_p$ is the semimajor axis of the planet's orbit relative to the Sun; $m_p$ and $m_s$ are the masses of the planet and Sun, respectively.

This simplification is sufficient to compute rough estimates of fuel requirements, and rough time-of-flight estimates, but it is not generally accurate enough to guide a spacecraft to its destination. For that, numerical methods are required.

### The universal variable formulation

To address computational shortcomings of traditional approaches for solving the 2-body problem, the universal variable formulation was developed. It works equally well for the circular, elliptical, parabolic, and hyperbolic cases, the differential equations converging well when integrated for any orbit. It also generalizes well to problems incorporating perturbation theory.

### Perturbations

The universal variable formulation works well with the variation of parameters technique, except now, instead of the six Keplerian orbital elements, we use a different set of orbital elements: namely, the satellite's initial position and velocity vectors $x_0$ and $v_0$ at a given epoch $t = 0$. In a two-body simulation, these elements are sufficient to compute the satellite's position and velocity at any time in the future, using the universal variable formulation. Conversely, at any moment in the satellite's orbit, we can measure its position and velocity, and then use the universal variable approach to determine what its initial position and velocity would have been at the epoch. In perfect two-body motion, these orbital elements would be invariant (just like the Keplerian elements would be).

However, perturbations cause the orbital elements to change over time. Hence, we write the position element as $x_0(t)$ and the velocity element as $v_0(t)$, indicating that they vary with time. The technique to compute the effect of perturbations becomes one of finding expressions, either exact or approximate, for the functions $x_0(t)$ and $v_0(t)$.

The following are some effects which make real orbits differ from the simple models based on a spherical earth. Most of them can be handled on short timescales (perhaps less than a few thousand orbits) by perturbation theory because they are small relative to the corresponding two-body effects.

• Equatorial bulges cause precession of the node and the perigee
• Tesseral harmonics[1] of the gravity field introduce additional perturbations
• Lunar and solar gravity perturbations alter the orbits
• Atmospheric drag reduces the semi-major axis unless make-up thrust is used

Over very long timescales (perhaps millions of orbits), even small perturbations can dominate, and the behaviour can become chaotic. On the other hand, the various perturbations can be orchestrated by clever astrodynamicists to assist with orbit maintenance tasks, such as station-keeping, ground track maintenance or adjustment, or phasing of perigee to cover selected targets at low altitude.

## Orbital maneuver

In spaceflight, an orbital maneuver is the use of propulsion systems to change the orbit of a spacecraft. For spacecraft far from Earth—for example those in orbits around the Sun—an orbital maneuver is called a deep-space maneuver (DSM).[not verified in body]

### Orbital transfer

A Hohmann transfer from a low circular orbit to a higher circular orbit.
A bi-elliptic transfer from a low circular starting orbit (dark blue), to a higher circular orbit (red).
A two-impulse transfer from a low circular orbit to a higher circular orbit.
A general transfer from a low circular orbit to a higher circular orbit.

Transfer orbits are usually elliptical orbits that allow spacecraft to move from one (usually substantially circular) orbit to another. Usually they require a burn at the start, a burn at the end, and sometimes one or more burns in the middle.

• The Hohmann transfer orbit requires a minimal delta-v.
• A Bi-elliptic transfer can require less energy than the Hohmann transfer, if the ratio of orbits is 11.94 or greater,[2] but comes at the cost of increased trip time over the Hohmann transfer.
• Faster transfers may use any orbit that intersects both the original and destination orbits, at the cost of higher delta-v.

For the case of orbital transfer between non-coplanar orbits, the change-of-plane thrust must be made at the point where the orbital plans intersect (the "node").

### Gravity assist and the Oberth effect

In a gravity assist, a spacecraft swings by a planet and leaves in a different direction, at a different speed. This is useful to speed or slow a spacecraft instead of carrying more fuel.

This maneuver can be approximated by an elastic collision at large distances, though the flyby does not involve any physical contact. Due to Newton's Third Law (equal and opposite reaction), any momentum gained by a spacecraft must be lost by the planet, or vice versa. However, because the planet is much, much more massive than the spacecraft, the effect on the planet's orbit is negligible.

The Oberth effect can be employed, particularly during a gravity assist operation. This effect is that use of a propulsion system works better at high speeds, and hence course changes are best done when close to a gravitating body; this can multiply the effective delta-v.

### Interplanetary Transport Network and fuzzy orbits

It is now possible to use computers to search for routes using the nonlinearities in the gravity of the planets and moons of the Solar System. For example, it is possible to plot an orbit from high earth orbit to Mars, passing close to one of the Earth's Trojan points. Collectively referred to as the Interplanetary Transport Network, these highly perturbative, even chaotic, orbital trajectories in principle need no fuel beyond that needed to reach the Lagrange point (in practice keeping to the trajectory requires some course corrections). The biggest problem with them is they can be exceedingly slow, taking many years to arrive. In addition launch windows can be very far apart.

They have, however, been employed on projects such as Genesis. This spacecraft visited the Earth-Sun Lagrange L1 point and returned using very little propellant.

X

YOU TUBE

### Orbital Peturbations

WIKI

Orbital perturbation analysis is the activity of determining why a satellite's orbit differs from the mathematical ideal orbit. A satellite's orbit in an ideal two-body system describes a conic section, or ellipse. In reality, there are several factors that cause the conic section to continually change. These deviations from the ideal Kepler's orbit are called perturbations. It has long been recognized that the Moon does not follow a perfect orbit, and many theories and models have been examined over the millennia to explain it. Isaac Newton determined the primary contributing factor to orbital perturbation of the moon was that the shape of the Earth is actually an oblate spheroid due to its spin, and he used the perturbations of the lunar orbit to estimate the oblateness of the Earth. In Newton's Philosophiæ Naturalis Principia Mathematica, he demonstrated that the gravitational force between two mass points is inversely proportional to the square of the distance between the points, and he fully solved the c

# Orbital perturbation analysis (spacecraft)

Orbital perturbation analysis is the activity of determining why a satellite's orbit differs from the mathematical ideal orbit. A satellite's orbit in an ideal two-body system describes a conic section, or ellipse. In reality, there are several factors that cause the conic section to continually change. These deviations from the ideal Kepler's orbit are called perturbations.

## Perturbation of spacecraft orbits

It has long been recognized that the Moon does not follow a perfect orbit, and many theories and models have been examined over the millennia to explain it. Isaac Newton determined the primary contributing factor to orbital perturbation of the moon was that the shape of the Earth is actually an oblate spheroid due to its spin, and he used the perturbations of the lunar orbit to estimate the oblateness of the Earth.

In Newton's Philosophiæ Naturalis Principia Mathematica, he demonstrated that the gravitational force between two mass points is inversely proportional to the square of the distance between the points, and he fully solved the corresponding "two-body problem" demonstrating that the radius vector between the two points would describe an ellipse. But no exact closed analytical form could be found for the three body problem. Instead, mathematical models called "orbital perturbation analysis" have been developed. With these techniques a quite accurate mathematical description of the trajectories of all the planets could be obtained. Newton recognized that the Moon's perturbations could not entirely be accounted for using just the solution to the three body problem, as the deviations from a pure Kepler orbit around the Earth are much larger than deviations of the orbits of the planets from their own Sun-centered Kepler orbits, caused by the gravitational attraction between the planets. With the availability of digital computers and the ease with which we can now compute orbits, this problem has partly disappeared, as the motion of all celestial bodies including planets, satellites, asteroids and comets can be modeled and predicted with almost perfect accuracy using the method of the numerical propagation of the trajectories. Nevertheless several analytical closed form expressions for the effect of such additional "perturbing forces" are still very useful.

All celestial bodies of the Solar System follow in first approximation a Kepler orbit around a central body. For a satellite (artificial or natural) this central body is a planet. But both due to gravitational forces caused by the Sun and other celestial bodies and due to the flattening of its planet (caused by its rotation which makes the planet slightly oblate and therefore the result of the Shell theorem not fully applicable) the satellite will follow an orbit around the Earth that deviates more than the Kepler orbits observed for the planets.

The precise modeling of the motion of the Moon has been a difficult task. The best and most accurate modeling for the lunar orbit before the availability of digital computers was obtained with the complicated Delaunay and Brown's lunar theories.

For man-made spacecraft orbiting the Earth at comparatively low altitudes the deviations from a Kepler orbit are much larger than for the Moon. The approximation of the gravitational force of the Earth to be that of a homogeneous sphere gets worse the closer one gets to the Earth surface and the majority of the artificial Earth satellites are in orbits that are only a few hundred kilometers over the Earth surface. Furthermore they are (as opposed to the Moon) significantly affected by the solar radiation pressure because of their large cross-section to mass ratio; this applies in particular to 3-axis stabilized spacecraft with large solar arrays. In addition they are significantly affected by rarefied air below 800–1000 km. The air drag at high altitudes is also dependent on solar activity.

## Mathematical approach

Consider any function

$g(x_1,x_2,x_3,v_1,v_2,v_3)\,$

of the position

$x_1,x_2,x_3\,$

and the velocity

$v_1,v_2,v_3\,$

From the chain rule of differentiation one gets that the time derivative of $g$ is

$\dot{g}\ =\ \frac{\partial g }{\partial x_1}\ v_1\ + \ \frac{\partial g }{\partial x_2}\ v_2\ + \frac{\partial g }{\partial x_3}\ v_3\ + \ \frac{\partial g }{\partial v_1}\ f_1\ + \ \frac{\partial g }{\partial v_2}\ f_2\ + \ \frac{\partial g }{\partial v_3}\ f_3$

where $f_1\ ,\ f_2\ ,\ f_3$ are the components of the force per unit mass acting on the body.

If now $g$ is a "constant of motion" for a Kepler orbit like for example an orbital element and the force is corresponding "Kepler force"

$(f_1\ ,\ f_2\ ,\ f_3)\ = \ - \frac {\mu} {r^3}\ (x_1\ ,\ x_2\ ,\ x_3)$

one has that $\dot{g}\ =\ 0\,$.

If the force is the sum of the "Kepler force" and an additional force (force per unit mass)

$(h_1\ ,\ h_2\ ,\ h_3)$

i.e.

$(f_1\ ,\ f_2\ ,\ f_3)\ = \ - \frac {\mu} {r^3}\ (x_1\ ,\ x_2\ ,\ x_3)\ +\ (h_1\ ,\ h_2\ ,\ h_3)$

one therefore has

$\dot{g}\ =\frac{\partial g }{\partial v_1}\ h_1\ + \ \frac{\partial g }{\partial v_2}\ h_2\ + \ \frac{\partial g }{\partial v_3}\ h_3$

and that the change of $g\,$ in the time from $t=t_1\,$ to $t=t_2\,$ is

$\Delta g\ =\ \int\limits_{t_1}^{t_2}\left(\frac{\partial g }{\partial v_1}\ h_1\ + \ \frac{\partial g }{\partial v_2}\ h_2\ + \ \frac{\partial g }{\partial v_3}\ h_3 \right)dt$

If now the additional force $(h_1\ ,\ h_2\ ,\ h_3)\,$ is sufficiently small that the motion will be close to that of a Kepler orbit one gets an approximate value for $\Delta g\,$ by evaluating this integral assuming $x_1(t),x_2(t),x_3(t)\,$ to precisely follow this Kepler orbit.

In general one wants to find an approximate expression for the change $\Delta g\,$ over one orbital revolution using the true anomaly $\theta\,$ as integration variable, i.e. as

$\Delta g\ =\ \int\limits_{0}^{2\pi}\left(\frac{\partial g }{\partial v_1}\ h_1\ + \ \frac{\partial g }{\partial v_2}\ h_2\ + \ \frac{\partial g }{\partial v_3}\ h_3 \right)\frac{r^2}{\sqrt{\mu p}}d\theta$

(1)

This integral is evaluated setting $r(\theta)=\frac {p}{1+e\cos \theta}\,$, the elliptical Kepler orbit in polar angles. For the transformation of integration variable from time to true anomaly it was used that the angular momentum $H\ =\ r^2\ \dot{\theta}\ =\ \sqrt{\mu p} \,$ by definition of the parameter $p\,$ for a Kepler orbit (see equation (13) of the Kepler orbit article).

For the special case where the Kepler orbit is circular or almost circular

$r\ =\ p$ and ( 1) takes the simpler form

$\Delta g\ =\ \frac{P}{2\pi}\ \int\limits_{0}^{2\pi}\left(\frac{\partial g }{\partial v_1}\ h_1\ + \ \frac{\partial g }{\partial v_2}\ h_2\ + \ \frac{\partial g }{\partial v_3}\ h_3 \right)d\theta$

(2)

where $P\ =\ 2\pi\ r\ \sqrt{\frac{r}{\mu}}\,$ is the orbital period

### Perturbation of the semi-major axis/orbital period

For an elliptic Kepler orbit, the sum of the kinetic and the potential energy

$g = \frac{V^2}{2}-\frac {\mu} {r}$,

where $V\,$ is the orbital velocity, is a constant and equal to

$g\ =\ -\frac {\mu} {2 \cdot a}$ (Equation ( 44) of the Kepler orbit article)

If $\bar{h}\,$ is the perturbing force and $\bar{V}\,$is the velocity vector of the Kepler orbit the equation (1) takes the form:

$\Delta g\ =\ \int\limits_{0}^{2\pi}\bar{V} \bar{h}\frac{r^2}{\sqrt{\mu p}}d\theta$

(3)

and for a circular or almost circular orbit

$\Delta g\ =\ \frac{P}{2\pi}\ \int\limits_{0}^{2\pi} \bar{V} \bar{h}d\theta$

(4)

From the change $\Delta g\,$ of the parameter $g\,$ the new semi-major axis $a\,$ and the new period $P\ =\ 2\pi\ a\ \sqrt{\frac{a}{\mu}}\,$ are computed (relations (43) and (44) of the Kepler orbit article).

### Perturbation of the orbital plane

Let $\hat{g}\,$ and $\hat{h}\,$ make up a rectangular coordinate system in the plane of the reference Kepler orbit. If $\omega\,$ is the argument of perigee relative the $\hat{g}\,$ and $\hat{h}\,$ coordinate system the true anomaly $\theta\,$ is given by $\theta=u-\omega\,$ and the approximate change $\Delta \hat{z}\,$ of the orbital pole $\hat{z}\,$ (defined as the unit vector in the direction of the angular momentum) is

$\Delta \hat{z}\ =\ \int\limits_{0}^{2\pi}\frac{f_z }{V_t} (\hat{g} \cos u + \hat{h} \sin u)\frac{r^2}{\sqrt{\mu p}}du \quad \times \ \hat{z}=\ \frac{1}{\mu p}\left[\hat{g}\int\limits_{0}^{2\pi}f_z r^3 \cos u \ du+\ \hat{h}\int\limits_{0}^{2\pi}f_z r^3 \sin u \ du \right]\quad \times \ \hat{z}$

(5)

where $f_z\,$ is the component of the perturbing force in the $\hat{z}\,$ direction, $V_t=\sqrt{\frac{\mu}{p}}\ (1+e\ \cos\theta)\,$ is the velocity component of the Kepler orbit orthogonal to radius vector and $r=\frac{p}{1+e\ \cos\theta}\,$ is the distance to the center of the Earth.

For a circular or almost circular orbit (5) simplifies to

$\Delta \hat{z}\ =\ \frac{r^2}{\mu}\left[\hat{g}\int\limits_{0}^{2\pi}f_z \cos u \ du+\ \hat{h}\int\limits_{0}^{2\pi}f_z \sin u \ du \right]\quad \times \ \hat{z}$

(6)

Example

In a circular orbit a low-force propulsion system (Ion thruster) generates a thrust (force per unit mass) of $F\ \hat{z}\,$ in the direction of the orbital pole in the half of the orbit for which $\sin u\,$ is positive and in the opposite direction in the other half. The resulting change of orbit pole after one orbital revolution of duration $P\ =\ 2\pi\ r\ \sqrt{\frac{r}{\mu}}\,$ is

$\Delta \hat{z}\ =\ \frac{r^2}{\mu}\left[\ 2\ F\int\limits_{0}^{\pi}\sin u \ du \right]\quad \hat{h}\times \hat{z} =\ \frac{r^2}{\mu}\ 4\ F\ \quad \hat{g}$

(7)

The average change rate $\frac{\Delta \hat{z}}{P}\,$ is therefore

$\frac{\Delta \hat{z}}{P} =\ \frac{2}{\pi}\ \frac{F}{V}\ \hat{g}$

(8)

where $V\ =\ \sqrt{\frac{\mu}{r}},$ is the orbital velocity in the circular Kepler orbit.

### Perturbation of the eccentricity vector

Rather than applying (1) and (2) on the partial derivatives of the orbital elements eccentricity and argument of perigee directly one should apply these relations for the eccentricity vector. First of all the typical application is a near-circular orbit. But there are also mathematical advantages working with the partial derivatives of the components of this vector also for orbits with a significant eccentricity.

Equations (60), (55) and (52) of the Kepler orbit article say that the eccentricity vector is

$\bar{e}=\frac{(V_t-V_0) \cdot \hat{r} - V_r \cdot \hat{t}}{V_0}$

(9)

where

$V_0 = \sqrt{\frac{\mu}{p}}$

(10)

$p = \frac{{(r \cdot V_t)}^2}{\mu }$

(11)

from which follows that

$\frac{\partial\bar{e}}{\partial V_r} = -\frac {1}{V_0} \hat{t}$

(12)

$\frac{\partial\bar{e}}{\partial V_t} = \frac {1}{V_0} \left(2\ \hat{r}-\frac{V_r}{V_t}\ \hat{t}\right)$

(13)

where

$V_r = \sqrt{\frac {\mu}{p}} \cdot e \cdot \sin \theta$

(14)

$V_t = \sqrt{\frac {\mu}{p}} \cdot (1 + e \cdot \cos \theta)$

(15)

(Equations (18) and (19) of the Kepler orbit article)

The eccentricity vector is by definition always in the osculating orbital plane spanned by $\hat{r}$ and $\hat{t}$ and formally there is also a derivative

$\frac{\partial\bar{e}}{\partial V_z} = -\frac {V_r}{V_0}\ \frac{\partial\hat{t}}{\partial V_z}$

with

$\frac{\partial\hat{t}}{\partial V_z} = \frac {1}{V_t}\ \hat{z}$

corresponding to the rotation of the orbital plane

But in practice the in-plane change of the eccentricity vector is computed as

\begin{align}\Delta \bar{e}\ = &\frac {1}{V_0}\ \int\limits_{0}^{2\pi}\left(-\hat{t}\ f_r\ + \ \left(2\ \hat{r}-\frac{V_r}{V_t}\ \hat{t}\right)\ f_t\right)\frac{r^2}{\sqrt{\mu p}}du\ = \\&\frac {1}{\mu}\ \int\limits_{0}^{2\pi}\left(-\hat{t}\ f_r\ + \ \left(2\ \hat{r}-\frac{V_r}{V_t}\ \hat{t}\right)\ f_t\right) r^2 du \end{align}

(16)

ignoring the out-of-plane force and the new eccentricity vector

$\bar{e} + \Delta \bar{e}$

is subsequently projected to the new orbital plane orthogonal to the new orbit normal

$\hat{z} + \Delta \hat{z}$

computed as described above.

Example

The Sun is in the orbital plane of a spacecraft in a circular orbit with radius $r\,$ and consequently with a constant orbital velocity $V_0\ =\ \sqrt{\frac{\mu}{r}}$ . If $\hat{k}\,$ and $\hat{l}\,$ make up a rectangular coordinate system in the orbital plane such that $\hat{k}\,$ points to the Sun and assuming that the solar radiation pressure force per unit mass $F\,$ is constant one gets that

$\hat{r}=\cos(u)\ \hat{k}\ +\ \sin(u)\ \hat{l}\,$
$\hat{t}=-\sin(u)\ \hat{k}\ +\ \cos(u)\ \hat{l}\,$
$F_r=-\cos(u)\ F\,$
$F_t= \sin(u)\ F\,$

where $u\,$ is the polar angle of $\hat{r}\,$ in the $\hat{k}\,$, $\hat{l}\,$ system. Applying (2) one gets that

\begin{align}\Delta \hat{e}\ & =\ \frac{P}{2\pi}\ \frac {1}{V_0}\ \int\limits_{0}^{2\pi}\left( (-\sin(u)\ \hat{k}\ +\ \cos(u)\ \hat{l}) \ F\ \cos(u)\ + \ 2\ (\cos(u)\ \hat{k}\ +\ \sin(u)\ \hat{l})\ F\ \sin(u)\right)\ du \\& = P\ \frac{3}{2}\ \frac {1}{V_0}\ \ F\ \hat{l} \end{align}

(17)

This means the eccentricity vector will gradually increase in the direction $\hat{l}\,$ orthogonal to the Sun direction. This is true for any orbit with a small eccentricity, the direction of the small eccentricity vector does not matter. As $P\,$ is the orbital period this means that the average rate of this increase will be $\frac{3}{2}\ \frac {F}{V_0}\,$

## The effect of the Earth flattening

Figure 1: The unit vectors $\hat{\phi}\ ,\ \hat{\lambda}\ ,\ \hat{r}$

In the article Geopotential model the modeling of the gravitational field as a sum of spherical harmonics is discussed. By far, the dominating term is the "J2-term". This is a "zonal term" and corresponding force is therefore completely in a longitudinal plane with one component $F_r\ \hat{r}\,$ in the radial direction and one component $F_\lambda\ \hat{\lambda}\,$ with the unit vector $\hat{\lambda}\,$ orthogonal to the radial direction towards north. These directions $\hat{r}\,$ and $\hat{\lambda}\,$ are illustrated in Figure 1.

Figure 2: The unit vector $\hat{t}\,$ orthogonal to $\hat{r}\,$ in the direction of motion and the orbital pole $\hat{z}\,$. The force component $F_\lambda$ is marked as "F"

To be able to apply relations derived in the previous section the force component $F_\lambda\ \hat{\lambda}\,$ must be split into two orthogonal components $F_t\ \hat{t}$ and $F_z\ \hat{z}$ as illustrated in figure 2

Let $\hat{a}\ ,\ \hat{b}\ ,\ \hat{n}\,$ make up a rectangular coordinate system with origin in the center of the Earth (in the center of the Reference ellipsoid) such that $\hat{n}\,$ points in the direction north and such that $\hat{a}\ ,\ \hat{b}\,$ are in the equatorial plane of the Earth with $\hat{a}\,$ pointing towards the ascending node, i.e. towards the blue point of Figure 2.

The components of the unit vectors

$\hat{r}\ ,\ \hat{t}\ ,\ \hat{z}\,$

making up the local coordinate system (of which $\hat{t}\ ,\ \hat{z},$ are illustrated in figure 2) relative the $\hat{a}\ ,\ \hat{b}\ ,\ \hat{n}\,$ are

$r_a= \cos u\,$
$r_b= \cos i \ \sin u\,$
$r_n= \sin i \ \sin u\,$
$t_a=-\sin u\,$
$t_b= \cos i \ \cos u\,$
$t_n= \sin i \ \cos u\,$
$z_a= 0\,$
$z_b=-\sin i\,$
$z_n= \cos i\,$

where $u\,$ is the polar argument of $\hat{r}\,$ relative the orthogonal unit vectors $\hat{g}=\hat{a}\,$ and $\hat{h}=\cos i\ \hat{b}\ +\ \sin i\ \hat{n}\,$ in the orbital plane

Firstly

$\sin \lambda =\ r_n\ =\ \sin i \ \sin u\,$

where $\lambda\,$ is the angle between the equator plane and $\hat{r}\,$ (between the green points of figure 2) and from equation (12) of the article Geopotential model one therefore gets that

$f_r = J_2\ \frac{1}{r^4}\ \frac{3}{2}\ \left(3\ \sin^2 i\ \sin^2 u\ -\ 1\right)$

(18)

Secondly the projection of direction north, $\hat{n}\,$, on the plane spanned by $\hat{t}\ ,\ \hat{z},$ is

$\sin i \ \cos u \ \hat{t}\ +\ \cos i \ \hat{z}\,$

and this projection is

$\cos \lambda \ \hat{\lambda}\,$

where $\hat{\lambda}\,$ is the unit vector $\hat{\lambda}$ orthogonal to the radial direction towards north illustrated in figure 1.

From equation (12) of the article Geopotential model one therefore gets that

$f_\lambda \ \hat{\lambda}\ =\ -J_2\ \frac{1}{r^4}\ 3\ \sin\lambda\ (\sin i \ \cos u \ \hat{t}\ +\ \cos i \ \hat{z}) =\ -J_2\ \frac{1}{r^4}\ 3\ \sin i \ \sin u\ (\sin i \ \cos u \ \hat{t}\ +\ \cos i \ \hat{z})\,$

and therefore:

$f_t =\ -J_2\ \frac{1}{r^4}\ 3\ \sin^2 i\ \sin u\ \cos u$

(19)

$f_z =\ -J_2\ \frac{1}{r^4}\ 3\ \sin i\ \cos i\ \sin u$

(20)

### Perturbation of the orbital plane

From (5) and (20) one gets that

$\Delta \hat{z}\ =\ -J_2\ \frac{3\ \sin i\ \cos i}{\mu p^2}\left[\hat{g}\int\limits_{0}^{2\pi}\frac{p}{r}\ \sin u\ \cos u \ du+\ \hat{h}\int\limits_{0}^{2\pi}\frac{p}{r}\ \sin^2 u\ du \right]\quad \times \ \hat{z}$

(21)

The fraction $\frac{p}{r}\,$ is

$\frac{p}{r}\ =\ 1\ +\ e\ \cos (u-\omega)\ =\ 1\ +\ e\ \cos u\ \cos\omega\ +\ e\ \sin u\ \sin\omega\,$

where $e\,$ is the eccentricity and $\omega\,$ is the argument of perigee of the reference Kepler orbit

As all integrals of type

$\int\limits_{0}^{2\pi} \cos^m u \ \sin^n u\ du\,$

are zero if not both $n\,$ and $m\,$ are even one gets from (21) that

$\Delta \hat{z}\ =\ -2\pi\ \frac{J_2}{\mu\ p^2}\ \frac{3}{2}\ \sin i\ \cos i\ \quad \hat{h} \times \hat{z}$

As

$\hat{n}\ =\ \cos i\ \hat{z}\ + \sin i\ \hat{h}$

this can be written

$\Delta \hat{z}\ =\ -2\pi\ \frac{J_2}{\mu\ p^2}\ \frac{3}{2}\ \cos i\ \quad \hat{n} \times \hat{z}$

(22)

As $\hat{n}$ is an inertially fixed vector (the direction of the spin axis of the Earth) relation (22) is the equation of motion for a unit vector $\hat{z}\,$ describing a cone around $\hat{n}$ with a precession rate (radians per orbit) of $-2\pi\ \frac{J_2}{\mu\ p^2}\ \frac{3}{2}\ \cos i\,$

In terms of orbital elements this is expressed as

$\Delta i\ =\ 0$

(23)

$\Delta \Omega\ =\ -2\pi\ \frac{J_2}{\mu\ p^2}\ \frac{3}{2}\ \cos i$

(24)

where

$i\,$ is the inclination of the orbit to the equatorial plane of the Earth
$\Omega\,$ is the right ascension of the ascending node

### Perturbation of the eccentricity vector

From (16), (18) and (19) follows that in-plane perturbation of the eccentricity vector is

$\Delta \bar{e}\ =\ \frac {J_2}{\mu\ p^2}\ \int\limits_{0}^{2\pi}\left(-\hat{t}\ \left(\frac{p}{r}\right)^2\ \frac{3}{2}\ \left(3\ \sin^2 i\ \sin^2 u\ -\ 1\right)\ - \ \left(2\ \hat{r}-\frac{V_r}{V_t}\ \hat{t}\right)\ \left(\frac{p}{r}\right)^2\ 3\ \sin^2 i \cos u\ \sin u\right)du$

(25)

the new eccentricity vector being the projection of

$\bar{e}+\Delta \bar{e}$

on the new orbital plane orthogonal to

$\hat{z}+\Delta \hat{z}$

where $\Delta \hat{z}\,$ is given by (22)

Relative the coordinate system

$\hat{g}=\hat{a}\,$
$\hat{h}=\cos i\ \hat{b}\ +\ \sin i\ \hat{n}\,$

one has that

$\hat{r}=\cos u\ \hat{g}\ +\ \sin u\ \hat{h}\,$
$\hat{t}=-\sin u\ \hat{g}\ +\ \cos u\ \hat{h}\,$

Using that

$\frac {p}{r}\ =\ 1 + e \cdot \cos \theta\ =\ 1 + e_g \cdot \cos u + e_h \cdot \sin u$

and that

$\frac {V_r}{V_t} = \frac {e_g \cdot \sin u\ -\ e_h \cdot \cos u}{\frac {p}{r}}$

where

$e_g =\ e\ \cos \omega$
$e_h =\ e\ \sin \omega$

are the components of the eccentricity vector in the $\hat{g}\ ,\ \hat{h}\,$ coordinate system this integral (25) can be evaluated analytically, the result is

$\Delta \bar{e}\ =\ -2\pi\ \frac {J_2}{\mu\ p^2}\ \frac{3}{2} \left(\frac{3}{2}\ \sin^2 i\ -\ 1\right)\ \left(-e_h \hat{g}\ +\ e_g \hat{h}\right)\ =\ -2\pi\ \frac {J_2}{\mu\ p^2} \frac{3}{2} \left(\frac{3}{2}\ \sin^2 i\ -\ 1\right)\ \hat{z}\ \times \ \bar{e}$

(26)

This the difference equation of motion for the eccentricity vector $\bar{e}\,$ to form a circle, the magnitude of the eccentricity $e\,$ staying constant.

