Global Positioning System

:GPS redirects here. For other uses of the acronym GPS, see GPS (disambiguation).

Technical description

The system consists of a "constellation" of at least 24 satellites in 6 orbital planes.

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The GPS satellites were initially manufactured by Rockwell; the first was launched in February 1978, and the most recent was launched September 25 2005.

Related Topics:
Rockwell - 1978 - September 25 - 2005

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Each satellite circles the Earth twice every day at an altitude of 20,200 kilometres (12,600 miles).

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The satellites carry atomic clocks and constantly broadcast the precise time according to their own clock, along with administrative information including the orbital elements of their own motion, as determined by a set of ground-based observatories.

Related Topics:
Atomic clock - Orbital element

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The receiver does not need a precise clock, but does need a clock with good short-term stability and the ability to receive signals from four satellites in order to determine its own latitude, longitude, elevation, and the precise time. The receiver computes the distance to each of the four satellites from the difference between local time and the time the satellite signals were sent (this distance is called a pseudorange). It then decodes the satellites' locations from their radio signals and an internal database.

Related Topics:
Latitude - Longitude - Elevation - Pseudorange

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The