Translating this to orbital elements it must be remembered that the new eccentricity vector obtained by adding $\Delta \bar{e}\ \,$ to the old $\bar{e}\ \,$ must be projected to the new orbital plane obtained by applying (23) and (24)

Figure 3: The change $\Delta\omega\,$ in "argument of perigee" after one orbit is the sum of a contribution $\Delta \omega_1\,$ caused by the in-plane force components and a contribution $\Delta \omega_2\,$ caused by the use of the ascending node as reference

This is illustrated in figure 3:

To the change in argument of the eccentricity vector

$\Delta \omega_1\ =\ -2\pi\ \frac {J_2}{\mu\ p^2}\ \frac{3}{2} \left(\frac{3}{2}\ \sin^2 i\ -\ 1\right)\,$

must be added an increment due to the precession of the orbital plane (caused by the out-of-plane force component) amounting to

$\Delta \omega_2\ =\ -\cos i\ \Delta\Omega \ =\ 2\pi\ \frac {J_2}{\mu\ p^2}\ \frac{3}{2}\ \cos^2 i\,$

One therefore gets that

$\Delta e\ =0$

(27)

$\Delta \omega\ =\Delta \omega_1\ +\ \Delta \omega_2\ =\ \ -2\pi\ \frac {J_2}{\mu\ p^2}\ 3 \left(\frac{5}{4}\ \sin^2 i\ -\ 1\right)$

(28)

In terms of the components of the eccentricity vector $e_g,e_h\,$ relative the coordinate system $\hat{g} ,\hat{h}\,$ that precesses around the polar axis of the Earth the same is expressed as follows

\begin{align}&(\Delta e_g,\Delta e_h)\ = \\&-2\pi\ \frac {J_2}{\mu\ p^2}\ \frac{3}{2} \left(\frac{3}{2}\ \sin^2 i\ -\ 1\right)\ (-e_h ,e_g)\ + \ 2\pi\ \frac {J_2}{\mu\ p^2}\ \frac{3}{2}\ \cos^2 i\ (-e_h ,e_g ) = \\&-2\pi\ \frac {J_2}{\mu\ p^2}\ 3 \left(\frac{5}{4}\ \sin^2 i\ -\ 1\right)\ (-e_h ,e_g) \end{align}

(29)

where the first term is the in-plane perturbation of the eccentricity vector and the second is the effect of the new position of the ascending node in the new plane

From (28) follows that $\Delta \omega\,$ is zero if $\sin^2 i\ =\frac{4}{5}\,$. This fact is used for Molniya orbits having an inclination of 63.4 deg. An orbit with an inclination of 180 - 63.4 deg = 116.6 deg would in the same way have a constant argument of perigee.

#### Proof

Proof that the integral

$\int\limits_{0}^{2\pi}\left(-\hat{t}\ \left(\frac{p}{r}\right)^2\ \frac{3}{2}\ \left(3\ \sin^2 i\ \sin^2 u\ -\ 1\right)\ - \ \left(2\ \hat{r}-\frac{V_r}{V_t}\ \hat{t}\right)\ \left(\frac{p}{r}\right)^2\ 3\ \sin^2 i \cos u\ \sin u\right)du$

(30)

where:

$\hat{r}=\cos u\ \hat{G}\ +\ \sin u\ \hat{H}\,$
$\hat{t}=-\sin u\ \hat{G}\ +\ \cos u\ \hat{H}\,$
$\frac{p}{r}\ =\ 1\ +\ e_g\ \cos u\ +\ e_h\ \sin u$
$\frac{V_r}{V_t}\ =\ \frac{e_g\ \sin u\ -\ e_h\ \cos u}{\frac{p}{r}}$

has the value

$-2\pi\ \frac{3}{2} \left(\frac{3}{2}\ \sin^2 i\ -\ 1\right)\ \left(-e_h \hat{G}\ +\ e_g \hat{H}\right)$

(31)

Integrating the first term of the integrand one gets:

\begin{align}&\int\limits_{0}^{2\pi}-t_g\ \left(\frac{p}{r}\right)^2\ \frac{3}{2}\ 3\ \sin^2 i\ \sin^2 u\ du\ =\ \frac{9}{2}\ \sin^2 i\ \int\limits_{0}^{2\pi}\ \left(1\ +\ e_g\ \cos u\ +\ e_h\ \sin u\right)^2\ \ \sin^3 u\ du\ = \\ &9\ \sin^2 i\ e_h\ \int\limits_{0}^{2\pi}\sin^4 u\ du\ =\ 2\pi \frac{27}{8}\ \sin^2 i\ e_h \end{align}

(32)

and

\begin{align}&\int\limits_{0}^{2\pi}-t_h\ \left(\frac{p}{r}\right)^2\ \frac{3}{2}\ 3\ \sin^2 i\ \sin^2 u\ du\ =\ -\frac{9}{2}\ \sin^2 i\ \int\limits_{0}^{2\pi}\ \left(1\ +\ e_g\ \cos u\ +\ e_h\ \sin u\right)^2\ \ \sin^2 u\ \cos u\ du\ = \\ &-9\ \sin^2 i\ e_g\ \int\limits_{0}^{2\pi}\sin^2 u\ \cos^2 u\ du\ =\ -2\pi \frac{9}{8}\ \sin^2 i\ e_g \end{align}

(33)

For the second term one gets:

$\int\limits_{0}^{2\pi} t_g\ \left(\frac{p}{r}\right)^2\ \frac{3}{2}\ du\ =\ -\frac{3}{2}\ \int\limits_{0}^{2\pi}\ \left(1\ +\ e_g\ \cos u\ +\ e_h\ \sin u\right)^2\ \ \sin u\ du\ =\ -3\ e_h\ \int\limits_{0}^{2\pi}\sin^2 u\ du\ =\ -2\pi \frac{3}{2}\ e_h$

(34)

and

$\int\limits_{0}^{2\pi} t_h\ \left(\frac{p}{r}\right)^2\ \frac{3}{2}\ du\ =\ \frac{3}{2}\ \int\limits_{0}^{2\pi}\ \left(1\ +\ e_g\ \cos u\ +\ e_h\ \sin u\right)^2\ \ \cos u\ du\ =\ 3\ e_g\ \int\limits_{0}^{2\pi}\cos^2 u\ du\ =\ 2\pi \frac{3}{2}\ e_g$

(35)

For the third term one gets:

\begin{align}&-\int\limits_{0}^{2\pi}\ 2\ r_g \ \left(\frac{p}{r}\right)^2\ 3\ \sin^2 i \cos u\ \sin u\ du\ =\ -6\ \sin^2 i \int\limits_{0}^{2\pi}\ \left(1\ +\ e_g\ \cos u\ +\ e_h\ \sin u\right)^2\ \cos^2 u\ \sin u\ du\ =\ \\&-12\ \sin^2 i\ e_h \int\limits_{0}^{2\pi}\ \cos^2 u\ \sin^2 u\ du\ =\ -2\pi \frac{3}{2}\ \sin^2 i\ e_h\end{align}

(36)

and

\begin{align}&-\int\limits_{0}^{2\pi}\ 2\ r_h \ \left(\frac{p}{r}\right)^2\ 3\ \sin^2 i \cos u\ \sin u\ du\ =\ -6\ \sin^2 i \int\limits_{0}^{2\pi}\ \left(1\ +\ e_g\ \cos u\ +\ e_h\ \sin u\right)^2\ \cos u\ \sin^2 u\ du\ =\ \\&-12\ \sin^2 i\ e_g \int\limits_{0}^{2\pi}\ \sin^2 u \cos^2 u\ du\ =\ -2\pi \ \frac{3}{2}\ \sin^2 i\ e_g\end{align}

(37)

For the fourth term one gets:

\begin{align}&\int\limits_{0}^{2\pi}t_g\ \frac{V_r}{V_t}\ \left(\frac{p}{r}\right)^2\ 3\ \sin i \cos^2 u\ \sin u\ du\ =-3\ \sin^2 i \int\limits_{0}^{2\pi}(e_g\ \sin u\ -\ e_h\ \cos u)\ \frac{p}{r}\ \cos u\ \sin^2 u\ du \ = \\ &-3\ \sin^2 i \int\limits_{0}^{2\pi}(e_g\ \sin u\ -\ e_h\ \cos u)\ (1\ +\ e_g\ \cos u\ +\ e_h\ \sin u)\ \cos u\ \sin^2 u\ du\ = \\&3\ \sin^2 i \ e_h\int\limits_{0}^{2\pi}\ \ \cos^2 u\ \sin^2 u\ du\ =\ 2\pi \frac{3}{8} \sin^2 i \ e_h\end{align}

(38)

and

\begin{align}&\int\limits_{0}^{2\pi}t_h\ \frac{V_r}{V_t}\ \left(\frac{p}{r}\right)^2\ 3\ \sin^2 i \cos u\ \sin u\ du\ =3\ \sin^2 i \int\limits_{0}^{2\pi}(e_g\ \sin u\ -\ e_h\ \cos u)\ \frac{p}{r}\ \cos^2 u\ \sin u\ du \ = \\ &3\ \sin^2 i \int\limits_{0}^{2\pi}(e_g\ \sin u\ -\ e_h\ \cos u)\ (1\ +\ e_g\ \cos u\ +\ e_h\ \sin u)\ \cos^2 u\ \sin u\ du\ = \\&3\ \sin^2 i \ e_g\int\limits_{0}^{2\pi}\ \ \cos^2 u\ \sin^2 u\ du\ =\ 2\pi \frac{3}{8} \sin^2 i \ e_g\end{align}

(39)

Adding the right hand sides of (32), (34), (36) and (38) one gets $2\pi \frac{27}{8}\ \sin^2 i\ e_h\ -\ 2\pi \frac{3}{2}\ e_h\ -\ 2\pi \frac{3}{2}\ \sin^2 i\ e_h\ +\ 2\pi \frac{3}{8} \sin^2 i \ e_h\ =\ 2\pi\ \frac{3}{2} \left(\frac{3}{2}\ \sin^2 i\ -\ 1\right)\ e_h$

Adding the right hand sides of (33), (35), (37) and (39) one gets $-2\pi \frac{9}{8}\ \sin^2 i\ e_g\ +\ 2\pi \frac{3}{2}\ e_g\ -\ 2\pi \ \frac{3}{2}\ \sin^2 i\ e_g\ +\ 2\pi \frac{3}{8} \sin^2 i \ e_g\ =\ -2\pi\ \frac{3}{2} \left(\frac{3}{2}\ \sin^2 i\ -\ 1\right)\ e_g$

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### Orbit Determination

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Orbit determination is a set of techniques for estimating the orbits of objects such as moons, planets, and spacecraft. Determining the orbits of newly observed asteroids is a common usage of these techniques, both so the asteroid can be followed up with future observations, and also to verify that it has not been previously discovered. Observations are the raw data fed into orbit determination algorithms. Observations made by a ground-based observer typically consist of time-tagged azimuth, elevation, range, and/or range-rate values. Telescopes or radar apparatus are used, because naked-eye observations are inadequate for precise orbit determination. After orbit determination has taken place, mathematical propagation techniques can be used to predict the future positions of orbiting objects. As time goes by, the actual path of an orbiting object tends to diverge from the predicted path (this is especially true if the object is subject to difficult-to-predict perturbations such as atmospheric drag), and a new

# Orbit determination

Orbit determination is a set of techniques for estimating the orbits of objects such as moons, planets, and spacecraft. Determining the orbits of newly observed asteroids is a common usage of these techniques, both so the asteroid can be followed up with future observations, and also to verify that it has not been previously discovered.

Observations are the raw data fed into orbit determination algorithms. Observations made by a ground-based observer typically consist of time-tagged azimuth, elevation, range, and/or range-rate values. Telescopes or radar apparatus are used, because naked-eye observations are inadequate for precise orbit determination.

After orbit determination has taken place, mathematical propagation techniques can be used to predict the future positions of orbiting objects. As time goes by, the actual path of an orbiting object tends to diverge from the predicted path (this is especially true if the object is subject to difficult-to-predict perturbations such as atmospheric drag), and a new orbit determination using new observations serves to re-calibrate knowledge of the orbit.

To the extent that optical, space fence, and other radar resources allow, the Joint Space Operations Center gathers observations of all objects in earth orbit. The observations are used in new orbit determination calculations that maintain the overall accuracy of the satellite catalog. Collision avoidance calculations may use this data to calculate the probability that one orbiting object will collide with another. A satellite's operator may decide to adjust the orbit, if the risk of collision in the present orbit is unacceptable. (It is not possible to adjust the orbit every time a very-low-probability situation is encountered; doing so would cause the satellite to quickly run out of propellant.) When the quantity or quality of observations improves, the accuracy of the orbit determination process also improves, and fewer "false alarms" are brought to the attention of satellite operators.

## History

Orbit determination has a long history, beginning with the prehistoric discovery of the planets and subsequent attempts to predict their motions. Johannes Kepler used Tycho Brahe's careful observations of Mars to deduce the elliptical shape of its orbit and its orientation in space, deriving his three laws of planetary motion in the process.

The beginning of modern understanding of orbit determination is considered to be Anders Johan Lexell's work on computing the orbit of the comet discovered in 1770 that later was named Lexell's Comet,[1] in which Lexell computed the interaction of comet with Jupiter that first made the comet fly close to Earth and then would have expelled it from the Solar system.[2]

Another milestone in orbit determination was Carl Friedrich Gauss' assistance in the "recovery" of the dwarf planet Ceres in 1801. He introduced a method which, when given three observations (in the form of pairs of right ascension and declination), would result in the six orbital elements that completely describe an orbit. The theory of orbit determination has subsequently been developed to the point where today it is applied in GPS receivers as well as the tracking and cataloguing of newly observed minor planets.

## Observational data

In order to determine the unknown orbit of a body, some observations of its motion with time are required. In early modern astronomy, the only available observational data for celestial objects were the right ascension and declination, obtained by observing the body as it moved relative to the fixed stars. This corresponds to knowing the object's relative direction in space, measured from the observer, but without knowledge of the distance of the object, i.e. the resultant measurement contains only direction information, like a unit vector.

With radar, relative distance measurements (by timing of the radar echo) and relative velocity measurements (by measuring the doppler effect of the radar echo) are possible. However, the returned signal strength from radar decreases rapidly, as the inverse fourth power of the range to the object. This limits radar observations to objects relatively near the Earth, such as artificial satellites and Near-Earth objects.

## Methods

Orbit determination must take into account that the apparent celestial motion of the body is influenced by the observer's own motion. For instance, an observer on Earth tracking an asteroid must take into account both the motion of the Earth around the Sun, the rotation of the Earth, and the observer's local latitude and longitude, as these affect the apparent position of the body.

A key observation is that (to a close approximation) all objects move in orbits that are conic sections, with the attracting body (such as the Sun or the Earth) in the prime focus, and that the orbit lies in a fixed plane. Vectors drawn from the attracting body to the body at different points in time will all lie in the orbital plane.

### Lambert's method

If the position and velocity relative to the observer are available (as is the case with radar observations), these observational data can be adjusted by the known position and velocity of the observer relative to the attracting body at the times of observation. This yields the position and velocity with respect to the attracting body. If two such observations are available, along with the time difference between them, the orbit can be determined using Lambert's method. See Lambert's problem for details.

### Gauss' method

Even if no distance information is available, an orbit can still be determined if three or more observations of the body's right ascension and declination have been made. A method, made famous by Gauss in his "recovery" of the dwarf planet Ceres, has been subsequently polished.

One use of this method is in the determination of asteroid masses via the dynamic method. In this procedure Gauss' method is used twice, both before and after a close interaction between two asteroids. After both orbits have been determined the mass of one or both of the asteroids can be worked out.[citation needed]

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### Orbital Launch Vehicles

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Sounding rockets are normally used for brief, inexpensive space and microgravity experiments. Current human-rated suborbital launch vehicles include SpaceShipOne and the upcoming SpaceShipTwo, among others (see space tourism). The delta-v needed for orbital launch using a rocket vehicle launching from the Earth's surface is at least 9300m/s. This delta-v is determined by a combination of air-drag, which is determined by ballistic coefficient as well as gravity losses, altitude gain and the horizontal speed necessary to give a suitable perigee. The delta-v required for altitude gain varies, but is around 2 kilometres per second (1.2 mi/s) for 200 kilometres (120 mi) altitude. [citation needed]

Minimising air-drag entails having a reasonably high ballistic coefficient, which generally means having a launch vehicle that is at least 20 metres (66 ft) long, or a ratio of length to diameter greater than ten. Leaving the atmosphere as early on in the flight as possible provides an air drag of around 300 metres per second (980 ft/s). The horizontal speed necessary to achieve low earth orbit is around 7,800 metres per second (26,000 ft/s).

The calculation of the total delta-v for launch is complicated, and in nearly all cases numerical integration is used; adding multiple delta-v values provides a pessimistic result, since the rocket can thrust while at an angle in order to reach orbit, thereby saving fuel as it can gain altitude and horizontal speed simultaneously.[citation needed]

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## SATELLITE SUBSYSTEMS

### Satellite Subsystems

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The satellite's functional versatility is imbedded within its technical components and its operations characteristics. Looking at the "anatomy" of a typical satellite, one discovers two modules. [12] Note that some novel architectural concepts such as Fractionated Spacecraft somewhat upset this taxonomy.

### Spacecraft bus or service module

This bus module consist of the following subsystems:

• The Structural Subsystems

The structural subsystem provides the mechanical base structure, shields the satellite from extreme temperature changes and micro-meteorite damage, and controls the satellite's spin functions.

• The Telemetry Subsystems (aka Command and Data Handling, C&DH)

The telemetry subsystem monitors the on-board equipment operations, transmits equipment operation data to the earth control station, and receives the earth control station's commands to perform equipment operation adjustments.

• The Power Subsystems

The power subsystem consists of solar panels and backup batteries that generate power when the satellite passes into the Earth's shadow. Nuclear power sources (Radioisotope thermoelectric generators) have been used in several successful satellite programs including the Nimbus program (1964–1978).[16]

• The Thermal Control Subsystems

The thermal control subsystem helps protect electronic equipment from extreme temperatures due to intense sunlight or the lack of sun exposure on different sides of the satellite's body (e.g. Optical Solar Reflector)

• The Attitude and Orbit Control Subsystems

The attitude and orbit control subsystem consists of small rocket thrusters that keep the satellite in the correct orbital position and keep antennas positioning in the right directions.

The second major module is the communication payload, which is made up of transponders. A transponder is capable of :

• Sorting the input signals and directing the output signals through input/output signal multiplexers to the proper downlink antennas for retransmission to earth satellite receiving stations (antennas).

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### Attitude Control

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Attitude control is the exercise of control over the orientation of an object with respect to an inertial frame of reference or another entity (the celestial sphere, certain fields, nearby objects, etc.). Controlling vehicle attitude requires sensors to measure vehicle orientation, actuators to apply the torques needed to re-orient the vehicle to a desired attitude, and algorithms to command the actuators based on (1) sensor measurements of the current attitude and (2) specification of a desired attitude. The integrated field that studies the combination of sensors, actuators and algorithms is called "Guidance, Navigation and Control" (GNC). A spacecraft's attitude must be stabilized and controlled so that its high-gain antenna may be accurately pointed to Earth for communications, so that onboard experiments may accomplish precise pointing for accurate collection and subsequent interpretation of data, so that the heating and cooling effects of sunlight and shadow may be used intelligently for thermal control

# Attitude control

Attitude control is the exercise of control over the orientation of an object with respect to an inertial frame of reference or another entity (the celestial sphere, certain fields, nearby objects, etc.).

Controlling vehicle attitude requires sensors to measure vehicle orientation, actuators to apply the torques needed to re-orient the vehicle to a desired attitude, and algorithms to command the actuators based on (1) sensor measurements of the current attitude and (2) specification of a desired attitude. The integrated field that studies the combination of sensors, actuators and algorithms is called "Guidance, Navigation and Control" (GNC).

## Introduction

A spacecraft's attitude must be stabilized and controlled so that its high-gain antenna may be accurately pointed to Earth for communications, so that onboard experiments may accomplish precise pointing for accurate collection and subsequent interpretation of data, so that the heating and cooling effects of sunlight and shadow may be used intelligently for thermal control, and also for guidance: short propulsive maneuvers must be executed in the right direction.

Spin: Stabilization can be accomplished by setting the vehicle spinning, like the Pioneer 10 and 11 spacecraft in the outer solar system, Lunar Prospector, and the Galileo Jupiter orbiter spacecraft, and its atmospheric probe. The gyroscopic action of the rotating spacecraft mass is the stabilizing mechanism. Propulsion system thrusters are fired only occasionally to make desired changes in spin rate, or in the spin-stabilized attitude. In the case of Galileo's Jupiter atmospheric probe, and the Huygens Titan probe, the proper attitude and spin are initially imparted by the mother ship.

3-Axis: Alternatively, a spacecraft may be designed for active three-axis stabilization. One method is to use small propulsion-system thrusters to incessantly nudge the spacecraft back and forth within a deadband of allowed attitude error. Space probes Voyager 1 and Voyager 2 have been doing that since 1977, and have used up a little over half their 100 kg of propellant as of April 2006. Thrusters are also referred to as mass-expulsion control systems, MEC, or reaction-control systems, RCS.

Another method for achieving three-axis stabilization is to use electrically-powered reaction wheels, also called momentum wheels. Massive wheels are mounted in three orthogonal axes aboard the spacecraft. They provide a means to trade angular momentum back and forth between spacecraft and wheels. To rotate the vehicle in one direction, you spin up the proper wheel in the opposite direction. To rotate the vehicle back, you slow down the wheel. Excess momentum that builds up in the system due to external torques, caused for example by solar photon pressure or gravity gradient, must be occasionally removed from the system by applying torque to the spacecraft, and allowing the wheels to acquire a desired speed under computer control. This is done during maneuvers called momentum desaturation, (desat), or momentum unload maneuvers. Many spacecraft use a system of thrusters to apply the torque for desats. The Hubble Space Telescope, though, has sensitive optics that could be contaminated by thruster exhaust, so it used magnetic torquers that interact with the Earth's magnetic field during its desat maneuvers.

There are advantages and disadvantages to both spin stabilization and 3-axis stabilization. Spin-stabilized craft provide a continuous sweeping motion that is desirable for fields and particles instruments, as well as some optical scanning instruments, but they may require complicated systems to de-spin antennas or optical instruments that must be pointed at targets for science observations or communications with Earth. Three-axis controlled craft can point optical instruments and antennas without having to de-spin them, but they may have to carry out special rotating maneuvers to best utilize their fields and particle instruments. If thrusters are used for routine stabilization, optical observations such as imaging must be designed knowing that the spacecraft is always slowly rocking back and forth, and not always exactly predictably. Reaction wheels provide a much steadier spacecraft from which to make observations, but they add mass to the spacecraft, they have a limited mechanical lifetime, and they require frequent momentum desaturation maneuvers, which can perturb navigation solutions because of accelerations imparted by their use of thrusters.

No matter what choices have been made — spin or 3-axis stabilization, thrusters or reaction wheels, or any combinations of these — the task of attitude and articulation control falls to an AACS computer running highly evolved, sophisticated software.

Articulation: Many spacecraft have components that require articulation. Voyager and Galileo, for example, were designed with scan platforms for pointing optical instruments at their targets largely independently of spacecraft orientation. Many spacecraft, such as Mars orbiters, have solar panels which must track the sun so they can provide electrical power to the spacecraft. Cassini's main engine nozzles are steerable. Knowing where to point a solar panel, or scan platform, or a nozzle — that is, how to articulate it — requires knowledge of the spacecraft's attitude. Since AACS keeps track of the spacecraft's attitude, the sun's location, and Earth's location, it can compute the proper direction to point the appendages. It logically falls to one subsystem, then, to manage both attitude and articulation. The name AACS may even be carried over to a spacecraft even if it has no appendages to articulate.

## Sensors

### Relative attitude sensors

Many sensors generate outputs that reflect the rate of change in attitude. These require a known initial attitude, or external information to use them to determine attitude. Many of this class of sensor have some noise, leading to inaccuracies if not corrected by absolute attitude sensors.

#### Gyroscopes

Gyroscopes are devices that sense rotation in three-dimensional space without reliance on the observation of external objects. Classically, a gyroscope consists of a spinning mass, but there are also "Laser Gyros" utilizing coherent light reflected around a closed path. Another type of "gyro" is a hemispherical resonator gyro where a crystal cup shaped like a wine glass can be driven into oscillation just as a wine glass "sings" as a finger is rubbed around its rim. The orientation of the oscillation is fixed in inertial space, so measuring the orientation of the oscillation relative to the spacecraft can be used to sense the motion of the spacecraft with respect to inertial space.[1]

#### Motion Reference Units

Motion Reference Units are a kind of Inertial measurement unit with single- or multi-axis motion sensors. They utilize MEMS gyroscopes. Some multi-axis MRUs are capable of measuring roll, pitch, yaw and heave. They have applications outside the aeronautical field, such as:
• Antenna motion compensation and stabilization
• Dynamic positioning
• Heave compensation of offshore cranes
• High speed craft motion control and damping systems
• Hydro acoustic positioning
• Motion compensation of single and multibeam echosounders
• Ocean wave measurements
• Offshore structure motion monitoring
• Orientation and attitude measurements on AUVs and ROVs
• Ship motion monitoring

### Absolute attitude sensors

This class of sensors sense the position or orientation of fields, objects or other phenomena outside the spacecraft.

#### Horizon sensor

A horizon sensor is an optical instrument that detects light from the 'limb' of the Earth's atmosphere, i.e., at the horizon. Thermal Infrared sensing is often used, which senses the comparative warmth of the atmosphere, compared to the much colder cosmic background. This sensor provides orientation with respect to the earth about two orthogonal axes. It tends to be less precise than sensors based on stellar observation. Sometimes referred to as an Earth Sensor.[citation needed]

#### Orbital gyrocompass

Similar to the way that a terrestrial gyrocompass uses a pendulum to sense local gravity and force its gyro into alignment with earth's spin vector, and therefore point north, an orbital gyrocompass uses a horizon sensor to sense the direction to earth's center, and a gyro to sense rotation about an axis normal to the orbit plane. Thus, the horizon sensor provides pitch and roll measurements, and the gyro provides yaw.[citation needed] See Tait-Bryan angles.

#### Sun sensor

A sun sensor is a device that senses the direction to the Sun. This can be as simple as some solar cells and shades, or as complex as a steerable telescope, depending on mission requirements.

#### Earth sensor

An earth sensor is a device that senses the direction to the Earth. It is usually an infrared camera; now the main method to detect attitude is the star tracker, but earth sensors are still integrated in satellites for their low cost and reliability.[citation needed]

#### Star tracker

The STARS real-time star tracking software operates on an image from EBEX 2012, a high altitude balloon-borne cosmology experiment launched from Antarctica on 2012-12-29

A star tracker is an optical device that measures the position(s) of star(s) using photocell(s) or a camera.[2]

Many models[3][4][5] are currently available. Star trackers, which require high sensitivity, may become confused by sunlight reflected from the spacecraft, or by exhaust gas plumes from the spacecraft thrusters (either sunlight reflection or contamination of the star tracker window). Star trackers are also susceptible to a variety of errors (low spatial frequency, high spatial frequency, temporal, ...) in addition to a variety of optical sources of error (spherical aberration, chromatic aberration, ...). There are also many potential sources of confusion for the star identification algorithm (planets, comets, supernovae, the bimodal character of the point spread function for adjacent stars, other nearby satellites, point-source light pollution from large cities on Earth, ...). There are roughly 57 bright navigational stars in common use. However, for more complex missions, entire star field databases are used to determine spacecraft orientation. A typical star catalog for high-fidelity attitude determination is originated from a standard base catalog (for example from the United States Naval Observatory) and then filtered to remove problematic stars, for example due to apparent magnitude variability, color index uncertainty, or a location within the Hertzsprung-Russell diagram implying unreliability. These types of star catalogs can have thousands of stars stored in memory on board the spacecraft, or else processed using tools at the ground station and then uploaded.

#### Magnetometer

A magnetometer is a device that senses magnetic field strength and, when used in a three-axis triad, magnetic field direction. As a spacecraft navigational aid, sensed field strength and direction is compared to a map of the Earth magnetic field stored in the memory of an on-board or ground-based guidance computer. If spacecraft position is known then attitude can be inferred.[citation needed]

## Algorithms

Control Algorithms are computer programs that receive data from vehicle sensors and derive the appropriate commands to the actuators to rotate the vehicle to the desired attitude. The algorithms range from very simple, e.g. proportional control, to complex nonlinear estimators or many in-between types, depending on mission requirements. Typically, the attitude control algorithms are part of the software running on the hardware which receives commands from the ground and formats vehicle data Telemetry for transmission to a ground station.

## Actuators

Attitude control can be obtained by several mechanisms, specifically:[citation needed]

### Thrusters

Vernier thrusters are the most common actuators, as they may be used for station keeping as well. Thrusters must be organized as a system to provide stabilization about all three axes, and at least two thrusters are generally used in each axis to provide torque as a couple in order to prevent imnparting a translation to the vehicle. Their limitations are fuel usage, engine wear, and cycles of the control valves. The fuel efficiency of an attitude control system is determined by its specific impulse (proportional to exhaust velocity) and the smallest torque impulse it can provide (which determines how often the thrusters must fire to provide precise control). Thrusters must be fired in one direction to start rotation, and again in the opposing direction if a new orientation is to be held. Thruster systems have been used on most manned space vehicles, including Vostok, Mercury, Gemini, Apollo, Soyuz, and the Space Shuttle.

To minimize the fuel limitation on mission duration, auxiliary attitude control systems may be used to reduce vehicle rotation to lower levels, such as small ion thrusters that accelerate ionized gases electrically to extreme velocities, using power from solar cells.

### Spin stabilization

The entire space vehicle itself can be spun up to stabilize the orientation of a single vehicle axis. This method is widely used to stabilize the final stage of a launch vehicle. The entire spacecraft and an attached solid rocket motor are spun up about the rocket's thrust axis, on a "spin table" oriented by the attitude control system of the lower stage on which the spin table is mounted. When final orbit is achieved, the satellite may be de-spun by various means, or left spinning. Spin stabilization of satellites is only applicable to those missions with a primary axis of orientation that need not change dramatically over the lifetime of the satellite and no need for extremely high precision pointing. It is also useful for missions with instruments that must scan the star field or the Earth's surface or atmosphere. [citation needed] See spin-stabilized satellite.

### Momentum wheels

These are electric motor driven rotors made to spin in the direction opposite to that required to re-orient the vehicle. Since momentum wheels make up a small fraction of the spacecraft's mass and are computer controlled, they give precise control. Momentum wheels are generally suspended on magnetic bearings to avoid bearing friction and breakdown problems. To maintain orientation in three dimensional space a minimum of three must be used, [6] with additional units providing single failure protection. See Euler angles.

### Control moment gyros

These are rotors spun at constant speed, mounted on gimbals to provide attitude control. While a CMG provides control about the two axes orthogonal to the gyro spin axis, triaxial control still requires two units. A CMG is a bit more expensive in terms of cost and mass, since gimbals and their drive motors must be provided. The maximum torque (but not the maximum angular momentum change) exerted by a CMG is greater than for a momentum wheel, making it better suited to large spacecraft. A major drawback is the additional complexity, which increases the number of failure points. For this reason, the International Space Station uses a set of four CMGs to provide dual failure tolerance.

### Solar sails

Small solar sails, (devices that produce thrust as a reaction force induced by reflecting incident light) may be used to make small attitude control and velocity adjustments. This application can save large amounts of fuel on a long-duration mission by producing control moments without fuel expenditure. For example, Mariner 10 adjusted its attitude using its solar cells and antennas as small solar sails.

In orbit, a spacecraft with one axis much longer than the other two will spontaneously orient so that its long axis points at the planet's center of mass. This system has the virtue of needing no active control system or expenditure of fuel. The effect is caused by a tidal force. The upper end of the vehicle feels less gravitational pull than the lower end. This provides a restoring torque whenever the long axis is not co-linear with the direction of gravity. Unless some means of damping is provided, the spacecraft will oscillate about the local vertical. Sometimes tethers are used to connect two parts of a satellite, to increase the stabilizing torque. A problem with such tethers is that meteoroids as small as a grain of sand can part them.

### Magnetic torquers

Coils or (on very small satellites) permanent magnets exert a moment against the local magnetic field. This method works only where there is a magnetic field to react against. One classic field "coil" is actually in the form of a conductive tether in a planetary magnetic field. Such a conductive tether can also generate electrical power, at the expense of orbital decay. Conversely, by inducing a counter-current, using solar cell power, the orbit may be raised. Due to massive variability in Earth magnetic field from an ideal radial field, control laws based on torques coupling to this field will be highly non-linear. Moreover, only two-axis control is available at any given time meaning that a vehicle reorient may be necessary to null all rates.

### Pure passive attitude control

There exists two main passive control types for satellites. The first one uses gravity gradient, and it leads to four stable states with the long axis (axis with smallest moment of inertia) pointing towards the Earth. As this system has four stable states, if the satellite has a preferred orientation, e.g. a camera pointed at the planet, some way to flip the satellite and its tether end-for-end is needed. The other passive system orients the satellite along the earth magnetic field thanks to a magnet. [7] These purely passive attitude control systems have limited pointing accuracy, because the spacecraft will oscillate around energy minima. This drawback is overcome by adding damper, which can be hysteretic materials or a viscous damper. The viscous damper is a small can or tank of fluid mounted in the spacecraft, possibly with internal baffles to increase internal friction. Friction within the damper will gradually convert oscillation energy into heat dissipated within the viscous damper.

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### Service Module Or Bus System

WIKI

This bus module consist of the following subsystems:

• The Structural Subsystems

The structural subsystem provides the mechanical base structure, shields the satellite from extreme temperature changes and micro-meteorite damage, and controls the satellite's spin functions.

• The Telemetry Subsystems (aka Command and Data Handling, C&DH)

The telemetry subsystem monitors the on-board equipment operations, transmits equipment operation data to the earth control station, and receives the earth control station's commands to perform equipment operation adjustments.

• The Power Subsystems

The power subsystem consists of solar panels and backup batteries that generate power when the satellite passes into the Earth's shadow. Nuclear power sources (Radioisotope thermoelectric generators) have been used in several successful satellite programs including the Nimbus program (1964–1978).[16]

• The Thermal Control Subsystems

The thermal control subsystem helps protect electronic equipment from extreme temperatures due to intense sunlight or the lack of sun exposure on different sides of the satellite's body (e.g. Optical Solar Reflector)

• The Attitude and Orbit Control Subsystems

The attitude and orbit control subsystem consists of small rocket thrusters that keep the satellite in the correct orbital position and keep antennas positioning in the right directions.

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### Communication System

WIKI

The second major module is the communication payload, which is made up of transponders. A transponder is capable of :

• Sorting the input signals and directing the output signals through input/output signal multiplexers to the proper downlink antennas for retransmission to earth satellite receiving stations (antennas).

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## MULTIPLE ACCESS

### Frequency Division Multiple Access

WIKI

Frequency Division Multiple Access or FDMA is a channel access method used in multiple-access protocols as a channelization protocol. FDMA gives users an individual allocation of one or several frequency bands, or channels. It is particularly commonplace in satellite communication. FDMA, like other Multiple Access systems, coordinates access between multiple users. Alternatives include TDMA, CDMA, or SDMA. These protocols are utilized differently, at different levels of the theoretical OSI model. Disadvantage: Crosstalk may cause interference among frequencies and disrupt the transmission. FDMA is distinct from frequency division duplexing (FDD). While FDMA allows multiple users simultaneous access to a transmission system, FDD refers to how the radio channel is shared between the uplink and downlink (for instance, the traffic going back and forth between a mobile-phone and a mobile phone base station). Frequency-division multiplexing (FDM) is also distinct from FDMA. FDM is a physical layer technique that co

# Frequency-division multiple access

(Redirected from Frequency division multiple access)

Frequency Division Multiple Access or FDMA is a channel access method used in multiple-access protocols as a channelization protocol. FDMA gives users an individual allocation of one or several frequency bands, or channels. It is particularly commonplace in satellite communication. FDMA, like other Multiple Access systems, coordinates access between multiple users. Alternatives include TDMA, CDMA, or SDMA. These protocols are utilized differently, at different levels of the theoretical OSI model.

Disadvantage: Crosstalk may cause interference among frequencies and disrupt the transmission.

## Features

• In FDMA all users share the satellite transponder or frequency channel simultaneously but each user transmits at single frequency.
• FDMA can be used with both analog and digital signal.
• FDMA requires high-performing filters in the radio hardware, in contrast to TDMA and CDMA.
• FDMA is not vulnerable to the timing problems that TDMA has. Since a predetermined frequency band is available for the entire period of communication, stream data (a continuous flow of data that may not be packetized) can easily be used with FDMA.
• Due to the frequency filtering, FDMA is not sensitive to near-far problem which is pronounced for CDMA.
• Each user transmits and receives at different frequencies as each user gets a unique frequency slots.

FDMA is distinct from frequency division duplexing (FDD). While FDMA allows multiple users simultaneous access to a transmission system, FDD refers to how the radio channel is shared between the uplink and downlink (for instance, the traffic going back and forth between a mobile-phone and a mobile phone base station). Frequency-division multiplexing (FDM) is also distinct from FDMA. FDM is a physical layer technique that combines and transmits low-bandwidth channels through a high-bandwidth channel. FDMA, on the other hand, is an access method in the data link layer.

FDMA also supports demand assignment in addition to fixed assignment. Demand assignment allows all users apparently continuous access of the radio spectrum by assigning carrier frequencies on a temporary basis using a statistical assignment process. The first FDMA demand-assignment system for satellite was developed by COMSAT for use on the Intelsat series IVA and V satellites.

There are two main techniques:

• Multi-channel per-carrier (MCPC)
• Single-channel per-carrier (SCPC)

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### Time Division Multiple Access

WIKI

Time division multiple access (TDMA) is a channel access method for shared medium networks. It allows several users to share the same frequency channel by dividing the signal into different time slots. The users transmit in rapid succession, one after the other, each using its own time slot. This allows multiple stations to share the same transmission medium (e.g. radio frequency channel) while using only a part of its channel capacity. TDMA is used in the digital 2G cellular systems such as Global System for Mobile Communications (GSM), IS-136, Personal Digital Cellular (PDC) and iDEN, and in the Digital Enhanced Cordless Telecommunications (DECT) standard for portable phones. It is also used extensively in satellite systems, combat-net radio systems, and PON networks for upstream traffic from premises to the operator. For usage of Dynamic TDMA packet mode communication, see below. TDMA is a type of Time-division multiplexing, with the special point that instead of having one transmitter connected to one rec

# Time division multiple access

This article is about the channel access method. The name "TDMA" is also commonly used in the United States to refer to Digital AMPS, which is an obsolete mobile telephone standard that uses TDMA to control channel access.

Time division multiple access (TDMA) is a channel access method for shared medium networks. It allows several users to share the same frequency channel by dividing the signal into different time slots. The users transmit in rapid succession, one after the other, each using its own time slot. This allows multiple stations to share the same transmission medium (e.g. radio frequency channel) while using only a part of its channel capacity. TDMA is used in the digital 2G cellular systems such as Global System for Mobile Communications (GSM), IS-136, Personal Digital Cellular (PDC) and iDEN, and in the Digital Enhanced Cordless Telecommunications (DECT) standard for portable phones. It is also used extensively in satellite systems, combat-net radio systems, and PON networks for upstream traffic from premises to the operator. For usage of Dynamic TDMA packet mode communication, see below.

TDMA frame structure showing a data stream divided into frames and those frames divided into time slots.

TDMA is a type of Time-division multiplexing, with the special point that instead of having one transmitter connected to one receiver, there are multiple transmitters. In the case of the uplink from a mobile phone to a base station this becomes particularly difficult because the mobile phone can move around and vary the timing advance required to make its transmission match the gap in transmission from its peers.

## TDMA characteristics

• Shares single carrier frequency with multiple users
• Non-continuous transmission makes handoff simpler
• Slots can be assigned on demand in dynamic TDMA
• Less stringent power control than CDMA due to reduced intra cell interference
• Higher synchronization overhead than CDMA
• Advanced equalization may be necessary for high data rates if the channel is "frequency selective" and creates Intersymbol interference
• Cell breathing (borrowing resources from adjacent cells) is more complicated than in CDMA
• Frequency/slot allocation complexity
• Pulsating power envelope: Interference with other devices

## TDMA in mobile phone systems

### 2G systems

Most 2G cellular systems, with the notable exception of IS-95, are based on TDMA. GSM, D-AMPS, PDC, iDEN, and PHS are examples of TDMA cellular systems. GSM combines TDMA with Frequency Hopping and wideband transmission to minimize common types of interference.

In the GSM system, the synchronization of the mobile phones is achieved by sending timing advance commands from the base station which instructs the mobile phone to transmit earlier and by how much. This compensates for the propagation delay resulting from the light speed velocity of radio waves. The mobile phone is not allowed to transmit for its entire time slot, but there is a guard interval at the end of each time slot. As the transmission moves into the guard period, the mobile network adjusts the timing advance to synchronize the transmission.

Initial synchronization of a phone requires even more care. Before a mobile transmits there is no way to actually know the offset required. For this reason, an entire time slot has to be dedicated to mobiles attempting to contact the network (known as the RACH in GSM). The mobile attempts to broadcast at the beginning of the time slot, as received from the network. If the mobile is located next to the base station, there will be no time delay and this will succeed. If, however, the mobile phone is at just less than 35 km from the base station, the time delay will mean the mobile's broadcast arrives at the very end of the time slot. In that case, the mobile will be instructed to broadcast its messages starting nearly a whole time slot earlier than would be expected otherwise. Finally, if the mobile is beyond the 35 km cell range in GSM, then the RACH will arrive in a neighbouring time slot and be ignored. It is this feature, rather than limitations of power, that limits the range of a GSM cell to 35 km when no special extension techniques are used. By changing the synchronization between the uplink and downlink at the base station, however, this limitation can be overcome.

### 3G systems

Although most major 3G systems are primarily based upon CDMA[citation needed], time division duplexing (TDD), packet scheduling (dynamic TDMA) and packet oriented multiple access schemes are available in 3G form, combined with CDMA to take advantage of the benefits of both technologies.

While the most popular form of the UMTS 3G system uses CDMA and frequency division duplexing (FDD) instead of TDMA, TDMA is combined with CDMA and Time Division Duplexing in two standard UMTS UTRA

## TDMA in wired networks

The ITU-T G.hn standard, which provides high-speed local area networking over existing home wiring (power lines, phone lines and coaxial cables) is based on a TDMA scheme. In G.hn, a "master" device allocates "Contention-Free Transmission Opportunities" (CFTXOP) to other "slave" devices in the network. Only one device can use a CFTXOP at a time, thus avoiding collisions. FlexRay protocol which is also a wired network used for safety-critical communication in modern cars, uses the TDMA method for data transmission control.

## Comparison with other multiple-access schemes

In radio systems, TDMA is usually used alongside Frequency-division multiple access (FDMA) and Frequency division duplex (FDD); the combination is referred to as FDMA/TDMA/FDD. This is the case in both GSM and IS-136 for example. Exceptions to this include the DECT and PHS micro-cellular systems, UMTS-TDD UMTS variant, and China's TD-SCDMA, which use Time Division duplexing, where different time slots are allocated for the base station and handsets on the same frequency.

A major advantage of TDMA is that the radio part of the mobile only needs to listen and broadcast for its own time slot. For the rest of the time, the mobile can carry out measurements on the network, detecting surrounding transmitters on different frequencies. This allows safe inter frequency handovers, something which is difficult in CDMA systems, not supported at all in IS-95 and supported through complex system additions in Universal Mobile Telecommunications System (UMTS). This in turn allows for co-existence of microcell layers with macrocell layers.

CDMA, by comparison, supports "soft hand-off" which allows a mobile phone to be in communication with up to 6 base stations simultaneously, a type of "same-frequency handover". The incoming packets are compared for quality, and the best one is selected. CDMA's "cell breathing" characteristic, where a terminal on the boundary of two congested cells will be unable to receive a clear signal, can often negate this advantage during peak periods.

A disadvantage of TDMA systems is that they create interference at a frequency which is directly connected to the time slot length. This is the buzz which can sometimes be heard if a TDMA phone is left next to a radio or speakers.[1] Another disadvantage is that the "dead time" between time slots limits the potential bandwidth of a TDMA channel. These are implemented in part because of the difficulty in ensuring that different terminals transmit at exactly the times required. Handsets that are moving will need to constantly adjust their timings to ensure their transmission is received at precisely the right time, because as they move further from the base station, their signal will take longer to arrive. This also means that the major TDMA systems have hard limits on cell sizes in terms of range, though in practice the power levels required to receive and transmit over distances greater than the supported range would be mostly impractical anyway.

## Dynamic TDMA

In dynamic time division multiple access, a scheduling algorithm dynamically reserves a variable number of time slots in each frame to variable bit-rate data streams, based on the traffic demand of each data stream. Dynamic TDMA is used in

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### Code Division Multiple Access

WIKI

Code division multiple access (CDMA) is a channel access method used by various radio communication technologies. CDMA is an example of multiple access, which is where several transmitters can send information simultaneously over a single communication channel. This allows several users to share a band of frequencies (see bandwidth). To permit this to be achieved without undue interference between the users CDMA employs spread-spectrum technology and a special coding scheme (where each transmitter is assigned a code). CDMA is used as the access method in many mobile phone standards such as cdmaOne, CDMA2000 (the 3G evolution of cdmaOne), and WCDMA (the 3G standard used by GSM carriers), which are often referred to as simply CDMA. The technology of code division multiple access channels has long been known. In the USSR, the first work devoted to this subject was published in 1935 by professor Dmitriy V. Ageev.[1] It was shown that through the use of linear methods, there are three types of signal separation: f

# Code division multiple access

Code division multiple access (CDMA) is a channel access method used by various radio communication technologies.

CDMA is an example of multiple access, which is where several transmitters can send information simultaneously over a single communication channel. This allows several users to share a band of frequencies (see bandwidth). To permit this to be achieved without undue interference between the users CDMA employs spread-spectrum technology and a special coding scheme (where each transmitter is assigned a code).

CDMA is used as the access method in many mobile phone standards such as cdmaOne, CDMA2000 (the 3G evolution of cdmaOne), and WCDMA (the 3G standard used by GSM carriers), which are often referred to as simply CDMA.

## History

The technology of code division multiple access channels has long been known. In the USSR, the first work devoted to this subject was published in 1935 by professor Dmitriy V. Ageev.[1] It was shown that through the use of linear methods, there are three types of signal separation: frequency, time and compensatory. The technology of CDMA was used in 1957, when the young military radio engineer Leonid Kupriyanovich in Moscow, made an experimental model of a wearable automatic mobile phone, called LK-1 by him, with a base station. LK-1 has a weight of 3 kg, 20–30 km operating distance, and 20–30 hours of battery life.[2][3] The base station, as described by the author, could serve several customers. In 1958, Kupriyanovich made the new experimental "pocket" model of mobile phone. This phone weighed 0.5 kg. To serve more customers, Kupriyanovich proposed the device, named by him as correllator.[4][5] In 1958, the USSR also started the development of the "Altai" national civil mobile phone service for cars, based on the Soviet MRT-1327 standard. The phone system weighed 11 kg and was approximately 3 cubic meters in size[dubious ]. It was placed in the trunk of the vehicles of high-ranking officials and used a standard handset in the passenger compartment. The main developers of the Altai system were VNIIS (Voronezh Science Research Institute of Communications) and GSPI (State Specialized Project Institute). In 1963 this service started in Moscow and in 1970 Altai service was used in 30 USSR cities.[citation needed]

## Uses

A CDMA2000 mobile phone
• One of the early applications for code division multiplexing is in GPS. This predates and is distinct from its use in mobile phones.
• The Qualcomm standard IS-95, marketed as cdmaOne.
• The Qualcomm standard IS-2000, known as CDMA2000. This standard is used by several mobile phone companies, including the Globalstar satellite phone network.
• The UMTS 3G mobile phone standard, which uses W-CDMA.
• CDMA has been used in the OmniTRACS satellite system for transportation logistics.

## Steps in CDMA Modulation

CDMA is a spread spectrum multiple access[6] technique. A spread spectrum technique spreads the bandwidth of the data uniformly for the same transmitted power. A spreading code is a pseudo-random code that has a narrow ambiguity function, unlike other narrow pulse codes. In CDMA a locally generated code runs at a much higher rate than the data to be transmitted. Data for transmission is combined via bitwise XOR (exclusive OR) with the faster code. The figure shows how a spread spectrum signal is generated. The data signal with pulse duration of $T_{b}$ (symbol period) is XOR’ed with the code signal with pulse duration of $T_{c}$ (chip period). (Note: bandwidth is proportional to $1/T$ where $T$ = bit time) Therefore, the bandwidth of the data signal is $1/T_{b}$ and the bandwidth of the spread spectrum signal is $1/T_{c}$. Since $T_{c}$ is much smaller than $T_{b}$, the bandwidth of the spread spectrum signal is much larger than the bandwidth of the original signal. The ratio $T_{b}/T_{c}$ is called the spreading factor or processing gain and determines to a certain extent the upper limit of the total number of users supported simultaneously by a base station.[7]

Each user in a CDMA system uses a different code to modulate their signal. Choosing the codes used to modulate the signal is very important in the performance of CDMA systems. The best performance will occur when there is good separation between the signal of a desired user and the signals of other users. The separation of the signals is made by correlating the received signal with the locally generated code of the desired user. If the signal matches the desired user's code then the correlation function will be high and the system can extract that signal. If the desired user's code has nothing in common with the signal the correlation should be as close to zero as possible (thus eliminating the signal); this is referred to as cross correlation. If the code is correlated with the signal at any time offset other than zero, the correlation should be as close to zero as possible. This is referred to as auto-correlation and is used to reject multi-path interference.[8]

An analogy to the problem of multiple access is a room (channel) in which people wish to talk to each other simultaneously. To avoid confusion, people could take turns speaking (time division), speak at different pitches (frequency division), or speak in different languages (code division). CDMA is analogous to the last example where people speaking the same language can understand each other, but other languages are perceived as noise and rejected. Similarly, in radio CDMA, each group of users is given a shared code. Many codes occupy the same channel, but only users associated with a particular code can communicate.

In general, CDMA belongs to two basic categories: synchronous (orthogonal codes) and asynchronous (pseudorandom codes).

## Code division multiplexing (Synchronous CDMA)

Synchronous CDMA exploits mathematical properties of orthogonality between vectors representing the data strings. For example, binary string 1011 is represented by the vector (1, 0, 1, 1). Vectors can be multiplied by taking their dot product, by summing the products of their respective components (for example, if u = (a, b) and v = (c, d), then their dot product u·v = ac + bd). If the dot product is zero, the two vectors are said to be orthogonal to each other. Some properties of the dot product aid understanding of how W-CDMA works. If vectors a and b are orthogonal, then $\scriptstyle\mathbf{a}\cdot\mathbf{b} \,=\, 0$ and:

\begin{align}\mathbf{a}\cdot(\mathbf{a}+\mathbf{b}) &= \|\mathbf{a}\|^2 &\quad\mathrm{since}\quad \mathbf{a}\cdot\mathbf{a}+\mathbf{a}\cdot\mathbf{b} &= \|a\|^2+0 \\\mathbf{a}\cdot(-\mathbf{a}+\mathbf{b}) &= -\|\mathbf{a}\|^2 &\quad\mathrm{since}\quad -\mathbf{a}\cdot\mathbf{a}+\mathbf{a}\cdot\mathbf{b} &= -\|a\|^2+0 \\\mathbf{b}\cdot(\mathbf{a}+\mathbf{b}) &= \|\mathbf{b}\|^2 &\quad\mathrm{since}\quad \mathbf{b}\cdot\mathbf{a}+\mathbf{b}\cdot\mathbf{b} &= 0+\|b\|^2 \\\mathbf{b}\cdot(\mathbf{a}-\mathbf{b}) &= -\|\mathbf{b}\|^2 &\quad\mathrm{since}\quad \mathbf{b}\cdot\mathbf{a}-\mathbf{b}\cdot\mathbf{b} &= 0-\|b\|^2\end{align}

Each user in synchronous CDMA uses a code orthogonal to the others' codes to modulate their signal. An example of four mutually orthogonal digital signals is shown in the figure. Orthogonal codes have a cross-correlation equal to zero; in other words, they do not interfere with each other. In the case of IS-95 64 bit Walsh codes are used to encode the signal to separate different users. Since each of the 64 Walsh codes are orthogonal to one another, the signals are channelized into 64 orthogonal signals. The following example demonstrates how each user's signal can be encoded and decoded.

### Example

An example of four mutually orthogonal digital signals.

Start with a set of vectors that are mutually orthogonal. (Although mutual orthogonality is the only condition, these vectors are usually constructed for ease of decoding, for example columns or rows from Walsh matrices.) An example of orthogonal functions is shown in the picture on the left. These vectors will be assigned to individual users and are called the code, chip code, or chipping code. In the interest of brevity, the rest of this example uses codes, v, with only 2 bits.

Each user is associated with a different code, say v. A 1 bit is represented by transmitting a positive code, v, and a 0 bit is represented by a negative code, –v. For example, if v = (v0, v1) = (1, –1) and the data that the user wishes to transmit is (1, 0, 1, 1), then the transmitted symbols would be (v, –v, v, v) = (v0, v1, –v0, –v1, v0, v1, v0, v1) = (1, –1, –1, 1, 1, –1, 1, –1). For the purposes of this article, we call this constructed vector the transmitted vector.

Each sender has a different, unique vector v chosen from that set, but the construction method of the transmitted vector is identical.

Now, due to physical properties of interference, if two signals at a point are in phase, they add to give twice the amplitude of each signal, but if they are out of phase, they subtract and give a signal that is the difference of the amplitudes. Digitally, this behaviour can be modelled by the addition of the transmission vectors, component by component.

If sender0 has code (1, –1) and data (1, 0, 1, 1), and sender1 has code (1, 1) and data (0, 0, 1, 1), and both senders transmit simultaneously, then this table describes the coding steps:

 Step Encode sender0 Encode sender1 0 code0 = (1, –1), data0 = (1, 0, 1, 1) code1 = (1, 1), data1 = (0, 0, 1, 1) 1 encode0 = 2(1, 0, 1, 1) – (1, 1, 1, 1)= (1, –1, 1, 1) encode1 = 2(0, 0, 1, 1) – (1, 1, 1, 1)= (–1, –1, 1, 1) 2 signal0 = encode0 ? code0= (1, –1, 1, 1) ? (1, –1)= (1, –1, –1, 1, 1, –1, 1, –1) signal1 = encode1 ? code1= (–1, –1, 1, 1) ? (1, 1)= (–1, –1, –1, –1, 1, 1, 1, 1)

Because signal0 and signal1 are transmitted at the same time into the air, they add to produce the raw signal:

(1, –1, –1, 1, 1, –1, 1, –1) + (–1, –1, –1, –1, 1, 1, 1, 1) = (0, –2, –2, 0, 2, 0, 2, 0)

This raw signal is called an interference pattern. The receiver then extracts an intelligible signal for any known sender by combining the sender's code with the interference pattern, the receiver combines it with the codes of the senders. The following table explains how this works and shows that the signals do not interfere with one another:

 Step Decode sender0 Decode sender1 0 code0 = (1, –1), signal = (0, –2, –2, 0, 2, 0, 2, 0) code1 = (1, 1), signal = (0, –2, –2, 0, 2, 0, 2, 0) 1 decode0 = pattern.vector0 decode1 = pattern.vector1 2 decode0 = ((0, –2), (–2, 0), (2, 0), (2, 0)).(1, –1) decode1 = ((0, –2), (–2, 0), (2, 0), (2, 0)).(1, 1) 3 decode0 = ((0 + 2), (–2 + 0), (2 + 0), (2 + 0)) decode1 = ((0 – 2), (–2 + 0), (2 + 0), (2 + 0)) 4 data0=(2, –2, 2, 2), meaning (1, 0, 1, 1) data1=(–2, –2, 2, 2), meaning (0, 0, 1, 1)

Further, after decoding, all values greater than 0 are interpreted as 1 while all values less than zero are interpreted as 0. For example, after decoding, data0 is (2, –2, 2, 2), but the receiver interprets this as (1, 0, 1, 1). Values of exactly 0 means that the sender did not transmit any data, as in the following example:

Assume signal0 = (1, –1, –1, 1, 1, –1, 1, –1) is transmitted alone. The following table shows the decode at the receiver:

 Step Decode sender0 Decode sender1 0 code0 = (1, –1), signal = (1, –1, –1, 1, 1, –1, 1, –1) code1 = (1, 1), signal = (1, –1, –1, 1, 1, –1, 1, –1) 1 decode0 = pattern.vector0 decode1 = pattern.vector1 2 decode0 = ((1, –1), (–1, 1), (1, –1), (1, –1)).(1, –1) decode1 = ((1, –1), (–1, 1), (1, –1), (1, –1)).(1, 1) 3 decode0 = ((1 + 1), (–1 – 1),(1 + 1), (1 + 1)) decode1 = ((1 – 1), (–1 + 1),(1 – 1), (1 – 1)) 4 data0 = (2, –2, 2, 2), meaning (1, 0, 1, 1) data1 = (0, 0, 0, 0), meaning no data

When the receiver attempts to decode the signal using sender1's code, the data is all zeros, therefore the cross correlation is equal to zero and it is clear that sender1 did not transmit any data.

## Asynchronous CDMA

When mobile-to-base links cannot be precisely coordinated, particularly due to the mobility of the handsets, a different approach is required. Since it is not mathematically possible to create signature sequences that are both orthogonal for arbitrarily random starting points and which make full use of the code space, unique "pseudo-random" or "pseudo-noise" (PN) sequences are used in asynchronous CDMA systems. A PN code is a binary sequence that appears random but can be reproduced in a deterministic manner by intended receivers. These PN codes are used to encode and decode a user's signal in Asynchronous CDMA in the same manner as the orthogonal codes in synchronous CDMA (shown in the example above). These PN sequences are statistically uncorrelated, and the sum of a large number of PN sequences results in multiple access interference (MAI) that is approximated by a Gaussian noise process (following the central limit theorem in statistics). Gold codes are an example of a PN suitable for this purpose, as there is low correlation between the codes. If all of the users are received with the same power level, then the variance (e.g., the noise power) of the MAI increases in direct proportion to the number of users. In other words, unlike synchronous CDMA, the signals of other users will appear as noise to the signal of interest and interfere slightly with the desired signal in proportion to number of users.

All forms of CDMA use spread spectrum process gain to allow receivers to partially discriminate against unwanted signals. Signals encoded with the specified PN sequence (code) are received, while signals with different codes (or the same code but a different timing offset) appear as wideband noise reduced by the process gain.

Since each user generates MAI, controlling the signal strength is an important issue with CDMA transmitters. A CDM (synchronous CDMA), TDMA, or FDMA receiver can in theory completely reject arbitrarily strong signals using different codes, time slots or frequency channels due to the orthogonality of these systems. This is not true for Asynchronous CDMA; rejection of unwanted signals is only partial. If any or all of the unwanted signals are much stronger than the desired signal, they will overwhelm it. This leads to a general requirement in any asynchronous CDMA system to approximately match the various signal power levels as seen at the receiver. In CDMA cellular, the base station uses a fast closed-loop power control scheme to tightly control each mobile's transmit power.

### Advantages of asynchronous CDMA over other techniques

#### Efficient practical utilization of fixed frequency spectrum

In theory, CDMA, TDMA and FDMA have exactly the same spectral efficiency but practically, each has its own challenges – power control in the case of CDMA, timing in the case of TDMA, and frequency generation/filtering in the case of FDMA.

TDMA systems must carefully synchronize the transmission times of all the users to ensure that they are received in the correct time slot and do not cause interference. Since this cannot be perfectly controlled in a mobile environment, each time slot must have a guard-time, which reduces the probability that users will interfere, but decreases the spectral efficiency. Similarly, FDMA systems must use a guard-band between adjacent channels, due to the unpredictable doppler shift of the signal spectrum because of user mobility. The guard-bands will reduce the probability that adjacent channels will interfere, but decrease the utilization of the spectrum.

#### Flexible allocation of resources

Asynchronous CDMA offers a key advantage in the flexible allocation of resources i.e. allocation of a PN codes to active users. In the case of CDM (synchronous CDMA), TDMA, and FDMA the number of simultaneous orthogonal codes, time slots and frequency slots respectively are fixed hence the capacity in terms of number of simultaneous users is limited. There are a fixed number of orthogonal codes, time slots or frequency bands that can be allocated for CDM, TDMA, and FDMA systems, which remain underutilized due to the bursty nature of telephony and packetized data transmissions. There is no strict limit to the number of users that can be supported in an asynchronous CDMA system, only a practical limit governed by the desired bit error probability, since the SIR (Signal to Interference Ratio) varies inversely with the number of users. In a bursty traffic environment like mobile telephony, the advantage afforded by asynchronous CDMA is that the performance (bit error rate) is allowed to fluctuate randomly, with an average value determined by the number of users times the percentage of utilization. Suppose there are 2N users that only talk half of the time, then 2N users can be accommodated with the same average bit error probability as N users that talk all of the time. The key difference here is that the bit error probability for N users talking all of the time is constant, whereas it is a random quantity (with the same mean) for 2N users talking half of the time.

In other words, asynchronous CDMA is ideally suited to a mobile network where large numbers of transmitters each generate a relatively small amount of traffic at irregular intervals. CDM (synchronous CDMA), TDMA, and FDMA systems cannot recover the underutilized resources inherent to bursty traffic due to the fixed number of orthogonal codes, time slots or frequency channels that can be assigned to individual transmitters. For instance, if there are N time slots in a TDMA system and 2N users that talk half of the time, then half of the time there will be more than N users needing to use more than N time slots. Furthermore, it would require significant overhead to continually allocate and deallocate the orthogonal code, time slot or frequency channel resources. By comparison, asynchronous CDMA transmitters simply send when they have something to say, and go off the air when they don't, keeping the same PN signature sequence as long as they are connected to the system.

Most modulation schemes try to minimize the bandwidth of this signal since bandwidth is a limited resource. However, spread spectrum techniques use a transmission bandwidth that is several orders of magnitude greater than the minimum required signal bandwidth. One of the initial reasons for doing this was military applications including guidance and communication systems. These systems were designed using spread spectrum because of its security and resistance to jamming. Asynchronous CDMA has some level of privacy built in because the signal is spread using a pseudo-random code; this code makes the spread spectrum signals appear random or have noise-like properties. A receiver cannot demodulate this transmission without knowledge of the pseudo-random sequence used to encode the data. CDMA is also resistant to jamming. A jamming signal only has a finite amount of power available to jam the signal. The jammer can either spread its energy over the entire bandwidth of the signal or jam only part of the entire signal.[9]

CDMA can also effectively reject narrow band interference. Since narrow band interference affects only a small portion of the spread spectrum signal, it can easily be removed through notch filtering without much loss of information. Convolution encoding and interleaving can be used to assist in recovering this lost data. CDMA signals are also resistant to multipath fading. Since the spread spectrum signal occupies a large bandwidth only a small portion of this will undergo fading due to multipath at any given time. Like the narrow band interference this will result in only a small loss of data and can be overcome.

Another reason CDMA is resistant to multipath interference is because the delayed versions of the transmitted pseudo-random codes will have poor correlation with the original pseudo-random code, and will thus appear as another user, which is ignored at the receiver. In other words, as long as the multipath channel induces at least one chip of delay, the multipath signals will arrive at the receiver such that they are shifted in time by at least one chip from the intended signal. The correlation properties of the pseudo-random codes are such that this slight delay causes the multipath to appear uncorrelated with the intended signal, and it is thus ignored.

Some CDMA devices use a rake receiver, which exploits multipath delay components to improve the performance of the system. A rake receiver combines the information from several correlators, each one tuned to a different path delay, producing a stronger version of the signal than a simple receiver with a single correlation tuned to the path delay of the strongest signal.[10]

Frequency reuse is the ability to reuse the same radio channel frequency at other cell sites within a cellular system. In the FDMA and TDMA systems frequency planning is an important consideration. The frequencies used in different cells must be planned carefully to ensure signals from different cells do not interfere with each other. In a CDMA system, the same frequency can be used in every cell, because channelization is done using the pseudo-random codes. Reusing the same frequency in every cell eliminates the need for frequency planning in a CDMA system; however, planning of the different pseudo-random sequences must be done to ensure that the received signal from one cell does not correlate with the signal from a nearby cell.[11]

Since adjacent cells use the same frequencies, CDMA systems have the ability to perform soft hand offs. Soft hand offs allow the mobile telephone to communicate simultaneously with two or more cells. The best signal quality is selected until the hand off is complete. This is different from hard hand offs utilized in other cellular systems. In a hard hand off situation, as the mobile telephone approaches a hand off, signal strength may vary abruptly. In contrast, CDMA systems use the soft hand off, which is undetectable and provides a more reliable and higher quality signal.[11]

## Collaborative CDMA

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WIKI

In telecommunication and radio communication, spread-spectrum techniques are methods by which a signal (e.g. an electrical, electromagnetic, or acoustic signal) generated with a particular bandwidth is deliberately spread in the frequency domain, resulting in a signal with a wider bandwidth. These techniques are used for a variety of reasons, including the establishment of secure communications, increasing resistance to natural interference, noise and jamming, to prevent detection, and to limit power flux density (e.g. in satellite downlinks). Spread-spectrum telecommunications This is a technique in which a telecommunication signal is transmitted on a bandwidth considerably larger than the frequency content of the original information. Frequency hopping is a basic modulation technique used in spread spectrum signal transmission. Spread-spectrum telecommunications is a signal structuring technique that employs direct sequence, frequency hopping, or a hybrid of these, which can be used for multiple access and/

In telecommunication and radio communication, spread-spectrum techniques are methods by which a signal (e.g. an electrical, electromagnetic, or acoustic signal) generated with a particular bandwidth is deliberately spread in the frequency domain, resulting in a signal with a wider bandwidth. These techniques are used for a variety of reasons, including the establishment of secure communications, increasing resistance to natural interference, noise and jamming, to prevent detection, and to limit power flux density (e.g. in satellite downlinks).

Spread-spectrum telecommunications This is a technique in which a telecommunication signal is transmitted on a bandwidth considerably larger than the frequency content of the original information. Frequency hopping is a basic modulation technique used in spread spectrum signal transmission.

Spread-spectrum telecommunications is a signal structuring technique that employs direct sequence, frequency hopping, or a hybrid of these, which can be used for multiple access and/or multiple functions. This technique decreases the potential interference to other receivers while achieving privacy. Spread spectrum generally makes use of a sequential noise-like signal structure to spread the normally narrowband information signal over a relatively wideband (radio) band of frequencies. The receiver correlates the received signals to retrieve the original information signal. Originally there were two motivations: either to resist enemy efforts to jam the communications (anti-jam, or AJ), or to hide the fact that communication was even taking place, sometimes called low probability of intercept (LPI).

Frequency-hopping spread spectrum (FHSS), direct-sequence spread spectrum (DSSS), time-hopping spread spectrum (THSS), chirp spread spectrum (CSS), and combinations of these techniques are forms of spread spectrum. Each of these techniques employs pseudorandom number sequences — created using pseudorandom number generators — to determine and control the spreading pattern of the signal across the allocated bandwidth. Ultra-wideband (UWB) is another modulation technique that accomplishes the same purpose, based on transmitting short duration pulses. Wireless standard IEEE 802.11 uses either FHSS or DSSS in its radio interface.

## Techniques

• Techniques known since the 1940s and used in military communication systems since the 1950s "spread" a radio signal over a wide frequency range several magnitudes higher than minimum requirement. The core principle of spread spectrum is the use of noise-like carrier waves, and, as the name implies, bandwidths much wider than that required for simple point-to-point communication at the same data rate.
• Resistance to jamming (interference). DS (direct sequence) is better at resisting continuous-time narrowband jamming, while FH (frequency hopping) is better at resisting pulse jamming. In DS systems, narrowband jamming affects detection performance about as much as if the amount of jamming power is spread over the whole signal bandwidth, when it will often not be much stronger than background noise. By contrast, in narrowband systems where the signal bandwidth is low, the received signal quality will be severely lowered if the jamming power happens to be concentrated on the signal bandwidth.
• Resistance to fading. The high bandwidth occupied by spread-spectrum signals offer some frequency diversity, i.e. it is unlikely that the signal will encounter severe multipath fading over its whole bandwidth, and in other cases the signal can be detected using e.g. a Rake receiver.
• Multiple access capability, known as code-division multiple access (CDMA) or code-division multiplexing (CDM). Multiple users can transmit simultaneously in the same frequency band as long as they use different spreading codes.

## Invention of frequency hopping

On March 17, 1903, Nicola Tesla was granted a patent for a system of frequency hopping between two or more channels to prevent communications being blocked. In 1908 Jonathan Zenneck wrote Wireless Telegraphy, which expanded on this concept. Starting in 1915, Zenneck's system was used by Germany to secure battle field communications.

Avant garde composer George Antheil and Golden Age actress Hedy Lamarr were granted US Patent 2,292,387 on August 11, 1942 for their Secret Communication System for use in radio guided torpedoes. Their approach was unique in that frequency coordination was done with paper player piano rolls - a novel approach which was never put in practice.

Spread spectrum of a modern switching power supply (heating up period) incl. waterfall diagram over a few minutes. Recorded with a NF-5030 EMC-Analyzer

Spread-spectrum clock generation (SSCG) is used in some synchronous digital systems, especially those containing microprocessors, to reduce the spectral density of the electromagnetic interference (EMI) that these systems generate. A synchronous digital system is one that is driven by a clock signal and, because of its periodic nature, has an unavoidably narrow frequency spectrum. In fact, a perfect clock signal would have all its energy concentrated at a single frequency (the desired clock frequency) and its harmonics. Practical synchronous digital systems radiate electromagnetic energy on a number of narrow bands spread on the clock frequency and its harmonics, resulting in a frequency spectrum that, at certain frequencies, can exceed the regulatory limits for electromagnetic interference (e.g. those of the FCC in the United States, JEITA in Japan and the IEC in Europe).

Spread-spectrum clocking avoids this problem by using one of the methods previously described to reduce the peak radiated energy and, therefore, its electromagnetic emissions and so comply with electromagnetic compatibility (EMC) regulations.

It has become a popular technique to gain regulatory approval because it requires only simple equipment modification. It is even more popular in portable electronics devices because of faster clock speeds and increasing integration of high-resolution LCD displays into ever smaller devices. Since these devices are designed to be lightweight and inexpensive, traditional passive, electronic measures to reduce EMI, such as capacitors or metal shielding, are not viable. Active EMI reduction techniques such as spread-spectrum clocking are needed in these cases.

However, spread-spectrum clocking, like other kinds of dynamic frequency change, can also create challenges for designers. Principal among these is clock/data misalignment, or clock skew.

Note that this method does not reduce total radiated energy, and therefore systems are not necessarily less likely to cause interference. Spreading energy over a larger bandwidth effectively reduces electrical and magnetic readings within narrow bandwidths. Typical measuring receivers used by EMC testing laboratories divide the electromagnetic spectrum into frequency bands approximately 120 kHz wide.[2] If the system under test were to radiate all its energy in a narrow bandwidth, it would register a large peak. Distributing this same energy into a larger bandwidth prevents systems from putting enough energy into any one narrowband to exceed the statutory limits. The usefulness of this method as a means to reduce real-life interference problems is often debated, since it is perceived that spread-spectrum clocking hides rather than resolves higher radiated energy issues by simple exploitation of loopholes in EMC legislation or certification procedures. This situation results in electronic equipment sensitive to narrow bandwidth(s) experiencing much less interference, while those with broadband sensitivity, or even operated at other frequencies (such as a radio receiver tuned to a different station), will experience more interference.

FCC certification testing is often completed with the spread-spectrum function enabled in order to reduce the measured emissions to within acceptable legal limits. However, the spread-spectrum functionality may be disabled by the user in some cases. As an example, in the area of personal computers, some BIOS writers include the ability to disable spread-spectrum clock generation as a user setting, thereby defeating the object of the EMI regulations. This might be considered a loophole, but is generally overlooked as long as spread-spectrum is enabled by default.

An ability to disable spread-spectrum clocking in computer systems is considered useful for overclocking, as spread spectrum can lower maximum clock speed achievable due to clock skew.

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## EARTH STATIONS

### Ground Station

WIKI

A ground station, earth station, or earth terminal is a terrestrial terminal station designed for extraplanetary telecommunication with spacecraft, or reception of radio waves from an astronomical radio source. Ground stations are located either on the surface of the Earth or in its atmosphere.[1] Earth stations communicate with spacecraft by transmitting and receiving radio waves in the super high frequency or extremely high frequency bands (e.g., microwaves). When a ground station successfully transmits radio waves to a spacecraft (or vice versa), it establishes a telecommunications link. A principal telecommunications device of the ground station is the parabolic antenna. Ground stations may have either a fixed or itinerant position. Article 1 § III of the ITU Radio Regulations describes various types of stationary and mobile ground stations, and their interrelationships.[2] Specialized satellite earth stations are used to telecommunicate with satellites—chiefly communications satellites. Other ground stat

# Ground station

The Raisting Satellite Earth Station is the largest satellite communications facility in Germany.

A ground station, earth station, or earth terminal is a terrestrial terminal station designed for extraplanetary telecommunication with spacecraft, or reception of radio waves from an astronomical radio source. Ground stations are located either on the surface of the Earth or in its atmosphere.[1] Earth stations communicate with spacecraft by transmitting and receiving radio waves in the super high frequency or extremely high frequency bands (e.g., microwaves). When a ground station successfully transmits radio waves to a spacecraft (or vice versa), it establishes a telecommunications link. A principal telecommunications device of the ground station is the parabolic antenna.

Ground stations may have either a fixed or itinerant position. Article 1 § III of the ITU Radio Regulations describes various types of stationary and mobile ground stations, and their interrelationships.[2]

Specialized satellite earth stations are used to telecommunicate with satellites—chiefly communications satellites. Other ground stations communicate with manned space stations or unmanned space probes. A ground station that primarily receives telemetry data, or that follows a satellite not in geostationary orbit, is called a tracking station.

When a satellite is within a ground station's line of sight, the station is said to have a view of the satellite. It is possible for a satellite to communicate with more than one ground station at a time. A pair of ground stations are said to have a satellite in mutual view when the stations share simultaneous, unobstructed, line-of-sight contact with the satellite.[3]

## Telecommunications port

A telecommunications port—or, more commonly, teleport—is a satellite ground station that functions as a hub connecting a satellite or geocentric orbital network with a terrestrial telecommunications network, such as the Internet.

Teleports may provide various broadcasting services among other telecommunications functions,[4] such as uploading computer programs or issuing commands over an uplink to a satellite.[5]

In May 1984, the Dallas/Fort Worth Teleport became the first American teleport to commence operation.[citation needed]

## Earth terminal complexes

In Federal Standard 1037C, the United States General Services Administration defined an earth terminal complex as the assemblage of equipment and facilities necessary to integrate an earth terminal (ground station) into a telecommunications network.[6][7] FS-1037C has since been subsumed by the ATIS Telecom Glossary, which is maintained by the Alliance for Telecommunications Industry Solutions, an international, business-oriented, non-governmental organization. The Telecommunications Industry Association also acknowledges this definition.

## Satellite communications standards

The ITU Radiocommunication Sector (ITU-R), a division of the International Telecommunication Union, codifies international standards agreed-upon through multinational discourse. From 1927 to 1932, standards and regulations now governed by the ITU-R were administered by the International Consultative Committee for Radio.

In addition to the body of standards defined by the ITU-R, each major satellite operator provides technical requirements and standards that ground stations must meet in order to communicate with the operator's satellites. For example, Intelsat publishes the Intelsat Earth Station Standards (IESS) which, among other things, classifies ground stations by the capabilities of their parabolic antennas, and pre-approves certain antenna models.[8] Eutelsat publishes similar standards and requirements, such as the Eutelsat Earth Station Standards (EESS).[9][10]

The Teleport (originally called a Telecommunications Satellite Park) innovation was conceived and developed by Joseph Milano in 1976 as part of a National Research Council study entitled, Telecommunications for Metropolitan Areas: Near-Term Needs and Opportunities."

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## LOW EARTH ORBIT AND GEO-STATIONARY SATELLITE SYSTEMS

### Geosynchrnous Satellite

WIKI

A geosynchronous satellite is a satellite in geosynchronous orbit, with an orbital period the same as the Earth's rotation period. Such a satellite returns to the same position in the sky after each sidereal day, and over the course of a day traces out a path in the sky that is typically some form of analemma. A special case of geosynchronous satellite is the geostationary satellite, which has a geostationary orbit – a circular geosynchronous orbit directly above the Earth's equator. Another type of geosynchronous orbit used by satellites is the Tundra elliptical orbit. Geosynchronous satellites have the advantage of remaining permanently in the same area of the sky, as viewed from a particular location on Earth, and so permanently within view of a given ground station. Geostationary satellites have the special property of remaining permanently fixed in exactly the same position in the sky, meaning that ground-based antennas do not need to track them but can remain fixed in one direction. Such satellites are

# Geosynchronous satellite

Satellites in geostationary orbit.

A geosynchronous satellite is a satellite in geosynchronous orbit, with an orbital period the same as the Earth's rotation period. Such a satellite returns to the same position in the sky after each sidereal day, and over the course of a day traces out a path in the sky that is typically some form of analemma. A special case of geosynchronous satellite is the geostationary satellite, which has a geostationary orbit – a circular geosynchronous orbit directly above the Earth's equator. Another type of geosynchronous orbit used by satellites is the Tundra elliptical orbit.

Geosynchronous satellites have the advantage of remaining permanently in the same area of the sky, as viewed from a particular location on Earth, and so permanently within view of a given ground station. Geostationary satellites have the special property of remaining permanently fixed in exactly the same position in the sky, meaning that ground-based antennas do not need to track them but can remain fixed in one direction. Such satellites are often used for communication purposes; a geosynchronous network is a communication network based on communication with or through geosynchronous satellites.

## Definition

The term "geosynchronous" refers to the satellite's orbital period being exactly one sidereal day which enables it to be synchronized with the rotation of the Earth ("geo-"). Along with this orbital period requirement, to be geostationary as well, the satellite must be placed in an orbit that puts it in the vicinity over the equator. These two requirements make the satellite appear in an unchanging area of visibility when viewed from the Earth's surface, enabling continuous operation from one point on the ground. The special case of a geostationary orbit is the most common type of orbit for communications satellites.

If a geosynchronous satellite's orbit is not exactly aligned with the Earth's equator, the orbit is known as an inclined orbit. It will appear (when viewed by someone on the ground) to oscillate daily around a fixed point. As the angle between the orbit and the equator decreases, the magnitude of this oscillation becomes smaller; when the orbit lies entirely over the equator in a circular orbit, the satellite remains stationary relative to the Earth's surface – it is said to be geostationary.

## Application

There are approximately 600 geosynchronous satellites some of which are not operational.[1]

A geostationary satellite above a marked spot on the Equator. An observer on the marked spot will see the satellite remain directly overhead unlike the other heavenly objects which sweep across the sky. This novel phenomenon, a straightforward consequence of Newton's theory of motion and gravity, is made possible by the fact that the earth spins.

Geostationary satellites appear to be fixed over one spot above the equator. Receiving and transmitting antennas on the earth do not need to track such a satellite. These antennas can be fixed in place and are much less expensive than tracking antennas. These satellites have revolutionized global communications, television broadcasting and weather forecasting, and have a number of important defense and intelligence applications.

One disadvantage of geostationary satellites is a result of their high altitude: radio signals take approximately 0.25 of a second to reach and return from the satellite, resulting in a small but significant signal delay. This delay increases the difficulty of telephone conversation and reduces the performance of common network protocols such as TCP/IP, but does not present a problem with non-interactive systems such as television broadcasts. There are a number of proprietary satellite data protocols that are designed to proxy TCP/IP connections over long-delay satellite links—these are marketed as being a partial solution to the poor performance of native TCP over satellite links. TCP presumes that all loss is due to congestion, not errors, and probes link capacity with its "slow-start" algorithm, which only sends packets once it is known that earlier packets have been received. Slow start is very slow over a path using a geostationary satellite.

Another disadvantage of geostationary satellites is the incomplete geographical coverage, since ground stations at higher than roughly 60 degrees latitude have difficulty reliably receiving signals at low elevations. Satellite dishes at such high latitudes would need to be pointed almost directly towards the horizon. The signals would have to pass through the largest amount of atmosphere, and could even be blocked by land topography, vegetation or buildings. In the USSR, a practical solution was developed for this problem with the creation of special Molniya / Orbita inclined path satellite networks with elliptical orbits. Similar elliptical orbits are used for the Sirius Radio satellites.

## History

The concept was first proposed by Herman Poto?nik in 1928 and popularised by the science fiction author Arthur C. Clarke in a paper in Wireless World in 1945.[2] Working prior to the advent of solid-state electronics, Clarke envisioned a trio of large, manned space stations arranged in a triangle around the planet. Modern satellites are numerous, unmanned, and often no larger than an automobile.

Widely known as the "father of the geosynchronous satellite", Harold Rosen, an engineer at Hughes Aircraft Company, invented the first operational geosynchronous satellite, Syncom 2.[3] It was launched on a Delta rocket B booster from Cape Canaveral July 26, 1963. A few months later Syncom 2 was used for the world's first satellite-relayed telephone call. It took place between United States President John F. Kennedy and Nigerian Prime minister Abubakar Tafawa Balewa.

The first geostationary communication satellite was Syncom 3, launched on August 19, 1964 with a Delta D launch vehicle from Cape Canaveral. The satellite, in orbit approximately above the International Date Line, was used to telecast the 1964 Summer Olympics in Tokyo to the United States. It was the first television program to cross the Pacific Ocean.

Westar 1 was America's first domestic and commercially launched geostationary communications satellite, launched by Western Union and NASA on April 13, 1974.

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## SATELLITE NAVIGATION & THE GLOBAL POSITIONING SYSTEM

WIKI

A satellite navigation or sat nav system is a system of satellites that provide autonomous geo-spatial positioning with global coverage. It allows small electronic receivers to determine their location (longitude, latitude, and altitude) to high precision (within a few metres) using time signals transmitted along a line of sight by radio from satellites. The signals also allow the electronic receivers to calculate the current local time to high precision, which allows time synchronisation. A satellite navigation system with global coverage may be termed a global navigation satellite system or GNSS. As of April 2013, only the United States NAVSTAR Global Positioning System (GPS) and the Russian GLONASS are global operational GNSSs. China is in the process of expanding its regional Beidou navigation system into the global Compass navigation system by 2020.[1] The European Union's Galileo positioning system is a GNSS in initial deployment phase, scheduled to be fully operational by 2020 at the earliest.[2] Franc

A satellite navigation or sat nav system is a system of satellites that provide autonomous geo-spatial positioning with global coverage. It allows small electronic receivers to determine their location (longitude, latitude, and altitude) to high precision (within a few metres) using time signals transmitted along a line of sight by radio from satellites. The signals also allow the electronic receivers to calculate the current local time to high precision, which allows time synchronisation. A satellite navigation system with global coverage may be termed a global navigation satellite system or GNSS.

As of April 2013, only the United States NAVSTAR Global Positioning System (GPS) and the Russian GLONASS are global operational GNSSs. China is in the process of expanding its regional Beidou navigation system into the global Compass navigation system by 2020.[1] The European Union's Galileo positioning system is a GNSS in initial deployment phase, scheduled to be fully operational by 2020 at the earliest.[2] France, India and Japan are in the process of developing regional navigation systems.

Global coverage for each system is generally achieved by a satellite constellation of 20–30 medium Earth orbit (MEO) satellites spread between several orbital planes. The actual systems vary, but use orbital inclinations of >50° and orbital periods of roughly twelve hours (at an altitude of about 20,000 kilometres (12,000 mi)).

## Classification

Satellite navigation systems that provide enhanced accuracy and integrity monitoring usable for civil navigation are classified as follows:[3]

• GNSS-2[citation needed] is the second generation of systems that independently provides a full civilian satellite navigation system, exemplified by the European Galileo positioning system. These systems will provide the accuracy and integrity monitoring necessary for civil navigation; including aircraft. This system consists of L1 and L2 frequencies for civil use and L5 for system integrity. Development is also in progress to provide GPS with civil use L2 and L5 frequencies, making it a GNSS-2 system.¹[citation needed]
• Core Satellite navigation systems, currently GPS (United States), GLONASS (Russian Federation), Galileo (European Union) and Compass (China).
• Global Satellite Based Augmentation Systems (SBAS) such as Omnistar and StarFire.
• Regional SBAS including WAAS (US), EGNOS (EU), MSAS (Japan) and GAGAN (India).
• Regional Satellite Navigation Systems such as China's Beidou, India's yet-to-be-operational IRNSS, and Japan's proposed QZSS.
• Continental scale Ground Based Augmentation Systems (GBAS) for example the Australian GRAS and the US Department of Transportation National Differential GPS (DGPS) service.
• Regional scale GBAS such as CORS networks.
• Local GBAS typified by a single GPS reference station operating Real Time Kinematic (RTK) corrections.

## History and theory

Early predecessors were the ground based DECCA, LORAN, GEE and Omega radio navigation systems, which used terrestrial longwave radio transmitters instead of satellites. These positioning systems broadcast a radio pulse from a known "master" location, followed by repeated pulses from a number of "slave" stations. The delay between the reception and sending of the signal at the slaves was carefully controlled, allowing the receivers to compare the delay between reception and the delay between sending. From this the distance to each of the slaves could be determined, providing a fix.

The first satellite navigation system was Transit, a system deployed by the US military in the 1960s. Transit's operation was based on the Doppler effect: the satellites traveled on well-known paths and broadcast their signals on a well known frequency. The received frequency will differ slightly from the broadcast frequency because of the movement of the satellite with respect to the receiver. By monitoring this frequency shift over a short time interval, the receiver can determine its location to one side or the other of the satellite, and several such measurements combined with a precise knowledge of the satellite's orbit can fix a particular position.

Part of an orbiting satellite's broadcast included its precise orbital data. In order to ensure accuracy, the US Naval Observatory (USNO) continuously observed the precise orbits of these satellites. As a satellite's orbit deviated, the USNO would send the updated information to the satellite. Subsequent broadcasts from an updated satellite would contain the most recent accurate information about its orbit.

Modern systems are more direct. The satellite broadcasts a signal that contains orbital data (from which the position of the satellite can be calculated) and the precise time the signal was transmitted. The orbital data is transmitted in a data message that is superimposed on a code that serves as a timing reference. The satellite uses an atomic clock to maintain synchronization of all the satellites in the constellation. The receiver compares the time of broadcast encoded in the transmission with the time of reception measured by an internal clock, thereby measuring the time-of-flight to the satellite. Several such measurements can be made at the same time to different satellites, allowing a continual fix to be generated in real time using an adapted version of trilateration: see GNSS positioning calculation for details.

Each distance measurement, regardless of the system being used, places the receiver on a spherical shell at the measured distance from the broadcaster. By taking several such measurements and then looking for a point where they meet, a fix is generated. However, in the case of fast-moving receivers, the position of the signal moves as signals are received from several satellites. In addition, the radio signals slow slightly as they pass through the ionosphere, and this slowing varies with the receiver's angle to the satellite, because that changes the distance through the ionosphere. The basic computation thus attempts to find the shortest directed line tangent to four oblate spherical shells centered on four satellites. Satellite navigation receivers reduce errors by using combinations of signals from multiple satellites and multiple correlators, and then using techniques such as Kalman filtering to combine the noisy, partial, and constantly changing data into a single estimate for position, time, and velocity.

## Civil and military uses

The original motivation for satellite navigation was for military applications. Satellite navigation allows for hitherto impossible precision in the delivery of weapons to targets, greatly increasing their lethality whilst reducing inadvertent casualties from mis-directed weapons. (See Guided bomb). Satellite navigation also allows forces to be directed and to locate themselves more easily, reducing the fog of war.

The ability to supply satellite navigation signals is also the ability to deny their availability. The operator of a satellite navigation system potentially has the ability to degrade or eliminate satellite navigation services over any territory it desires.

Comparison of GPS, GLONASS, Galileo and Compass (medium earth orbit) satellite navigation system orbits with the International Space Station, Hubble Space Telescope and Iridium constellation orbits, Geostationary Earth Orbit, and the nominal size of the Earth. [a] The Moon's orbit is around 9 times larger (in radius and length) than geostationary orbit. [b]
launched GNSS satellites 1978 to 2012

### Operational

#### GPS

The United States' Global Positioning System (GPS) consists of up to 32 medium Earth orbit satellites in six different orbital planes, with the exact number of satellites varying as older satellites are retired and replaced. Operational since 1978 and globally available since 1994, GPS is currently the world's most utilized satellite navigation system.

#### GLONASS

The formerly Soviet, and now Russian, Global'naya Navigatsionnaya Sputnikovaya Sistema (GLObal NAvigation Satellite System), or GLONASS, was a fully functional navigation constellation in 1995. After the collapse of the Soviet Union, it fell into disrepair, leading to gaps in coverage and only partial availability. It was recovered and fully restored in 2011.

### In development

#### Compass

China has indicated they intend to expand their regional navigation system, called Beidou or Big Dipper, into a global navigation system by 2020[1] a program that has been called Compass in China's official news agency Xinhua. The Compass system is proposed to utilize 30 medium Earth orbit satellites and five geostationary satellites. A 10-satellite regional version (covering Asia and Pacific area) was completed by December 2011.

#### Galileo

The European Union and European Space Agency agreed in March 2002 to introduce their own alternative to GPS, called the Galileo positioning system. At an estimated cost of EUR 3.0 billion,[4] the system of 30 MEO satellites was originally scheduled to be operational in 2010. The estimated year to become operational is 2014.[5] The first experimental satellite was launched on 28 December 2005[citation needed]. Galileo is expected to be compatible with the modernized GPS system. The receivers will be able to combine the signals from both Galileo and GPS satellites to greatly increase the accuracy. Galileo is now not expected to be in full service until 2020 at the earliest and at a substantially higher cost.[2]

### Comparison of systems

System GPS GLONASS COMPASS Galileo IRNSS
Political entity United States Russian Federation China European Union India
Coding CDMA FDMA/CDMA CDMA CDMA CDMA
Orbital height 20,180 km (12,540 mi) 19,130 km (11,890 mi) 21,150 km (13,140 mi) 23,220 km (14,430 mi) 36,000 km (22,000 mi)
Period 11.97 hours (11?h 58?m) 11.26 hours (11?h 16?m) 12.63 hours (12?h 38?m) 14.08 hours (14?h 5?m) N/A
Evolution
per sidereal day
2 17/8 17/10 17/10 N/A (geostationary)
Number of
satellites
At least 24 31, including
24 operational
1 in preparation
2 on maintenance
3 reserve
1 on tests[6]
5 geostationary orbit (GEO) satellites,
30 medium Earth orbit (MEO) satellites
4 test bed satellites in orbit,
22 operational satellites budgeted
7 geostationary orbit (GEO) satellites
Frequency 1.57542 GHz (L1 signal)
1.2276 GHz (L2 signal)
Around 1.602 GHz (SP)
Around 1.246 GHz (SP)
1.561098 GHz (B1)
1.589742 GHz (B1-2)
1.20714 GHz (B2)
1.26852 GHz (B3)
1.164–1.215 GHz (E5a and E5b)
1.260–1.300 GHz (E6)
1.559–1.592 GHz (E2-L1-E11)
N/A
Status Operational Operational,
CDMA in preparation
15 satellites operational,
In preparation 1 satellite launched,

### Beidou 1

Chinese regional network to be expanded into the global Compass navigation system.

### DORIS

Doppler Orbitography and Radio-positioning Integrated by Satellite (DORIS) is a French precision navigation system.[7]

### IRNSS

The Indian Regional Navigational Satellite System (IRNSS) is an autonomous regional satellite navigation system being developed by Indian Space Research Organisation (ISRO) which would be under the total control of Indian government. The government approved the project in May 2006, with the intention of the system to be completed and implemented by 2014.[8] It will consist of a constellation of 7 navigational satellites.[9] All the 7 satellites will be placed in the Geostationary orbit (GEO) to have a larger signal footprint and lower number of satellites to map the region. It is intended to provide an all-weather absolute position accuracy of better than 7.6 meters throughout India and within a region extending approximately 1,500 km around it.[10] A goal of complete Indian control has been stated, with the space segment, ground segment and user receivers all being built in India.[11] The first satellite IRNSS-1A of the proposed constellation was launched on 1 July 2013 from Satish Dhawan Space Centre[12]

### QZSS

The Quasi-Zenith Satellite System (QZSS), is a proposed three-satellite regional time transfer system and enhancement for GPS covering Japan. The first demonstration satellite was launched in September 2010.[13]

## Augmentation

Examples of augmentation systems include the Wide Area Augmentation System, the European Geostationary Navigation Overlay Service, the Multi-functional Satellite Augmentation System, Differential GPS, and Inertial Navigation Systems.

## Low Earth orbit satellite phone networks

The two current operational low Earth orbit satellite phone networks are able to track transceiver units with accuracy of a few kilometers using doppler shift calculations from the satellite. The coordinates are sent back to the transceiver unit where they can be read using AT commands or a graphical user interface.[14][15] This can also be used by the gateway to enforce restrictions on geographically bound calling plans.

## Positioning calculation

X

YOU TUBE

### Global Positioning System

WIKI

The Global Positioning System (GPS) is a space-based satellite navigation system that provides location and time information in all weather conditions, anywhere on or near the Earth where there is an unobstructed line of sight to four or more GPS satellites.[1] The system provides critical capabilities to military, civil and commercial users around the world. It is maintained by the United States government and is freely accessible to anyone with a GPS receiver. The GPS project was developed in 1973 to overcome the limitations of previous navigation systems,[2] integrating ideas from several predecessors, including a number of classified engineering design studies from the 1960s. GPS was created and realized by the U.S. Department of Defense (DoD) and was originally run with 24 satellites. It became fully operational in 1994. Bradford Parkinson, Roger L. Easton, and Ivan A. Getting are credited with inventing it. Advances in technology and new demands on the existing system have now led to efforts to moderniz

# Global Positioning System

Artist's conception of GPS Block II-F satellite in Earth orbit.
GPS receivers are now integrated in many mobile phones.
U.S. Air Force Senior Airman runs through a checklist during Global Positioning System satellite operations.

The Global Positioning System (GPS) is a space-based satellite navigation system that provides location and time information in all weather conditions, anywhere on or near the Earth where there is an unobstructed line of sight to four or more GPS satellites.[1] The system provides critical capabilities to military, civil and commercial users around the world. It is maintained by the United States government and is freely accessible to anyone with a GPS receiver.

The GPS project was developed in 1973 to overcome the limitations of previous navigation systems,[2] integrating ideas from several predecessors, including a number of classified engineering design studies from the 1960s. GPS was created and realized by the U.S. Department of Defense (DoD) and was originally run with 24 satellites. It became fully operational in 1994. Bradford Parkinson, Roger L. Easton, and Ivan A. Getting are credited with inventing it.

Advances in technology and new demands on the existing system have now led to efforts to modernize the GPS system and implement the next generation of GPS III satellites and Next Generation Operational Control System (OCX).[3] Announcements from Vice President Al Gore and the White House in 1998 initiated these changes. In 2000, the U.S. Congress authorized the modernization effort, GPS III.

In addition to GPS, other systems are in use or under development. The Russian Global Navigation Satellite System (GLONASS) was developed contemporaneously with GPS, but suffered from incomplete coverage of the globe until the mid-2000s.[4] There are also the planned European Union Galileo positioning system, Chinese Compass navigation system, and Indian Regional Navigational Satellite System.

## History

The design of GPS is based partly on similar ground-based radio-navigation systems, such as LORAN and the Decca Navigator, developed in the early 1940s and used during World War II.

### Predecessors

In 1956, the German-American physicist Friedwardt Winterberg[5] proposed a test of general relativity (for time slowing in a strong gravitational field) using accurate atomic clocks placed in orbit inside artificial satellites. Without the use of general relativity to correct for time running more quickly by 38 microseconds per day in orbit, GPS would suffer gross malfunction.[6] Additional inspiration for GPS came when the Soviet Union launched the first man-made satellite, Sputnik, in 1957. Two American physicists, William Guier and George Weiffenbach, at Johns Hopkins's Applied Physics Laboratory (APL), decided to monitor Sputnik's radio transmissions.[7] Within hours they realized that, because of the Doppler effect, they could pinpoint where the satellite was along its orbit. The Director of the APL gave them access to their UNIVAC to do the heavy calculations required. The next spring, Frank McClure, the deputy director of the APL, asked Guier and Weiffenbach to investigate the inverse problem—pinpointing the user's location given that of the satellite. (The Navy was developing the submarine-launched Polaris missile, which required them to know the submarine's location.) This led them and APL to develop the Transit system.[8] In 1959, ARPA (renamed DARPA in 1972) also played a role in Transit.[9][10][11]

 Official logo for NAVSTAR GPS Emblem of the 50th Space Wing

The first satellite navigation system, Transit, used by the United States Navy, was first successfully tested in 1960.[12] It used a constellation of five satellites and could provide a navigational fix approximately once per hour. In 1967, the U.S. Navy developed the Timation satellite that proved the ability to place accurate clocks in space, a technology required by GPS. In the 1970s, the ground-based Omega Navigation System, based on phase comparison of signal transmission from pairs of stations,[13] became the first worldwide radio navigation system. Limitations of these systems drove the need for a more universal navigation solution with greater accuracy.

While there were wide needs for accurate navigation in military and civilian sectors, almost none of those was seen as justification for the billions of dollars it would cost in research, development, deployment, and operation for a constellation of navigation satellites. During the Cold War arms race, the nuclear threat to the existence of the United States was the one need that did justify this cost in the view of the United States Congress. This deterrent effect is why GPS was funded. It is also the reason for the ultra secrecy at that time. The nuclear triad consisted of the United States Navy's submarine-launched ballistic missiles (SLBMs) along with United States Air Force (USAF) strategic bombers and intercontinental ballistic missiles (ICBMs). Considered vital to the nuclear-deterrence posture, accurate determination of the SLBM launch position was a force multiplier.

Precise navigation would enable United States submarines to get an accurate fix of their positions before they launched their SLBMs.[14] The USAF, with two thirds of the nuclear triad, also had requirements for a more accurate and reliable navigation system. The Navy and Air Force were developing their own technologies in parallel to solve what was essentially the same problem. To increase the survivability of ICBMs, there was a proposal to use mobile launch platforms (such as Russian SS-24 and SS-25) and so the need to fix the launch position had similarity to the SLBM situation.

In 1960, the Air Force proposed a radio-navigation system called MOSAIC (MObile System for Accurate ICBM Control) that was essentially a 3-D LORAN. A follow-on study, Project 57, was worked in 1963 and it was "in this study that the GPS concept was born". That same year, the concept was pursued as Project 621B, which had "many of the attributes that you now see in GPS"[15] and promised increased accuracy for Air Force bombers as well as ICBMs. Updates from the Navy Transit system were too slow for the high speeds of Air Force operation. The Naval Research Laboratory continued advancements with their Timation (Time Navigation) satellites, first launched in 1967, and with the third one in 1974 carrying the first atomic clock into orbit.[16]

Another important predecessor to GPS came from a different branch of the United States military. In 1964, the United States Army orbited its first Sequential Collation of Range (SECOR) satellite used for geodetic surveying.[17] The SECOR system included three ground-based transmitters from known locations that would send signals to the satellite transponder in orbit. A fourth ground-based station, at an undetermined position, could then use those signals to fix its location precisely. The last SECOR satellite was launched in 1969.[18] Decades later, during the early years of GPS, civilian surveying became one of the first fields to make use of the new technology, because surveyors could reap benefits of signals from the less-than-complete GPS constellation years before it was declared operational. GPS can be thought of as an evolution of the SECOR system where the ground-based transmitters have been migrated into orbit.

### Development

With these parallel developments in the 1960s, it was realized that a superior system could be developed by synthesizing the best technologies from 621B, Transit, Timation, and SECOR in a multi-service program.

During Labor Day weekend in 1973, a meeting of about 12 military officers at the Pentagon discussed the creation of a Defense Navigation Satellite System (DNSS). It was at this meeting that "the real synthesis that became GPS was created." Later that year, the DNSS program was named Navstar, or Navigation System Using Timing and Ranging.[19] With the individual satellites being associated with the name Navstar (as with the predecessors Transit and Timation), a more fully encompassing name was used to identify the constellation of Navstar satellites, Navstar-GPS, which was later shortened simply to GPS.[20]

After Korean Air Lines Flight 007, a Boeing 747 carrying 269 people, was shot down in 1983 after straying into the USSR's prohibited airspace,[21] in the vicinity of Sakhalin and Moneron Islands, President Ronald Reagan issued a directive making GPS freely available for civilian use, once it was sufficiently developed, as a common good.[22] The first satellite was launched in 1989, and the 24th satellite was launched in 1994. The GPS program cost at this point, not including the cost of the user equipment, but including the costs of the satellite launches, has been estimated to be about USD\$5 billion (then-year dollars).[23] Roger L. Easton is widely credited as the primary inventor of GPS.

Initially, the highest quality signal was reserved for military use, and the signal available for civilian use was intentionally degraded (Selective Availability). This changed with President Bill Clinton ordering Selective Availability to be turned off at midnight May 1, 2000, improving the precision of civilian GPS from 100 meters (330 ft) to 20 meters (66 ft). The executive order signed in 1996 to turn off Selective Availability in 2000 was proposed by the U.S. Secretary of Defense, William Perry, because of the widespread growth of differential GPS services to improve civilian accuracy and eliminate the U.S. military advantage. Moreover, the U.S. military was actively developing technologies to deny GPS service to potential adversaries on a regional basis.[24]

Over the last decade, the U.S. has implemented several improvements to the GPS service, including new signals for civil use and increased accuracy and integrity for all users, all while maintaining compatibility with existing GPS equipment.

GPS modernization[25] has now become an ongoing initiative to upgrade the Global Positioning System with new capabilities to meet growing military, civil, and commercial needs. The program is being implemented through a series of satellite acquisitions, including GPS Block III and the Next Generation Operational Control System (OCX). The U.S. Government continues to improve the GPS space and ground segments to increase performance and accuracy.

GPS is owned and operated by the United States Government as a national resource. Department of Defense (DoD) is the steward of GPS. Interagency GPS Executive Board (IGEB) oversaw GPS policy matters from 1996 to 2004. After that the National Space-Based Positioning, Navigation and Timing Executive Committee was established by presidential directive in 2004 to advise and coordinate federal departments and agencies on matters concerning the GPS and related systems.[26] The executive committee is chaired jointly by the deputy secretaries of defense and transportation. Its membership includes equivalent-level officials from the departments of state, commerce, and homeland security, the joint chiefs of staff, and NASA. Components of the executive office of the president participate as observers to the executive committee, and the FCC chairman participates as a liaison.

The DoD is required by law to "maintain a Standard Positioning Service (as defined in the federal radio navigation plan and the standard positioning service signal specification) that will be available on a continuous, worldwide basis," and "develop measures to prevent hostile use of GPS and its augmentations without unduly disrupting or degrading civilian uses."

### Timeline and modernization

Summary of satellites [27]
Block Launch
Period
Satellite launches Currently in orbit
and healthy
Suc-
cess
Fail-
ure
In prep-
aration
Plan-
ned
I 1978–1985 10 1 0 0 0
II 1989–1990 9 0 0 0 0
IIA 1990–1997 19 0 0 0 9
IIR 1997–2004 12 1 0 0 12
IIR-M 2005–2009 8 0 0 0 7
IIF From 2010 3 0 10 0 3
IIIA From 2014 0 0 0 12 0
IIIB 0 0 0 8 0
IIIC 0 0 0 16 0
Total 61 2 10 36 31
(Last update: October 8, 2012)

PRN 01 from Block IIR-M is unhealthy
PRN 25 from Block IIA is unhealthy
PRN 32 from Block IIA is unhealthy
PRN 27 from Block IIA is unhealthy
[28] For a more complete list, see list of GPS satellite launches

• In 1972, the USAF Central Inertial Guidance Test Facility (Holloman AFB), conducted developmental flight tests of two prototype GPS receivers over White Sands Missile Range, using ground-based pseudo-satellites.[citation needed]
• In 1978, the first experimental Block-I GPS satellite was launched.
• In 1983, after Soviet interceptor aircraft shot down the civilian airliner KAL 007 that strayed into prohibited airspace because of navigational errors, killing all 269 people on board, U.S. President Ronald Reagan announced that GPS would be made available for civilian uses once it was completed,[29][30] although it had been previously published [in Navigation magazine] that the CA code (Coarse Acquisition code) would be available to civilian users.
• By 1985, ten more experimental Block-I satellites had been launched to validate the concept. Command & Control of these satellites had moved from Onizuka AFS, CA and turned over to the 2nd Satellite Control Squadron (2SCS) located at Falcon Air Force Station in Colorado Springs, Colorado.[31][32]
• On February 14, 1989, the first modern Block-II satellite was launched.
• The Gulf War from 1990 to 1991 was the first conflict in which GPS was widely used.[33]
• In 1992, the 2nd Space Wing, which originally managed the system, was inactivated and replaced by the 50th Space Wing.
• By December 1993, GPS achieved initial operational capability (IOC), indicating a full constellation (24 satellites) was available and providing the Standard Positioning Service (SPS).[34]
• Full Operational Capability (FOC) was declared by Air Force Space Command (AFSPC) in April 1995, signifying full availability of the military's secure Precise Positioning Service (PPS).[34]
• In 1996, recognizing the importance of GPS to civilian users as well as military users, U.S. President Bill Clinton issued a policy directive[35] declaring GPS to be a dual-use system and establishing an Interagency GPS Executive Board to manage it as a national asset.
• In 1998, United States Vice President Al Gore announced plans to upgrade GPS with two new civilian signals for enhanced user accuracy and reliability, particularly with respect to aviation safety and in 2000 the United States Congress authorized the effort, referring to it as GPS III.
• On May 2, 2000 "Selective Availability" was discontinued as a result of the 1996 executive order, allowing users to receive a non-degraded signal globally.
• In 2004, the United States Government signed an agreement with the European Community establishing cooperation related to GPS and Europe's planned Galileo system.
• In 2004, United States President George W. Bush updated the national policy and replaced the executive board with the National Executive Committee for Space-Based Positioning, Navigation, and Timing.[36]
• November 2004, Qualcomm announced successful tests of assisted GPS for mobile phones.[37]
• In 2005, the first modernized GPS satellite was launched and began transmitting a second civilian signal (L2C) for enhanced user performance.[38]
• On September 14, 2007, the aging mainframe-based Ground Segment Control System was transferred to the new Architecture Evolution Plan.[39]
• On May 19, 2009, the United States Government Accountability Office issued a report warning that some GPS satellites could fail as soon as 2010.[40]
• On May 21, 2009, the Air Force Space Command allayed fears of GPS failure saying "There's only a small risk we will not continue to exceed our performance standard."[41]
• On January 11, 2010, an update of ground control systems caused a software incompatibility with 8000 to 10000 military receivers manufactured by a division of Trimble Navigation Limited of Sunnyvale, Calif.[42]
• On February 25, 2010,[43] the U.S. Air Force awarded the contract to develop the GPS Next Generation Operational Control System (OCX) to improve accuracy and availability of GPS navigation signals, and serve as a critical part of GPS modernization.
• A GPS satellite was launched on May 28, 2010.[44] The oldest GPS satellite still in operation was launched on November 26, 1990, and became operational on December 10, 1990.[45]
• The GPS satellite, GPS IIF-2, was launched on July 16, 2011 at 06:41 GMT from Space Launch Complex 37B at the Cape Canaveral Air Force Station.[46]
• The GPS satellite, GPS IIF-3, was launched on October 4, 2012 at 12:10 GMT from Space Launch Complex 37B at the Cape Canaveral Air Force Station.[47]
• The GPS satellite, GPS IIF-4, was launched on May 15, 2013 at 21:38 GMT from Space Launch Complex 41 at the Cape Canaveral Air Force Station.[48]

### Awards

On February 10, 1993, the National Aeronautic Association selected the GPS Team as winners of the 1992 Robert J. Collier Trophy, the nation's most prestigious aviation award. This team combines researchers from the Naval Research Laboratory, the USAF, the Aerospace Corporation, Rockwell International Corporation, and IBM Federal Systems Company. The citation honors them "for the most significant development for safe and efficient navigation and surveillance of air and spacecraft since the introduction of radio navigation 50 years ago."

Two GPS developers received the National Academy of Engineering Charles Stark Draper Prize for 2003:

In 1998, GPS technology was inducted into the Space Foundation Space Technology Hall of Fame.[50]

Francis X. Kane (Col. USAF, ret.) was inducted into the U.S. Air Force Space and Missile Pioneers Hall of Fame at Lackland A.F.B., San Antonio, Texas, March 2, 2010 for his role in space technology development and the engineering design concept of GPS conducted as part of Project 621B.

On October 4, 2011, the International Astronautical Federation (IAF) awarded the Global Positioning System (GPS) its 60th Anniversary Award, nominated by IAF member, the American Institute for Aeronautics and Astronautics (AIAA). The IAF Honors and Awards Committee recognized the uniqueness of the GPS program and the exemplary role it has played in building international collaboration for the benefit of humanity.

## Basic concept of GPS

A GPS receiver calculates its position by precisely timing the signals sent by GPS satellites high above the Earth. Each satellite continually transmits messages that include

• the time the message was transmitted
• satellite position at time of message transmission

The receiver uses the messages it receives to determine the transit time of each message and computes the distance to each satellite using the speed of light. Each of these distances and satellites' locations defines a sphere. The receiver is on the surface of each of these spheres when the distances and the satellites' locations are correct. These distances and satellites' locations are used to compute the location of the receiver using the navigation equations. This location is then displayed, perhaps with a moving map display or latitude and longitude; elevation or altitude information may be included, based on height above the geoid (e.g. EGM96). Many GPS units show derived information such as direction and speed, calculated from position changes.

In typical GPS operation, four or more satellites must be visible to obtain an accurate result. Four sphere surfaces typically do not intersect. [a] Because of this, it can be said with confidence that when the navigation equations are solved to find an intersection, this solution gives the position of the receiver along with the difference between the time kept by the receiver's on-board clock and the true time-of-day, thereby eliminating the need for a very large, expensive, and power hungry clock. The very accurately computed time is used only for display or not at all in many GPS applications, which use only the location. A number of applications for GPS do make use of this cheap and highly accurate timing. These include time transfer, traffic signal timing, and synchronization of cell phone base stations.

Although four satellites are required for normal operation, fewer apply in special cases. If one variable is already known, a receiver can determine its position using only three satellites. For example, a ship or aircraft may have known elevation. Some GPS receivers may use additional clues or assumptions such as reusing the last known altitude, dead reckoning, inertial navigation, or including information from the vehicle computer, to give a (possibly degraded) position when fewer than four satellites are visible.[51][52][53]

## Structure

The current GPS consists of three major segments. These are the space segment (SS), a control segment (CS), and a user segment (US).[54] The U.S. Air Force develops, maintains, and operates the space and control segments. GPS satellites broadcast signals from space, and each GPS receiver uses these signals to calculate its three-dimensional location (latitude, longitude, and altitude) and the current time.[55]

The space segment is composed of 24 to 32 satellites in medium Earth orbit and also includes the payload adapters to the boosters required to launch them into orbit. The control segment is composed of a master control station, an alternate master control station, and a host of dedicated and shared ground antennas and monitor stations. The user segment is composed of hundreds of thousands of U.S. and allied military users of the secure GPS Precise Positioning Service, and tens of millions of civil, commercial, and scientific users of the Standard Positioning Service (see GPS navigation devices).

### Space segment

Unlaunched GPS block II-A satellite on display at the San Diego Air & Space Museum
A visual example of a 24 satellite GPS constellation in motion with the Earth rotating. Notice how the number of satellites in view from a given point on the Earth's surface, in this example at 45°N, changes with time.

The space segment (SS) is composed of the orbiting GPS satellites, or Space Vehicles (SV) in GPS parlance. The GPS design originally called for 24 SVs, eight each in three approximately circular orbits,[56] but this was modified to six orbital planes with four satellites each.[57] The six orbit planes have approximately 55° inclination (tilt relative to Earth's equator) and are separated by 60° right ascension of the ascending node (angle along the equator from a reference point to the orbit's intersection).[58] The orbital period is one-half a sidereal day, i.e., 11 hours and 58 minutes so that the satellites pass over the same locations[59] or almost the same locations[60] every day. The orbits are arranged so that at least six satellites are always within line of sight from almost everywhere on Earth's surface.[61] The result of this objective is that the four satellites are not evenly spaced (90 degrees) apart within each orbit. In general terms, the angular difference between satellites in each orbit is 30, 105, 120, and 105 degrees apart which sum to 360 degrees.

Orbiting at an altitude of approximately 20,200 km (12,600 mi); orbital radius of approximately 26,600 km (16,500 mi), each SV makes two complete orbits each sidereal day, repeating the same ground track each day.[62] This was very helpful during development because even with only four satellites, correct alignment means all four are visible from one spot for a few hours each day. For military operations, the ground track repeat can be used to ensure good coverage in combat zones.

As of December 2012,[63] there are 32 satellites in the GPS constellation. The additional satellites improve the precision of GPS receiver calculations by providing redundant measurements. With the increased number of satellites, the constellation was changed to a nonuniform arrangement. Such an arrangement was shown to improve reliability and availability of the system, relative to a uniform system, when multiple satellites fail.[64] About nine satellites are visible from any point on the ground at any one time (see animation at right), ensuring considerable redundancy over the minimum four satellites needed for a position.

### Control segment

Ground monitor station used from 1984 to 2007, on display at the Air Force Space & Missile Museum

The control segment is composed of

1. a master control station (MCS),
2. an alternate master control station,
3. four dedicated ground antennas and
4. six dedicated monitor stations

The MCS can also access U.S. Air Force Satellite Control Network (AFSCN) ground antennas (for additional command and control capability) and NGA (National Geospatial-Intelligence Agency) monitor stations. The flight paths of the satellites are tracked by dedicated U.S. Air Force monitoring stations in Hawaii, Kwajalein Atoll, Ascension Island, Diego Garcia, Colorado Springs, Colorado and Cape Canaveral, along with shared NGA monitor stations operated in England, Argentina, Ecuador, Bahrain, Australia and Washington DC.[65] The tracking information is sent to the Air Force Space Command MCS at Schriever Air Force Base 25 km (16 mi) ESE of Colorado Springs, which is operated by the 2nd Space Operations Squadron (2 SOPS) of the U.S. Air Force. Then 2 SOPS contacts each GPS satellite regularly with a navigational update using dedicated or shared (AFSCN) ground antennas (GPS dedicated ground antennas are located at Kwajalein, Ascension Island, Diego Garcia, and Cape Canaveral). These updates synchronize the atomic clocks on board the satellites to within a few nanoseconds of each other, and adjust the ephemeris of each satellite's internal orbital model. The updates are created by a Kalman filter that uses inputs from the ground monitoring stations, space weather information, and various other inputs.[66]

Satellite maneuvers are not precise by GPS standards. So to change the orbit of a satellite, the satellite must be marked unhealthy, so receivers will not use it in their calculation. Then the maneuver can be carried out, and the resulting orbit tracked from the ground. Then the new ephemeris is uploaded and the satellite marked healthy again.

The Operation Control Segment (OCS) currently serves as the control segment of record. It provides the operational capability that supports global GPS users and keeps the GPS system operational and performing within specification.

OCS successfully replaced the legacy 1970s-era mainframe computer at Schriever Air Force Base in September 2007. After installation, the system helped enable upgrades and provide a foundation for a new security architecture that supported the U.S. armed forces. OCS will continue to be the ground control system of record until the new segment, Next Generation GPS Operation Control System[3] (OCX), is fully developed and functional.

The new capabilities provided by OCX will be the cornerstone for revolutionizing GPS's mission capabilities, and enabling[67] Air Force Space Command to greatly enhance GPS operational services to U.S. combat forces, civil partners and myriad domestic and international users.

The GPS OCX program also will reduce cost, schedule and technical risk. It is designed to provide 50%[68] sustainment cost savings through efficient software architecture and Performance-Based Logistics. In addition, GPS OCX expected to cost millions less than the cost to upgrade OCS while providing four times the capability.

The GPS OCX program represents a critical part of GPS modernization and provides significant information assurance improvements over the current GPS OCS program.

• OCX will have the ability to control and manage GPS legacy satellites as well as the next generation of GPS III satellites, while enabling the full array of military signals.
• Built on a flexible architecture that can rapidly adapt to the changing needs of today's and future GPS users allowing immediate access to GPS data and constellations status through secure, accurate and reliable information.
• Empowers the warfighter with more secure, actionable and predictive information to enhance situational awareness.
• Enables new modernized signals (L1C, L2C, and L5) and has M-code capability, which the legacy system is unable to do.
• Provides significant information assurance improvements over the current program including detecting and preventing cyber attacks, while isolating, containing and operating during such attacks.
• Supports higher volume near real-time command and control capabilities and abilities.

On September 14, 2011,[69] the U.S. Air Force announced the completion of GPS OCX Preliminary Design Review and confirmed that the OCX program is ready for the next phase of development.

The GPS OCX program has achieved major milestones and is on track to support the GPS IIIA launch in May 2014.

### User segment

GPS receivers come in a variety of formats, from devices integrated into cars, phones, and watches, to dedicated devices such as these.

The user segment is composed of hundreds of thousands of U.S. and allied military users of the secure GPS Precise Positioning Service, and tens of millions of civil, commercial and scientific users of the Standard Positioning Service. In general, GPS receivers are composed of an antenna, tuned to the frequencies transmitted by the satellites, receiver-processors, and a highly stable clock (often a crystal oscillator). They may also include a display for providing location and speed information to the user. A receiver is often described by its number of channels: this signifies how many satellites it can monitor simultaneously. Originally limited to four or five, this has progressively increased over the years so that, as of 2007, receivers typically have between 12 and 20 channels.[b]

A typical OEM GPS receiver module measuring 15×17 mm.

GPS receivers may include an input for differential corrections, using the RTCM SC-104 format. This is typically in the form of an RS-232 port at 4,800 bit/s speed. Data is actually sent at a much lower rate, which limits the accuracy of the signal sent using RTCM.[citation needed] Receivers with internal DGPS receivers can outperform those using external RTCM data.[citation needed] As of 2006, even low-cost units commonly include Wide Area Augmentation System (WAAS) receivers.

A typical GPS receiver with integrated antenna.

Many GPS receivers can relay position data to a PC or other device using the NMEA 0183 protocol. Although this protocol is officially defined by the National Marine Electronics Association (NMEA),[70] references to this protocol have been compiled from public records, allowing open source tools like gpsd to read the protocol without violating intellectual property laws.[clarification needed] Other proprietary protocols exist as well, such as the SiRF and MTK protocols. Receivers can interface with other devices using methods including a serial connection, USB, or Bluetooth.

## Applications

While originally a military project, GPS is considered a dual-use technology, meaning it has significant military and civilian applications.

GPS has become a widely deployed and useful tool for commerce, scientific uses, tracking, and surveillance. GPS's accurate time facilitates everyday activities such as banking, mobile phone operations, and even the control of power grids by allowing well synchronized hand-off switching.[55]

### Civilian

This antenna is mounted on the roof of a hut containing a scientific experiment needing precise timing.

Many civilian applications use one or more of GPS's three basic components: absolute location, relative movement, and time transfer.

#### Restrictions on civilian use

The U.S. Government controls the export of some civilian receivers. All GPS receivers capable of functioning above 18 kilometres (11 mi) altitude and 515 metres per second (1,001 kn) or designed, modified for use with unmanned air vehicles like e.g. ballistic or cruise missile systems are classified as munitions (weapons) for which State Department export licenses are required.[73]

This rule applies even to otherwise purely civilian units that only receive the L1 frequency and the C/A (Coarse/Acquisition) code and cannot correct for Selective Availability (U.S. government discontinued SA on May 1, 2000, resulting in a much- improved autonomous GPS accuracy),[74] etc.

Disabling operation above these limits exempts the receiver from classification as a munition. Vendor interpretations differ. The rule refers to operation at both the target altitude and speed, but some receivers stop operating even when stationary. This has caused problems with some amateur radio balloon launches that regularly reach 30 kilometres (19 mi).

These limits only apply to units exported from (or which have components exported from) the USA – there is a growing trade in various components, including GPS units, supplied by other countries, which are expressly sold as ITAR-free.

### Military

Attaching a GPS guidance kit to a 'dumb' bomb, March 2003.

As of 2009, military applications of GPS include:

• Navigation: GPS allows soldiers to find objectives, even in the dark or in unfamiliar territory, and to coordinate troop and supply movement. In the United States armed forces, commanders use the Commanders Digital Assistant and lower ranks use the Soldier Digital Assistant.[75][76][77][78]
• Target tracking: Various military weapons systems use GPS to track potential ground and air targets before flagging them as hostile.[citation needed] These weapon systems pass target coordinates to precision-guided munitions to allow them to engage targets accurately. Military aircraft, particularly in air-to-ground roles, use GPS to find targets (for example, gun camera video from AH-1 Cobras in Iraq show GPS co-ordinates that can be viewed with specialized software).
• Missile and projectile guidance: GPS allows accurate targeting of various military weapons including ICBMs, cruise missiles, precision-guided munitions and Artillery projectiles. Embedded GPS receivers able to withstand accelerations of 12,000 g or about 118 km/s2 have been developed for use in 155 millimetres (6.1 in) howitzers.[79]
• Search and Rescue: Downed pilots can be located faster if their position is known.
• Reconnaissance: Patrol movement can be managed more closely.
• GPS satellites carry a set of nuclear detonation detectors consisting of an optical sensor (Y-sensor), an X-ray sensor, a dosimeter, and an electromagnetic pulse (EMP) sensor (W-sensor), that form a major portion of the United States Nuclear Detonation Detection System.[80][81] General William Shelton has stated that this feature may be dropped from future satellites in order to save money.[82]

## Communication

The navigational signals transmitted by GPS satellites encode a variety of information including satellite positions, the state of the internal clocks, and the health of the network. These signals are transmitted on two separate carrier frequencies that are common to all satellites in the network. Two different encodings are used: a public encoding that enables lower resolution navigation, and an encrypted encoding used by the U.S. military.

### Message format

GPS message format
Subframes Description
1 Satellite clock,
GPS time relationship
2–3 Ephemeris
(precise satellite orbit)
4–5 Almanac component
(satellite network synopsis,
error correction)

Each GPS satellite continuously broadcasts a navigation message on L1 C/A and L2 P/Y frequencies at a rate of 50 bits per second (see bitrate). Each complete message takes 750 seconds (12 1/2 minutes) to complete. The message structure has a basic format of a 1500-bit-long frame made up of five subframes, each subframe being 300 bits (6 seconds) long. Subframes 4 and 5 are subcommutated 25 times each, so that a complete data message requires the transmission of 25 full frames. Each subframe consists of ten words, each 30 bits long. Thus, with 300 bits in a subframe times 5 subframes in a frame times 25 frames in a message, each message is 37,500 bits long. At a transmission rate of 50 bit/s, this gives 750 seconds to transmit an entire almanac message. Each 30-second frame begins precisely on the minute or half-minute as indicated by the atomic clock on each satellite.[83]

The first subframe of each frame encodes the week number and the time within the week,[84] as well as the data about the health of the satellite. The second and the third subframes contain the ephemeris – the precise orbit for the satellite. The fourth and fifth subframes contain the almanac, which contains coarse orbit and status information for up to 32 satellites in the constellation as well as data related to error correction. Thus, in order to obtain an accurate satellite location from this transmitted message the receiver must demodulate the message from each satellite it includes in its solution for 18 to 30 seconds. In order to collect all the transmitted almanacs the receiver must demodulate the message for 732 to 750 seconds or 12 1/2 minutes.[85]

All satellites broadcast at the same frequencies. Signals are encoded using code division multiple access (CDMA) allowing messages from individual satellites to be distinguished from each other based on unique encodings for each satellite (that the receiver must be aware of). Two distinct types of CDMA encodings are used: the coarse/acquisition (C/A) code, which is accessible by the general public, and the precise (P(Y)) code, which is encrypted so that only the U.S. military can access it.[86]

The ephemeris is updated every 2 hours and is generally valid for 4 hours, with provisions for updates every 6 hours or longer in non-nominal conditions. The almanac is updated typically every 24 hours. Additionally, data for a few weeks following is uploaded in case of transmission updates that delay data upload.[citation needed]

Subframe # Page # Name Word # Bits Scale Signed
1 all Week Number 3 1–10 1:1 No
1 all CA or P On L2 3 11,12 1:1 No
1 all URA Index 3 13–16 1:1 No
1 all SV_Health 3 17–22 1:1 No
1 all IODC(MSB) 3 23,24 1:1 No
1 all L2Pdata flag 4 1 1:1 No
1 all ResW4 4 2–24 N/A N/A
1 all ResW5 5 1–24 N/A N/A
1 all ResW6 6 1–24 N/A N/A
1 all ResW7 7 1–16 N/A N/A
1 all TGD 7 17–24 2^-31 Yes
1 all IODC (LSB) 8 1–8 1:1 No
1 all TOC 8 9–24 2^4 No
1 all AF2 9 1–8 2^-55 Yes
1 all AF1 9 9–24 2^-43 Yes
1 all AF0 10 1–22 2^-31 Yes
Subframe # Page # Name Word # Bits Scale Signed
2 all IODE 3 1–8 1:1 No
2 all CRS 3 9–24 2^-5 Yes
2 all Delta N 4 1–16 2^-43 Yes
2 all M0 (MSB) 4 17–24 2^-31 Yes
2 all M0 (LSB) 5 1–24
2 all CUC 6 1–16 2^-29 Yes
2 all e (MSB) 6 17–24 2^-33 No
2 all e (LSB) 7 1–24
2 all CUS 8 1–16 2^-29 Yes
2 all root A (MSB) 8 17–24 2^-19 No
2 all root A (LSB) 9 1–24
2 all TOE 10 1–16 2^4 No
2 all FitInt 10 17 1:1 No
2 all AODO 10 18–22 900 No
Subframe # Page # Name Word # Bits Scale Signed
3 all CIC 3 1–16 2^-29 Yes
3 all Omega 0 (MSB) 3 17–24 2^-31 Yes
3 all Omega 0 (LSB) 4 1–24
3 all CIS 5 1–16 2^-29 Yes
3 all i0 (MSB) 5 17–24 2^-31 Yes
3 all i0 (LSB) 6 1–24
3 all CRC 7 1–16 2^-5 Yes
3 all Omega (MSB) 7 17–24 2^-31 Yes
3 all Omega (LSB) 8 1–24
3 all Omega Dot 9 1–24 2^-43 Yes
3 all IODE 10 1–8 1:1 No
3 all IDOT 10 9–22 2^-43 Yes

### Satellite frequencies

GPS frequency overview
Band Frequency Description
L1 1575.42 MHz Coarse-acquisition (C/A) and encrypted precision (P(Y)) codes, plus the L1 civilian (L1C) and military (M) codes on future Block III satellites.
L2 1227.60 MHz P(Y) code, plus the L2C and military codes on the Block IIR-M and newer satellites.
L3 1381.05 MHz Used for nuclear detonation (NUDET) detection.
L4 1379.913 MHz Being studied for additional ionospheric correction.[citation needed]
L5 1176.45 MHz Proposed for use as a civilian safety-of-life (SoL) signal.

All satellites broadcast at the same two frequencies, 1.57542 GHz (L1 signal) and 1.2276 GHz (L2 signal). The satellite network uses a CDMA spread-spectrum technique[citation needed] where the low-bitrate message data is encoded with a high-rate pseudo-random (PRN) sequence that is different for each satellite. The receiver must be aware of the PRN codes for each satellite to reconstruct the actual message data. The C/A code, for civilian use, transmits data at 1.023 million chips per second, whereas the P code, for U.S. military use, transmits at 10.23 million chips per second. The actual internal reference of the satellites is 10.22999999543 MHz to compensate for relativistic effects[87][88] that make observers on Earth perceive a different time reference with respect to the transmitters in orbit. The L1 carrier is modulated by both the C/A and P codes, while the L2 carrier is only modulated by the P code.[89] The P code can be encrypted as a so-called P(Y) code that is only available to military equipment with a proper decryption key. Both the C/A and P(Y) codes impart the precise time-of-day to the user.

The L3 signal at a frequency of 1.38105 GHz is used to transmit data from the satellites to ground stations. This data is used by the United States Nuclear Detonation (NUDET) Detection System (USNDS) to detect, locate, and report nuclear detonations (NUDETs) in the Earth's atmosphere and near space.[90] One usage is the enforcement of nuclear test ban treaties.

The L4 band at 1.379913 GHz is being studied for additional ionospheric correction.[citation needed]

The L5 frequency band at 1.17645 GHz was added in the process of GPS modernization. This frequency falls into an internationally protected range for aeronautical navigation, promising little or no interference under all circumstances. The first Block IIF satellite that provides this signal was launched in 2010.[91] The L5 consists of two carrier components that are in phase quadrature with each other. Each carrier component is bi-phase shift key (BPSK) modulated by a separate bit train. "L5, the third civil GPS signal, will eventually support safety-of-life applications for aviation and provide improved availability and accuracy."[92]

A conditional waiver has recently been granted to LightSquared to operate a terrestrial broadband service near the L1 band. Although LightSquared had applied for a license to operate in the 1525 to 1559 band as early as 2003 and it was put out for public comment, the FCC asked LightSquared to form a study group with the GPS community to test GPS receivers and identify issue that might arise due to the larger signal power from the LightSquared terrestrial network. The GPS community had not objected to the LightSquared (formerly MSV and SkyTerra) applications until November 2010, when LightSquared applied for a modification to its Ancillary Terrestrial Component (ATC) authorization. This filing (SAT-MOD-20101118-00239) amounted to a request to run several orders of magnitude more power in the same frequency band for terrestrial base stations, essentially repurposing what was supposed to be a "quiet neighborhood" for signals from space as the equivalent of a cellular network. Testing in the first half of 2011 has demonstrated that the impact of the lower 10 MHz of spectrum is minimal to GPS devices (less than 1% of the total GPS devices are affected). The upper 10 MHz intended for use by LightSquared may have some impact on GPS devices. There is some concern that this will seriously degrade the GPS signal for many consumer uses.[93][94] Aviation Week magazine reports that the latest testing (June 2011) confirms "significant jamming" of GPS by LightSquared's system.[95]

### Demodulation and decoding

Demodulating and Decoding GPS Satellite Signals using the Coarse/Acquisition Gold code.

Because all of the satellite signals are modulated onto the same L1 carrier frequency, the signals must be separated after demodulation. This is done by assigning each satellite a unique binary sequence known as a Gold code. The signals are decoded after demodulation using addition of the Gold codes corresponding to the satellites monitored by the receiver.[96][97]

If the almanac information has previously been acquired, the receiver picks the satellites to listen for by their PRNs, unique numbers in the range 1 through 32. If the almanac information is not in memory, the receiver enters a search mode until a lock is obtained on one of the satellites. To obtain a lock, it is necessary that there be an unobstructed line of sight from the receiver to the satellite. The receiver can then acquire the almanac and determine the satellites it should listen for. As it detects each satellite's signal, it identifies it by its distinct C/A code pattern. There can be a delay of up to 30 seconds before the first estimate of position because of the need to read the ephemeris data.

Processing of the navigation message enables the determination of the time of transmission and the satellite position at this time. For more information see Demodulation and Decoding, Advanced.

The receiver uses messages received from satellites to determine the satellite positions and time sent. The x, y, and z components of satellite position and the time sent are designated as [xi, yi, zi, ti] where the subscript i denotes the satellite and has the value 1, 2, ..., n, where $n \ge 4.$ When the time of message reception indicated by the on-board clock is $\, \tilde{t}_\text{r}$, the true reception time is $\, t_\text{r} = \tilde{t}_\text{r} + b$ where $\, b$ is receiver's clock bias (i.e., clock delay). The message's transit time is $\, \tilde{t}_\text{r} + b - t_i$. Assuming the message traveled at the speed of light, $\, c$, the distance traveled is $\, \left( \tilde{t}_\text{r} + b - t_i \right) c$. Knowing the distance from receiver to satellite and the satellite's position implies that the receiver is on the surface of a sphere centered at the satellite's position with radius equal to this distance. Thus the receiver is at or near the intersection of the surfaces of the four or more spheres. In the ideal case of no errors, the receiver is at the intersection of the surfaces of the spheres.

The clock error or bias, b, is the amount that the receiver's clock is off. The receiver has four unknowns, the three components of GPS receiver position and the clock bias [x, y, z, b]. The equations of the sphere surfaces are given by:

$(x-x_i)^2 + (y-y_i)^2 + (z-z_i)^2 = \bigl([ \tilde{t}_\text{r} + b - t_i]c\bigr)^2, \; i=1,2,\dots,n$

or in terms of pseudoranges, $p_i = \left ( \tilde{t}_\text{r} - t_i \right )c$, as

$p_i = \sqrt{(x-x_i)^2 + (y-y_i)^2 + (z-z_i)^2}- bc, \;i=1,2,...,n$ .

These equations can be solved by algebraic or numerical methods.

### Least squares method

When more than four satellites are available, the calculation can use the four best or more than four, considering number of channels, processing capability, and geometric dilution of precision (GDOP). Using more than four is an over-determined system of equations with no unique solution, which must be solved by a least-squares method.[98] Errors can be estimated through the residuals. With each combination of four or more satellites, a GDOP factor can be calculated, based on the relative sky directions of the satellites used.[99] The location is expressed in a specific coordinate system or as latitude and longitude, using the WGS 84 geodetic datum or a country-specific system.[100]

$\left( \hat{x},\hat{y},\hat{z},\hat{b} \right) = \underset{\left( x,y,z,b \right)}{\arg \min} \sum_i \left( \sqrt{(x-x_i)^2 + (y-y_i)^2 + (z-z_i)^2}- bc - p_i \right)^2$

### Bancroft's method

Bancroft's method involves an algebraic as opposed to numerical method and can be used for the case of four or more satellites.[101][102] Bancroft's method provides one or two solutions for the four unknowns. However when there are two solutions, only one of these two solutions will be a near earth sensible solution. When there are four satellites, we use the inverse of the B matrix in section 2 of.[102] If there are more than four satellites then we use the Generalized inverse (i.e. the pseudoinvers) of the B matrix since in this case the B matrix is no longer square.

## Error sources and analysis

GPS error analysis examines the sources of errors in GPS results and the expected size of those errors. GPS makes corrections for receiver clock errors and other effects but there are still residual errors which are not corrected. Sources of error include signal arrival time measurements, numerical calculations, atmospheric effects, ephemeris and clock data, multipath signals, and natural and artificial interference. The magnitude of the residual errors resulting from these sources is dependent on geometric dilution of precision.

Artificial errors may result from jamming devices and threaten ships and aircraft.[103]

## Accuracy enhancement and surveying

### Augmentation

Integrating external information into the calculation process can materially improve accuracy. Such augmentation systems are generally named or described based on how the information arrives. Some systems transmit additional error information (such as clock drift, ephemera, or ionospheric delay), others characterize prior errors, while a third group provides additional navigational or vehicle information.

Examples of augmentation systems include the Wide Area Augmentation System (WAAS), European Geostationary Navigation Overlay Service (EGNOS), Differential GPS, Inertial Navigation Systems (INS) and Assisted GPS.

### Precise monitoring

Accuracy can be improved through precise monitoring and measurement of existing GPS signals in additional or alternate ways.

The largest remaining error is usually the unpredictable delay through the ionosphere. The spacecraft broadcast ionospheric model parameters, but some errors remain. This is one reason GPS spacecraft transmit on at least two frequencies, L1 and L2. Ionospheric delay is a well-defined function of frequency and the total electron content (TEC) along the path, so measuring the arrival time difference between the frequencies determines TEC and thus the precise ionospheric delay at each frequency.

Military receivers can decode the P(Y) code transmitted on both L1 and L2. Without decryption keys, it is still possible to use a codeless technique to compare the P(Y) codes on L1 and L2 to gain much of the same error information. However, this technique is slow, so it is currently available only on specialized surveying equipment. In the future, additional civilian codes are expected to be transmitted on the L2 and L5 frequencies (see GPS modernization). Then all users will be able to perform dual-frequency measurements and directly compute ionospheric delay errors.

A second form of precise monitoring is called Carrier-Phase Enhancement (CPGPS). This corrects the error that arises because the pulse transition of the PRN is not instantaneous, and thus the correlation (satellite-receiver sequence matching) operation is imperfect. CPGPS uses the L1 carrier wave, which has a period of $\frac{1\,\mathrm{s}}{1575.42 \times 10^6} = 0.63475\,\mathrm{ns} \approx 1\, \mathrm{ns} \$, which is about one-thousandth of the C/A Gold code bit period of $\frac{1\, \mathrm{s}}{1023 \times 10^3} = 977.5 \, \mathrm{ns} \approx 1000 \, \mathrm{ns} \$, to act as an additional clock signal and resolve the uncertainty. The phase difference error in the normal GPS amounts to 2–3 metres (6.6–9.8 ft) of ambiguity. CPGPS working to within 1% of perfect transition reduces this error to 3 centimetres (1.2 in) of ambiguity. By eliminating this error source, CPGPS coupled with DGPS normally realizes between 20–30 centimetres (7.9–12 in) of absolute accuracy.

Relative Kinematic Positioning (RKP) is a third alternative for a precise GPS-based positioning system. In this approach, determination of range signal can be resolved to a precision of less than 10 centimetres (3.9 in). This is done by resolving the number of cycles that the signal is transmitted and received by the receiver by using a combination of differential GPS (DGPS) correction data, transmitting GPS signal phase information and ambiguity resolution techniques via statistical tests—possibly with processing in real-time (real-time kinematic positioning, RTK).

### Timekeeping

#### Leap seconds

While most clocks derive their time from Coordinated Universal Time (UTC), the atomic clocks on the satellites are set to GPS time (GPST; see the page of United States Naval Observatory). The difference is that GPS time is not corrected to match the rotation of the Earth, so it does not contain leap seconds or other corrections that are periodically added to UTC. GPS time was set to match UTC in 1980, but has since diverged. The lack of corrections means that GPS time remains at a constant offset with International Atomic Time (TAI) (TAI ? GPS = 19 seconds). Periodic corrections are performed to the on-board clocks to keep them synchronized with ground clocks.[104]

The GPS navigation message includes the difference between GPS time and UTC. As of July 2012, GPS time is 16 seconds ahead of UTC because of the leap second added to UTC June 30, 2012.[105] Receivers subtract this offset from GPS time to calculate UTC and specific timezone values. New GPS units may not show the correct UTC time until after receiving the UTC offset message. The GPS-UTC offset field can accommodate 255 leap seconds (eight bits).

#### Accuracy

GPS time is theoretically accurate to about 14 nanoseconds.[106] However, most receivers lose accuracy in the interpretation of the signals and are only accurate to 100 nanoseconds.[107][108]

#### Format

As opposed to the year, month, and day format of the Gregorian calendar, the GPS date is expressed as a week number and a seconds-into-week number. The week number is transmitted as a ten-bit field in the C/A and P(Y) navigation messages, and so it becomes zero again every 1,024 weeks (19.6 years). GPS week zero started at 00:00:00 UTC (00:00:19 TAI) on January 6, 1980, and the week number became zero again for the first time at 23:59:47 UTC on August 21, 1999 (00:00:19 TAI on August 22, 1999). To determine the current Gregorian date, a GPS receiver must be provided with the approximate date (to within 3,584 days) to correctly translate the GPS date signal. To address this concern the modernized GPS navigation message uses a 13-bit field that only repeats every 8,192 weeks (157 years), thus lasting until the year 2137 (157 years after GPS week zero).

### Carrier phase tracking (surveying)

Another method that is used in surveying applications is carrier phase tracking. The period of the carrier frequency multiplied by the speed of light gives the wavelength, which is about 0.19 meters for the L1 carrier. Accuracy within 1% of wavelength in detecting the leading edge reduces this component of pseudorange error to as little as 2 millimeters. This compares to 3 meters for the C/A code and 0.3 meters for the P code.

However, 2 millimeter accuracy requires measuring the total phase—the number of waves multiplied by the wavelength plus the fractional wavelength, which requires specially equipped receivers. This method has many surveying applications.

Triple differencing followed by numerical root finding, and a mathematical technique called least squares can estimate the position of one receiver given the position of another. First, compute the difference between satellites, then between receivers, and finally between epochs. Other orders of taking differences are equally valid. Detailed discussion of the errors is omitted.

The satellite carrier total phase can be measured with ambiguity as to the number of cycles. Let $\ \phi(r_i, s_j, t_k)$ denote the phase of the carrier of satellite j measured by receiver i at time $\ \ t_k$. This notation shows the meaning of the subscripts i, j, and k. The receiver (r), satellite (s), and time (t) come in alphabetical order as arguments of $\ \phi$ and to balance readability and conciseness, let $\ \phi_{i,j,k} = \phi(r_i, s_j, t_k)$ be a concise abbreviation. Also we define three functions, :$\ \Delta^r, \Delta^s, \Delta^t$, which return differences between receivers, satellites, and time points, respectively. Each function has variables with three subscripts as its arguments. These three functions are defined below. If $\ \alpha_{i,j,k}$ is a function of the three integer arguments, i, j, and k then it is a valid argument for the functions, :$\ \Delta^r, \Delta^s, \Delta^t$, with the values defined as

$\ \Delta^r(\alpha_{i,j,k}) = \alpha_{i+1,j,k} - \alpha_{i,j,k}$,
$\ \Delta^s(\alpha_{i,j,k}) = \alpha_{i,j+1,k} - \alpha_{i,j,k}$, and
$\ \Delta^t(\alpha_{i,j,k}) = \alpha_{i,j,k+1} - \alpha_{i,j,k}$ .

Also if $\ \alpha_{i,j,k}\ and\ \beta_{l,m,n}$ are valid arguments for the three functions and a and b are constants then $\ ( a\ \alpha_{i,j,k} + b\ \beta_{l,m,n} )$ is a valid argument with values defined as

$\ \Delta^r(a\ \alpha_{i,j,k} + b\ \beta_{l,m,n}) = a \ \Delta^r(\alpha_{i,j,k}) + b \ \Delta^r(\beta_{l,m,n})$,
$\ \Delta^s(a\ \alpha_{i,j,k} + b\ \beta_{l,m,n} )= a \ \Delta^s(\alpha_{i,j,k}) + b \ \Delta^s(\beta_{l,m,n})$, and
$\ \Delta^t(a\ \alpha_{i,j,k} + b\ \beta_{l,m,n} )= a \ \Delta^t(\alpha_{i,j,k}) + b \ \Delta^t(\beta_{l,m,n})$ .

Receiver clock errors can be approximately eliminated by differencing the phases measured from satellite 1 with that from satellite 2 at the same epoch.[109] This difference is designated as $\ \Delta^s(\phi_{1,1,1}) = \phi_{1,2,1} - \phi_{1,1,1}$

Double differencing[110] computes the difference of receiver 1's satellite difference from that of receiver 2. This approximately eliminates satellite clock errors. This double difference is:

\begin{align}\Delta^r(\Delta^s(\phi_{1,1,1}))\,&=\,\Delta^r(\phi_{1,2,1} - \phi_{1,1,1}) &=\,\Delta^r(\phi_{1,2,1}) - \Delta^r(\phi_{1,1,1}) &=\,(\phi_{2,2,1} - \phi_{1,2,1}) - (\phi_{2,1,1} - \phi_{1,1,1})\end{align}

Triple differencing[111] subtracts the receiver difference from time 1 from that of time 2. This eliminates the ambiguity associated with the integral number of wavelengths in carrier phase provided this ambiguity does not change with time. Thus the triple difference result eliminates practically all clock bias errors and the integer ambiguity. Atmospheric delay and satellite ephemeris errors have been significantly reduced. This triple difference is:

$\ \Delta^t(\Delta^r(\Delta^s(\phi_{1,1,1})))$

## Regulatory spectrum issues concerning GPS receivers

In the United States, GPS receivers are regulated under the Federal Communications Commission's (FCC) Part 15 rules. As indicated in the manuals of GPS-enabled devices sold in the United States, as a Part 15 device, it "must accept any interference received, including interference that may cause undesired operation."[114] With respect to GPS devices in particular, the FCC states that GPS receiver manufacturers, "must use receivers that reasonably discriminate against reception of signals outside their allocated spectrum."[115]

The spectrum allocated for GPS L1 use by the FCC is 1559 to 1610 MHz.[116] Since 1996, the FCC has authorized licensed use of the spectrum neighboring the GPS band of 1525 to 1559 MHz to the Virginia company LightSquared. On March 1, 2001, the FCC received an application from LightSquared's predecessor, Motient Services to use their allocated frequencies for an integrated satellite-terrestrial service.[117] In 2002, the U.S. GPS Industry Council came to an out-of-band-emissions (OOBE) agreement with LightSquared to prevent transmissions from LightSquared's ground-based stations from emitting transmissions into the neighboring GPS band of 1559 to 1610 MHz.[118] In 2004, the FCC adopted the OOBE agreement in its authorization for LightSquared to deploy a ground-based network that used its allocated frequencies of 1525 to 1559 MHz.[119] This authorization was reviewed and approved by the U.S. Interdepartment Radio Advisory Committee, which includes the U.S. Department of Agriculture, U.S. Air Force, U.S. Army, U.S. Coast Guard, Federal Aviation Administration, National Aeronautics and Space Administration, Interior, and U.S. Department of Transportation.[120]

In January 2011, the FCC conditionally authorized LightSquared's wholesale customers, such as Best Buy, Sharp, and C Spire, to be able to only purchase an integrated satellite-ground-based service from LightSquared and re-sell that integrated service on devices that are equipped to only use the ground-based signal using LightSquared's allocated frequencies of 1525 to 1559 MHz.[121] In December 2010, GPS receiver manufacturers expressed concerns to the FCC that LightSquared's signal would interfere with GPS receiver devices[122] although the FCC's policy considerations leading up to the January 2011 order did not pertain to any proposed changes to the maximum number of ground-based LightSquared stations or the maximum power at which these stations could operate. The January 2011 order makes final authorization contingent upon studies of GPS interference issues carried out by a LightSquared led working group along with GPS industry and Federal agency participation.

GPS receiver manufacturers design GPS receivers to use spectrum beyond the GPS-allocated band. In some cases, GPS receivers are designed to use up to 400 MHz of spectrum in either direction of the L1 frequency of 1575.42 MHz.[123] However, as regulated under the FCC's Part 15 rules, GPS receivers are not warranted protection from signals outside GPS-allocated spectrum.[115]

The FCC adopted rules in February 2003 that allowed Mobile Satellite Service (MSS) licensees such as LightSquared to construct ground-based towers in their licensed spectrum to "promote more efficient use of terrestrial wireless spectrum."[124] In July 2010, the FCC stated that it expected LightSquared to use its authority to offer an integrated satellite-terrestrial service to "provide mobile broadband services similar to those provided by terrestrial mobile providers and enhance competition in the mobile broadband sector."[125] However, GPS receiver manufacturers have argued that LightSquared's licensed spectrum of 1525 to 1559 MHz was never envisioned as being used for high-speed wireless broadband although there is no regulatory or legal backing of this claim.[126] To build public support of efforts to reverse the 2004 FCC authorization of LightSquared's network, GPS receiver manufacturer Trimble Navigation Ltd. formed the "Coalition To Save Our GPS."[127]

The FCC and LightSquared have each made public commitments to solve the GPS interference issue before the network is allowed to operate.[128][129] However, according to Chris Dancy of the Aircraft Owners and Pilots Association, airline pilots with the type of systems that would be affected "may go off course and not even realize it."[130] The problems could also affect the Federal Aviation Administration upgrade to the air traffic control system, United States Defense Department guidance, and local emergency services including 911.[130]

On February 14, 2012, the U.S. Federal Communications Commission (FCC) moved to bar LightSquared's planned national broadband network after being informed by the National Telecommunications and Information Administration (NTIA), the federal agency that coordinates spectrum uses for the military and other federal government entities, that "there is no practical way to mitigate potential interference at this time".[131][132] LightSquared is challenging the FCC's action.

## Other systems

Comparison of GPS, GLONASS, Galileo and Compass (medium earth orbit) satellite navigation system orbits with the International Space Station, Hubble Space Telescope and Iridium constellation orbits, Geostationary Earth Orbit, and the nominal size of the Earth. [c] The Moon's orbit is around 9 times larger (in radius and length) than geostationary orbit. [d]

Other satellite navigation systems in use or various states of development include:

• GLONASS – Russia's global navigation system. Fully operational worldwide.
• Galileo – a global system being developed by the European Union and other partner countries, planned to be operational by 2014 (and fully deployed by 2019)
• Beidou – People's Republic of China's regional system, currently limited to Asia and the West Pacific[133]
• COMPASS – People's Republic of China's global system, planned to be operational by 2020[134][135]
• IRNSS – India's regional navigation system, planned to be operational by 2014, covering India and Northern Indian Ocean[136]
• QZSS – Japanese regional system covering Asia and Oceania

X

YOU TUBE

### Gps Signals

WIKI

Global Positioning System (GPS) satellites broadcast microwave signals to enable GPS receivers on or near the Earth's surface to determine location and synchronized time. The GPS system itself is operated by the U.S. Department of Defense (DoD) for use by both the military and the general public. GPS signals include ranging signals, used to measure the distance to the satellite, and navigation messages. The navigation messages include ephemeris data, used to calculate the position of each satellite in orbit, and information about the time and status of the entire satellite constellation, called the almanac. The original GPS design contains two ranging codes: the Coarse/Acquisition (C/A) code, which is freely available to the public, and the restricted Precision (P) code, usually reserved for military applications. The C/A code is a 1,023 bit deterministic sequence called pseudorandom noise (also pseudorandom binary sequence) (PN or PRN code) which, when transmitted at 1.023 megabits per second (Mbit/s), repea

# GPS signals

Artist's conception of GPS Block II-F satellite in Earth orbit.

Global Positioning System (GPS) satellites broadcast microwave signals to enable GPS receivers on or near the Earth's surface to determine location and synchronized time. The GPS system itself is operated by the U.S. Department of Defense (DoD) for use by both the military and the general public.

GPS signals include ranging signals, used to measure the distance to the satellite, and navigation messages. The navigation messages include ephemeris data, used to calculate the position of each satellite in orbit, and information about the time and status of the entire satellite constellation, called the almanac.

## Basic GPS signals

The original GPS design contains two ranging codes: the Coarse/Acquisition (C/A) code, which is freely available to the public, and the restricted Precision (P) code, usually reserved for military applications.

### Coarse/Acquisition code

The C/A code is a 1,023 bit deterministic sequence called pseudorandom noise (also pseudorandom binary sequence) (PN or PRN code) which, when transmitted at 1.023 megabits per second (Mbit/s), repeats every millisecond. These sequences only match up, or strongly correlate, when they are exactly aligned. Each satellite transmits a unique PRN code, which does not correlate well with any other satellite's PRN code. In other words, the PRN codes are highly orthogonal to one another. This is a form of code division multiple access (CDMA), which allows the receiver to recognize multiple satellites on the same frequency.

### Precision code

The P-code is also a PRN; however, each satellite's P-code PRN code is 6.1871 × 1012 bits long (6,187,100,000,000 bits, ~720.213 gigabytes) and only repeats once a week (it is transmitted at 10.23 Mbit/s). The extreme length of the P-code increases its correlation gain and eliminates any range ambiguity within the Solar System. However, the code is so long and complex it was believed that a receiver could not directly acquire and synchronize with this signal alone. It was expected that the receiver would first lock onto the relatively simple C/A code and then, after obtaining the current time and approximate position, synchronize with the P-code.

Whereas the C/A PRNs are unique for each satellite, the P-code PRN is actually a small segment of a master P-code approximately 2.35 × 1014 bits in length (235,000,000,000,000 bits, ~26.716 terabytes) and each satellite repeatedly transmits its assigned segment of the master code.

To prevent unauthorized users from using or potentially interfering with the military signal through a process called spoofing, it was decided to encrypt the P-code. To that end the P-code was modulated with the W-code, a special encryption sequence, to generate the Y-code. The Y-code is what the satellites have been transmitting since the anti-spoofing module was set to the "on" state. The encrypted signal is referred to as the P(Y)-code.

The details of the W-code are kept secret, but it is known that it is applied to the P-code at approximately 500 kHz,[1] which is a slower rate than that of the P-code itself by a factor of approximately 20. This has allowed companies to develop semi-codeless approaches for tracking the P(Y) signal, without knowledge of the W-code itself.

GPS message format
Subframes Words Description
1 1–2 Telemetry and handover words
(TLM and HOW)
3–10 Satellite clock,
GPS time relationship
2/3 1–2 Telemetry and handover words
(TLM and HOW)
3–10 Ephemeris
(precise satellite orbit)
4/5 1–2 Telemetry and handover words
(TLM and HOW)
3–10 Almanac component
(satellite network synopsis,
error correction)

In addition to the PRN ranging codes, a receiver needs to know detailed information about each satellite's position and the network. The GPS design has this information modulated on top of both the C/A and P(Y) ranging codes at 50 bit/s and calls it the Navigation Message.

The navigation message is made up of three major components. The first part contains the GPS date and time, plus the satellite's status and an indication of its health. The second part contains orbital information called ephemeris data and allows the receiver to calculate the position of the satellite. The third part, called the almanac, contains information and status concerning all the satellites; their locations and PRN numbers.

Whereas ephemeris information is highly detailed and considered valid for no more than four hours, almanac information is more general and is considered valid for up to 180 days. The almanac assists the receiver in determining which satellites to search for, and once the receiver picks up each satellite's signal in turn, it then downloads the ephemeris data directly from that satellite. A position fix using any satellite can not be calculated until the receiver has an accurate and complete copy of that satellite's ephemeris data. If the signal from a satellite is lost while its ephemeris data is being acquired, the receiver must discard that data and start again.

The navigation message itself is constructed from a 1,500 bit frame, which is divided into five subframes of 300 bits each and transmitted at 50 bit/s. Each subframe, therefore, requires 6 seconds to transmit. Each subframe has the GPS time. Subframe 1 contains the GPS date (week number) and information to correct the satellite's time to GPS time, plus satellite status and health. Subframes 2 and 3 together contain the transmitting satellite's ephemeris data. Subframes 4 and 5 contain components of the almanac. Each frame contains only 1/25th of the total almanac; a receiver must process 25 whole frames worth of data to retrieve the entire 15,000 bit almanac message. At this rate, 12.5 minutes are required to receive the entire almanac from a single satellite.

The orbital position data, or ephemeris, from the navigation message is used to calculate precisely where the satellite was at the start of the message. A more sensitive receiver will potentially acquire the ephemeris data more quickly than a less sensitive receiver, especially in a noisy environment.[2]

Each subframe is divided into 10 words. It begins with a Telemetry Word (TLM), which enables the receiver to detect the beginning of a subframe and determine the receiver clock time at which the navigation subframe begins. The next word is the handover word (HOW), which gives the GPS time (actually the time when the first bit of the next subframe will be transmitted) and identifies the specific subframe within a complete frame.[3][4] The remaining eight words of the subframe contain the actual data specific to that subframe.

After a subframe has been read and interpreted, the time the next subframe was sent can be calculated through the use of the clock correction data and the HOW. The receiver knows the receiver clock time of when the beginning of the next subframe was received from detection of the Telemetry Word thereby enabling computation of the transit time and thus the pseudorange. The receiver is potentially capable of getting a new pseudorange measurement at the beginning of each subframe or every 6 seconds.

### Almanac

The almanac, provided in subframes 4 and 5 of the frames, consists of coarse orbit and status information for each satellite in the constellation, an ionospheric model, and information to relate GPS derived time to Coordinated Universal Time (UTC). Each frame contains a part of the almanac (in subframes 4 and 5) and the complete almanac is transmitted by each satellite in 25 frames total (requiring 12.5 minutes).[5] The almanac serves several purposes. The first is to assist in the acquisition of satellites at power-up by allowing the receiver to generate a list of visible satellites based on stored position and time, while an ephemeris from each satellite is needed to compute position fixes using that satellite. In older hardware, lack of an almanac in a new receiver would cause long delays before providing a valid position, because the search for each satellite was a slow process. Advances in hardware have made the acquisition process much faster, so not having an almanac is no longer an issue. The second purpose is for relating time derived from the GPS (called GPS time) to the international time standard of UTC. Finally, the almanac allows a single-frequency receiver to correct for ionospheric error by using a global ionospheric model. The corrections are not as accurate as augmentation systems like WAAS or dual-frequency receivers. However, it is often better than no correction, since ionospheric error is the largest error source for a single-frequency GPS receiver.

Satellite data is updated typically every 24 hours, with up to 60 days data loaded in case there is a disruption in the ability to make updates regularly. Typically the updates contain new ephemerides, with new almanacs uploaded less frequently. The Control Segment guarantees that during normal operations a new almanac will be uploaded at least every 6 days.

Satellites broadcast a new ephemeris every two hours. The ephemeris is generally valid for 4 hours, with provisions for updates every 4 hours or longer in non-nominal conditions. The time needed to acquire the ephemeris is becoming a significant element of the delay to first position fix, because as the hardware becomes more capable, the time to lock onto the satellite signals shrinks; however, the ephemeris data requires 18 to 36 seconds before it is received, due to the low data transmission rate.

### Frequency information

For the ranging codes and navigation message to travel from the satellite to the receiver, they must be modulated onto a carrier frequency. In the case of the original GPS design, two frequencies are utilized; one at 1575.42 MHz (10.23 MHz × 154) called L1; and a second at 1227.60 MHz (10.23 MHz × 120), called L2.

The C/A code is transmitted on the L1 frequency as a 1.023 MHz signal using a bi-phase shift keying (BPSK) modulation technique. The P(Y)-code is transmitted on both the L1 and L2 frequencies as a 10.23 MHz signal using the same BPSK modulation, however the P(Y)-code carrier is in quadrature with the C/A carrier (meaning it is 90° out of phase).

Besides redundancy and increased resistance to jamming, a critical benefit of having two frequencies transmitted from one satellite is the ability to measure directly, and therefore remove, the ionospheric delay error for that satellite. Without such a measurement, a GPS receiver must use a generic model or receive ionospheric corrections from another source (such as the Wide Area Augmentation System or EGNOS). Advances in the technology used on both the GPS satellites and the GPS receivers has made ionospheric delay the largest remaining source of error in the signal. A receiver capable of performing this measurement can be significantly more accurate and is typically referred to as a dual frequency receiver.

#### Demodulation and decoding

Demodulating and Decoding GPS Satellite Signals using the Coarse/Acquisition Gold code.

Since all of the satellite signals are modulated onto the same L1 carrier frequency, there is a need to separate the signals after demodulation. This is done by assigning each satellite a unique binary sequence known as a Gold code, and the signals are decoded, after demodulation, using modulo 2 addition of the Gold codes corresponding to satellites n1 through nk, where k is the number of channels in the GPS receiver and n1 through nk are the PRN identifiers of the satellites. Each satellite's PRN identifier is unique and in the range from 1 through 32.[6] The results of these modulo 2 additions are the 50 bit/s navigation messages from satellites n1 through nk. The Gold codes used in GPS are a sequence of 1,023 bits with a period of one millisecond. These Gold codes are highly mutually orthogonal, so that it is unlikely that one satellite signal will be misinterpreted as another. As well, the Gold codes have good auto-correlation properties.[7]

There are 1,025 different Gold codes of length 1,023 bits, but only 32 are used. These Gold codes are quite often referred to as pseudo random noise since they contain no data and are said to look like random sequences.[8] However, this may be misleading since they are actually deterministic sequences.

If the almanac information has previously been acquired, the receiver picks which satellites to listen for by their PRNs. If the almanac information is not in memory, the receiver enters a search mode and cycles through the PRN numbers until a lock is obtained on one of the satellites. To obtain a lock, it is necessary that there be an unobstructed line of sight from the receiver to the satellite. The receiver can then acquire the almanac and determine the satellites it should listen for. As it detects each satellite's signal, it identifies it by its distinct C/A code pattern.

The receiver uses the C/A Gold code with the same PRN number as the satellite to compute an offset, O, that generates the best correlation. The offset, O, is computed in a trial and error manner. The 1,023 bits of the satellite PRN signal are compared with the receiver PRN signal. If correlation is not achieved, the 1,023 bits of the receiver's internally generated PRN code are shifted by one bit relative to the satellite's PRN code and the signals are again compared. This process is repeated until correlation is achieved or all 1,023 possible cases have been tried.[9] If all 1,023 cases have been tried without achieving correlation, the frequency oscillator is offset to the next value and the process is repeated.

After a subframe has been read and interpreted, the time the next subframe was sent can be calculated through the use of the clock correction data and the HOW. The receiver knows the receiver clock time of when the beginning of the next subframe was received from detection of the Telemetry Word thereby enabling computation of the transit time and thus the pseudorange. The receiver is potentially capable of getting a new pseudorange measurement at the beginning of each subframe or every 6 seconds.

Then the orbital position data, or ephemeris, from the navigation message is used to calculate precisely where the satellite was at the start of the message. A more sensitive receiver will potentially acquire the ephemeris data more quickly than a less sensitive receiver, especially in a noisy environment.[2]

## Modernization and additional GPS signals

Having reached full operational capability on July 17, 1995[12] the GPS system had completed its original design goals. However, additional advances in technology and new demands on the existing system led to the effort to "modernize" the GPS system. Announcements from the Vice President and the White House in 1998 heralded the beginning of these changes and in 2000, the U.S. Congress reaffirmed the effort, referred to as GPS III.

The project involves new ground stations and new satellites, with additional navigation signals for both civilian and military users, and aims to improve the accuracy and availability for all users. A goal of 2013 has been established with incentives offered to the contractors if they can complete it by 2011.[dated info]

### General features

A visual example of the GPS constellation in motion with the Earth rotating. Notice how the number of satellites in view from a given point on the Earth's surface, in this example at 45°N, changes with time.

Modernized GPS civilian signals have two general improvements over their legacy counterparts: a dataless acquisition aid and forward error correction (FEC) coding of the NAV message.

A dataless acquisition aid is an additional signal, called a pilot carrier in some cases, broadcast alongside the data signal. This dataless signal is designed to be easier to acquire than the data encoded and, upon successful acquisition, can be used to acquire the data signal. This technique improves acquisition of the GPS signal and boosts power levels at the correlator.

The second advancement is to use forward error correction (FEC) coding on the NAV message itself. Due to the relatively slow transmission rate of NAV data (usually 50 bits per second), small interruptions can have potentially large impacts. Therefore, FEC on the NAV message is a significant improvement in overall signal robustness.

### L2C

One of the first announcements was the addition of a new civilian-use signal, to be transmitted on a frequency other than the L1 frequency used for the coarse/acquisition (C/A) signal. Ultimately, this became the L2C signal, so called because it is broadcast on the L2 frequency. Because it requires new hardware on board the satellite, it is only transmitted by the so-called Block IIR-M and later design satellites. The L2C signal is tasked with improving accuracy of navigation, providing an easy to track signal, and acting as a redundant signal in case of localized interference.

Unlike the C/A code, L2C contains two distinct PRN code sequences to provide ranging information; the Civilian Moderate length code (called CM), and the Civilian Long length code (called CL). The CM code is 10,230 bits long, repeating every 20 ms. The CL code is 767,250 bits long, repeating every 1500 ms. Each signal is transmitted at 511,500 bits per second (bit/s); however, they are multiplexed together to form a 1,023,000 bit/s signal.

CM is modulated with the CNAV Navigation Message (see below), whereas CL does not contain any modulated data and is called a dataless sequence. The long, dataless sequence provides for approximately 24 dB greater correlation (~250 times stronger) than L1 C/A-code.

When compared to the C/A signal, L2C has 2.7 dB greater data recovery and 0.7 dB greater carrier-tracking, although its transmission power is 2.3 dB weaker.

The CNAV data is an upgraded version of the original NAV navigation message. It contains higher precision representation and nominally more accurate data than the NAV data. The same type of information (Time, Status, Ephemeris, and Almanac) is still transmitted using the new CNAV format; however, instead of using a frame / subframe architecture, it features a new pseudo-packetized format made up of 12-second 300-bit message packets.

In CNAV, two out of every four packets are ephemeris data and at least one of every four packets will include clock data, but the design allows for a wide variety of packets to be transmitted. With a 32-satellite constellation, and the current requirements of what needs to be sent, less than 75% of the bandwidth is used. Only a small fraction of the available packet types have been defined; this enables the system to grow and incorporate advances.

There are many important changes in the new CNAV message:

• It uses forward error correction (FEC) in a rate 1/2 convolution code, so while the navigation message is 25 bit/s, a 50 bit/s signal is transmitted.
• The GPS week number is now represented as 13 bits, or 8192 weeks, and only repeats every 157.0 years, meaning the next return to zero won't occur until the year 2137. This is longer compared to the L1 NAV message's use of a 10-bit week number, which returns to zero every 19.6 years.
• There is a packet that contains a GPS-to-GNSS time offset. This allows for interoperability with other global time-transfer systems, such as Galileo and GLONASS, both of which are supported.
• The extra bandwidth enables the inclusion of a packet for differential correction, to be used in a similar manner to satellite based augmentation systems and which can be used to correct the L1 NAV clock data.
• Every packet contains an alert flag, to be set if the satellite data can not be trusted. This means users will know within 6 seconds if a satellite is no longer usable. Such rapid notification is important for safety-of-life applications, such as aviation.
• Finally, the system is designed to support 63 satellites, compared with 32 in the L1 NAV message.

#### L2C Frequency information

An immediate effect of having two civilian frequencies being transmitted is the civilian receivers can now directly measure the ionospheric error in the same way as dual frequency P(Y)-code receivers. However, if a user is utilizing the L2C signal alone, they can expect 65% more position uncertainty than with the L1 signal.[13]

### Military (M-code)

A major component of the modernization process is a new military signal. Called the Military code, or M-code, it was designed to further improve the anti-jamming and secure access of the military GPS signals.

Very little has been published about this new, restricted code. It contains a PRN code of unknown length transmitted at 5.115 MHz. Unlike the P(Y)-code, the M-code is designed to be autonomous, meaning that a user can calculate their position using only the M-code signal. From the P(Y)-code's original design, users had to first lock onto the C/A code and then transfer the lock to the P(Y)-code. Later, direct-acquisition techniques were developed that allowed some users to operate autonomously with the P(Y)-code.

A little more is known about the new navigation message, which is called MNAV. Similar to the new CNAV, this new MNAV is packeted instead of framed, allowing for very flexible data payloads. Also like CNAV it can utilize Forward Error Correction (FEC) and advanced error detection (such as a CRC).

#### M-code Frequency Information

The M-code is transmitted in the same L1 and L2 frequencies already in use by the previous military code, the P(Y)-code. The new signal is shaped to place most of its energy at the edges (away from the existing P(Y) and C/A carriers).

In a major departure from previous GPS designs, the M-code is intended to be broadcast from a high-gain directional antenna, in addition to a full-Earth antenna. This directional antenna's signal, called a spot beam, is intended to be aimed at a specific region (several hundred kilometers in diameter) and increase the local signal strength by 20 dB, or approximately 100 times stronger. A side effect of having two antennas is that the GPS satellite will appear to be two GPS satellites occupying the same position to those inside the spot beam. While the whole Earth M-code signal is available on the Block IIR-M satellites, the spot beam antennas will not be deployed until the Block III satellites are deployed, tentatively in 2013.

An interesting side effect of having each satellite transmit four separate signals is that the MNAV can potentially transmit four different data channels, offering increased data bandwidth.

The modulation method is binary offset carrier, using a 10.23 MHz subcarrier against the 5.115 MHz code. This signal will have an overall bandwidth of approximately 24 MHz, with significantly separated sideband lobes. The sidebands can be used to improve signal reception.

### L5, Safety of Life

Civilian, safety of life signal planned to be available with first GPS IIF launch (2010).[dated info]

Two PRN ranging codes are transmitted on L5: the in-phase code (denoted as the I5-code); and the quadrature-phase code (denoted as the Q5-code). Both codes are 10,230 bits long and transmitted at 10.23 MHz (1ms repetition). In addition, the I5 stream is modulated with a 10-bit Neuman-Hoffman code that is clocked at 1 kHz and the Q5-code is modulated with a 20-bit Neuman-Hoffman code that is also clocked at 1 kHz.

• Improves signal structure for enhanced performance
• Higher transmitted power than L1/L2 signal (~3 db, or twice as powerful)
• Wider bandwidth provides a 10× processing gain
• Longer spreading codes (10× longer than C/A)

The recently launched GPS IIR-M7 satellite transmits a demonstration of this signal.[14]

The L5 CNAV data includes SV ephemerides, system time, SV clock behavior data, status messages and time information, etc. The 50 bit/s data is coded in a rate 1/2 convolution coder. The resulting 100 symbols per second (sps) symbol stream is modulo-2 added to the I5-code only; the resultant bit-train is used to modulate the L5 in-phase (I5) carrier. This combined signal is called the L5 Data signal. The L5 quadrature-phase (Q5) carrier has no data and is called the L5 Pilot signal.

#### L5 Frequency information

Broadcast on the L5 frequency (1176.45 MHz, 10.23 MHz × 115), which is an aeronautical navigation band. The frequency was chosen so that the aviation community can manage interference to L5 more effectively than L2.[15]

### L1C

Civilian use signal, broadcast on the L1 frequency (1575.42 MHz), which contains the C/A signal used by all current GPS users. The L1C will be available with first Block III launch, scheduled for 2014.

The PRN codes are 10,230 bits long and transmitted at 1.023 Mbit/s. It uses both Pilot and Data carriers like L2C.

The modulation technique used is BOC(1,1) for the data signal and TMBOC for the pilot. The time multiplexed binary offset carrier (TMBOC) is BOC(1,1) for all except 4 of 33 cycles, when it switches to BOC(6,1). Of the total L1C signal power, 25% is allocated to the data and 75% to the pilot.[16]

• Implementation will provide C/A code to ensure backward compatibility
• Assured of 1.5 dB increase in minimum C/A code power to mitigate any noise floor increase
• Data-less signal component pilot carrier improves tracking
• Enables greater civil interoperability with Galileo L1

The L1C navigation message, called CNAV-2, is 1800 bits (including FEC) and is transmitted at 100 bit/s. It contains 9 bits of time information, 600 bits of ephemeris data, and 274 bits of packetized data payload.

## Frequencies used by GPS

GPS Frequencies
Band Frequency
(MHz)
Phase Original Usage Modernized Usage
L1 1575.42
(10.23×154)
In-Phase (I) Encrypted Precision P(Y) code
Phase (Q)
Coarse-acquisition (C/A) code C/A, L1 Civilian (L1C), and
Military (M) code
L2 1227.60
(10.23×120)
In-Phase (I) Encrypted Precision P(Y) code
Phase (Q)
Unmodulated carrier L2 Civilian (L2C) code and
Military (M) code
L3 1381.05
(10.23×135)
Used by Nuclear Detonation (NUDET)
signals nuclear detonations/
high-energy infrared events.
Used to enforce nuclear test
ban treaties.
L4 1379.913
(10.23×1214/9)
(No transmission) Being studied for additional
ionospheric correction
L5 1176.45
(10.23×115)
In-Phase (I) (No transmission) Safety-of-Life (SoL) Data signal
Phase (Q)
Safety-of-Life (SoL) Pilot signal

All satellites broadcast at the same two frequencies, 1.57542 GHz (L1 signal) and 1.2276 GHz (L2 signal). The satellite network uses a CDMA spread-spectrum technique where the low-bitrate message data is encoded with a high-rate pseudo-random (PRN) sequence that is different for each satellite. The receiver must be aware of the PRN codes for each satellite to reconstruct the actual message data. The C/A code, for civilian use, transmits data at 1.023 million chips per second, whereas the P code, for U.S. military use, transmits at 10.23 million chips per second. The L1 carrier is modulated by both the C/A and P codes, while the L2 carrier is only modulated by the P code.[17] The P code can be encrypted as a so-called P(Y) code which is only available to military equipment with a proper decryption key. Both the C/A and P(Y) codes impart the precise time-of-day to the user.

Each composite signal (in-phase and quadrature phase) becomes:

$S(t) = \sqrt{P_\text{I}} X_\text{I} (t) \cos (\omega t + \phi_0) \underbrace{{} - \sqrt{P_\text{Q}} X_\text{Q} (t) \sin (\omega t + \phi_0)}_{+ \sqrt{P_\text{Q}} X_\text{Q} (t) \cos\left(\omega t + \phi_0 + \frac{\pi}{2}\right)} ,$

where $\scriptstyle\ P_\text{I}\,$ and $\scriptstyle\ P_\text{Q}\,$ represent signal powers; $\scriptstyle\ X_\text{I}(t)\,$ and $\scriptstyle\ X_\text{Q}(t)\,$ represent codes with/without data $(\scriptstyle\ = \pm 1)\,$.

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In addition to the PRN ranging codes, a receiver needs to know detailed information about each satellite's position and the network. The GPS design has this information modulated on top of both the C/A and P(Y) ranging codes at 50 bit/s and calls it the Navigation Message.

The navigation message is made up of three major components. The first part contains the GPS date and time, plus the satellite's status and an indication of its health. The second part contains orbital information called ephemeris data and allows the receiver to calculate the position of the satellite. The third part, called the almanac, contains information and status concerning all the satellites; their locations and PRN numbers.

Whereas ephemeris information is highly detailed and considered valid for no more than four hours, almanac information is more general and is considered valid for up to 180 days. The almanac assists the receiver in determining which satellites to search for, and once the receiver picks up each satellite's signal in turn, it then downloads the ephemeris data directly from that satellite. A position fix using any satellite can not be calculated until the receiver has an accurate and complete copy of that satellite's ephemeris data. If the signal from a satellite is lost while its ephemeris data is being acquired, the receiver must discard that data and start again.

The navigation message itself is constructed from a 1,500 bit frame, which is divided into five subframes of 300 bits each and transmitted at 50 bit/s. Each subframe, therefore, requires 6 seconds to transmit. Each subframe has the GPS time. Subframe 1 contains the GPS date (week number) and information to correct the satellite's time to GPS time, plus satellite status and health. Subframes 2 and 3 together contain the transmitting satellite's ephemeris data. Subframes 4 and 5 contain components of the almanac. Each frame contains only 1/25th of the total almanac; a receiver must process 25 whole frames worth of data to retrieve the entire 15,000 bit almanac message. At this rate, 12.5 minutes are required to receive the entire almanac from a single satellite.

The orbital position data, or ephemeris, from the navigation message is used to calculate precisely where the satellite was at the start of the message. A more sensitive receiver will potentially acquire the ephemeris data more quickly than a less sensitive receiver, especially in a noisy environment.[2]

Each subframe is divided into 10 words. It begins with a Telemetry Word (TLM), which enables the receiver to detect the beginning of a subframe and determine the receiver clock time at which the navigation subframe begins. The next word is the handover word (HOW), which gives the GPS time (actually the time when the first bit of the next subframe will be transmitted) and identifies the specific subframe within a complete frame.[3][4] The remaining eight words of the subframe contain the actual data specific to that subframe.

After a subframe has been read and interpreted, the time the next subframe was sent can be calculated through the use of the clock correction data and the HOW. The receiver knows the receiver clock time of when the beginning of the next subframe was received from detection of the Telemetry Word thereby enabling computation of the transit time and thus the pseudorange. The receiver is potentially capable of getting a new pseudorange measurement at the beginning of each subframe or every 6 seconds.

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### Differential Gps

WIKI

Differential Global Positioning System (DGPS) is an enhancement to Global Positioning System that provides improved location accuracy, from the 15-meter nominal GPS accuracy to about 10 cm in case of the best implementations. DGPS uses a network of fixed, ground-based reference stations to broadcast the difference between the positions indicated by the satellite systems and the known fixed positions. These stations broadcast the difference between the measured satellite pseudoranges and actual (internally computed) pseudoranges, and receiver stations may correct their pseudoranges by the same amount. The digital correction signal is typically broadcast locally over ground-based transmitters of shorter range. The term refers to a general technique of augmentation. The United States Coast Guard (USCG) and Canadian Coast Guard (CCG) each run such systems in the U.S. and Canada on the longwave radio frequencies between 285 kHz and 325 kHz near major waterways and harbors. The USCG's DGPS system has been named NDG

# Differential GPS

Transportable DGPS reference station Baseline HD by CLAAS for use in satellite-assisted steering systems in modern agriculture

Differential Global Positioning System (DGPS) is an enhancement to Global Positioning System that provides improved location accuracy, from the 15-meter nominal GPS accuracy to about 10 cm in case of the best implementations.

DGPS uses a network of fixed, ground-based reference stations to broadcast the difference between the positions indicated by the satellite systems and the known fixed positions. These stations broadcast the difference between the measured satellite pseudoranges and actual (internally computed) pseudoranges, and receiver stations may correct their pseudoranges by the same amount. The digital correction signal is typically broadcast locally over ground-based transmitters of shorter range.

The term refers to a general technique of augmentation. The United States Coast Guard (USCG) and Canadian Coast Guard (CCG) each run such systems in the U.S. and Canada on the longwave radio frequencies between 285 kHz and 325 kHz near major waterways and harbors. The USCG's DGPS system has been named NDGPS (National DGPS) and is now jointly administered by the Coast Guard and the U.S. Department of Transportation’s Federal Highway Administration. It consists of broadcast sites located throughout the inland and coastal portions of the United States including Alaska, Hawaii and Puerto Rico.[1]

A similar system that transmits corrections from orbiting satellites instead of ground-based transmitters is called a Wide-Area DGPS (WADGPS)[2] or Satellite Based Augmentation System.

## History

When GPS was first being put into service, the US military was concerned about the possibility of enemy forces using the globally available GPS signals to guide their own weapon systems. Originally, the government thought the "coarse acquisition" (C/A) signal would only give about 100 meter accuracy, but with improved receiver designs, the actual accuracy was 20 to 30 meters.[3] Starting in March 1990,[4] to avoid providing such unexpected accuracy, the C/A signal transmitted on the L1 frequency (1575.42 MHz) was deliberately degraded by offsetting its clock signal by a random amount, equivalent to about 100 meters of distance. This technique, known as "Selective Availability", or SA for short, seriously degraded the usefulness of the GPS signal for non-military users. More accurate guidance was possible for users of dual frequency GPS receivers that also received the L2 frequency (1227.6 MHz), but the L2 transmission, intended for military use, was encrypted and was only available to authorised users with the encryption keys.

This presented a problem for civilian users who relied upon ground-based radio navigation systems such as LORAN, VOR and NDB systems costing millions of dollars each year to maintain. The advent of a global navigation satellite system (GNSS) could provide greatly improved accuracy and performance at a fraction of the cost. The accuracy inherent in the S/A signal was however too poor to make this realistic. The military received multiple requests from the Federal Aviation Administration (FAA), United States Coast Guard (USCG) and United States Department of Transportation (DOT) to set S/A aside to enable civilian use of GNSS, but remained steadfast in its objection on grounds of security.

Through the early to mid 1980s, a number of agencies developed a solution to the SA "problem".[dubious ] Since the SA signal was changed slowly, the effect of its offset on positioning was relatively fixed – that is, if the offset was "100 meters to the east", that offset would be true over a relatively wide area. This suggested that broadcasting this offset to local GPS receivers could eliminate the effects of SA, resulting in measurements closer to GPS's theoretical performance, around 15 meters. Additionally, another major source of errors in a GPS fix is due to transmission delays in the ionosphere, which could also be measured and corrected for in the broadcast. This offered an improvement to about 5 meters accuracy, more than enough for most civilian needs.[1]

The US Coast Guard was one of the more aggressive proponents of the DGPS system, experimenting with the system on an ever-wider basis through the late 1980s and early 1990s. These signals are broadcast on marine longwave frequencies, which could be received on existing radiotelephones and fed into suitably equipped GPS receivers. Almost all major GPS vendors offered units with DGPS inputs, not only for the USCG signals, but also aviation units on either VHF or commercial AM radio bands.

They started sending out "production quality" DGPS signals on a limited basis in 1996, and rapidly expanded the network to cover most US ports of call, as well as the Saint Lawrence Seaway in partnership with the Canadian Coast Guard. Plans were put into place to expand the system across the US, but this would not be easy. The quality of the DGPS corrections generally fell with distance, and largest transmitters capable of covering large areas tend to cluster near cities. This meant that lower-population areas, notably in the midwest and Alaska, would have little coverage by ground-based GPS. As of January 2012 the USCG's national DGPS system comprises 86 broadcast sites which provide dual coverage to almost the entire US coastline and inland navigable waterways including Alaska, Hawaii, and Puerto Rico. In addition the system provides single or dual coverage to a majority of the inland portion of United States.[5] Instead, the FAA (and others) started studies for broadcasting the signals across the entire hemisphere from communications satellites in geostationary orbit. This has led to the Wide Area Augmentation System (WAAS) and similar systems, although these are generally not referred to as DGPS, or alternatively, "wide-area DGPS". WAAS offers accuracy similar to the USCG's ground-based DGPS networks, and there has been some argument that the latter will be turned off as WAAS becomes fully operational.

By the mid-1990s it was clear that the SA system was no longer useful in its intended role. DGPS would render it ineffective over the US, precisely where it was considered most needed. Additionally, experience during the Gulf War demonstrated that the widespread use of civilian receivers by U.S. forces meant that leaving SA turned on was thought to harm the U.S. more than if it were turned off.[6][citation needed] After many years of pressure, it took an executive order by President Bill Clinton to get SA turned off permanently in 2000.[7]

Nevertheless, by this point DGPS had evolved into a system for providing more accuracy than even a non-SA GPS signal could provide on its own. There are several other sources of error that share the same characteristics as SA in that they are the same over large areas and for "reasonable" amounts of time. These include the ionospheric effects mentioned earlier, as well as errors in the satellite position ephemeris data and clock drift on the satellites. Depending on the amount of data being sent in the DGPS correction signal, correcting for these effects can reduce the error significantly, the best implementations offering accuracies of under 10 cm.

In addition to continued deployments of the USCG and FAA sponsored systems, a number of vendors have created commercial DGPS services, selling their signal (or receivers for it) to users who require better accuracy than the nominal 15 meters GPS offers. Almost all commercial GPS units, even hand-held units, now offer DGPS data inputs, and many also support WAAS directly. To some degree, a form of DGPS is now a natural part of most GPS operations.

## Operation

A reference station calculates differential corrections for its own location and time. Users may be up to 200 nautical miles (370 km) from the station, however, and some of the compensated errors vary with space: specifically, satellite ephemeris errors and those introduced by ionospheric and tropospheric distortions. For this reason, the accuracy of DGPS decreases with distance from the reference station. The problem can be aggravated if the user and the station lack "inter visibility"—when they are unable to see the same satellites.

## Accuracy

The United States Federal Radionavigation Plan and the IALA Recommendation on the Performance and Monitoring of DGNSS Services in the Band 283.5–325 kHz cite the United States Department of Transportation's 1993 estimated error growth of 0.67 m per 100 km from the broadcast site[8] but measurements of accuracy across the Atlantic, in Portugal, suggest a degradation of just 0.22 m per 100 km.[9]

## Variations

DGPS can refer to any type of Ground Based Augmentation System (GBAS). There are many operational systems in use throughout the world, according to the US Coast Guard, 47 countries operate systems similar to the US NDGPS (Nationwide Differential Global Positioning System).

A list can be found at World DGPS Database for Dxers

### European DGPS Network

The European DGPS network has been mainly developed by the Finnish and Swedish maritime administrations in order to improve safety in the archipelago between the two countries.

In the UK and Ireland, the system was implemented as a maritime navigation aid to fill the gap left by the demise of the Decca Navigator System in 2000. With a network of 12 transmitters sited around the coastline and three control stations, it was set up in 1998 by the countries' respective General Lighthouse Authorities (GLA) — Trinity House covering England, Wales and the Channel Islands, the Northern Lighthouse Board covering Scotland and the Isle of Man and the Commissioners of Irish Lights, covering the whole of Ireland. Transmitting on the 300 kHz band, the system underwent testing and two additional transmitters were added before the system was declared operational in 2002.[10][11]

Effective Solutions (Data Products) - European Differential Beacon Transmitters - Details and map

### United States NDGPS

The United States Department of Transportation, in conjunction with the Federal Highway Administration, the Federal Railroad Administration and the National Geodetic Survey appointed the Coast Guard as the maintaining agency for the U.S. Nationwide DGPS network (NDGPS). The system is an expansion of the previous Maritime Differential GPS (MDGPS), which the Coast Guard began in the late 1980s and completed in March 1999. MDGPS only covered coastal waters, the Great Lakes, and the Mississippi River inland waterways, while NDGPS expands this to include complete coverage of the continental United States.[12] The centralized Command and Control unit is the USCG Navigation Center, based in Alexandria, VA.[13] There are currently 86 NDGPS sites in the US network, and there are plans for up to 128 total sites to be online within the next 15 years.[citation needed]

The Canadian system is similar to the US system and is primarily for maritime usage covering the Atlantic and Pacific coast as well as the Great Lakes and Saint Lawrence Seaway.

### Australia

Australia runs three DGPS systems: one is mainly for marine navigation, broadcasting its signal on the longwave band;[14] another is used for land surveys and land navigation, and has corrections broadcast on the Commercial FM radio band. While the third at Sydney airport is currently undergoing testing for precision landing of aircraft (2011), as a backup to the Instrument Landing System at least until 2015. It is called the Ground Based Augmentation System. Corrections to aircraft position are broadcast via the aviation VHF band.

## Post processing

Post-processing is used in Differential GPS to obtain precise positions of unknown points by relating them to known points such as survey markers.

The GPS measurements are usually stored in computer memory in the GPS receivers, and are subsequently transferred to a computer running the GPS post-processing software. The software computes baselines using simultaneous measurement data from two or more GPS receivers.

The baselines represent a three-dimensional line drawn between the two points occupied by each pair of GPS antennas. The post-processed measurements allow more precise positioning, because most GPS errors affect each receiver nearly equally, and therefore can be cancelled out in the calculations.

Differential GPS measurements can also be computed in real-time by some GPS receivers if they receive a correction signal using a separate radio receiver, for example in Real Time Kinematic (RTK) surveying or navigation.

The improvement of GPS positioning doesn't require simultaneous measurements of two or more receivers in any case, but can also be done by special use of a single device. In the 1990s when even handheld receivers were quite expensive, some methods of quasi-differential GPS were developed, using the receiver by quick turns of positions or loops of 3-10 survey points.

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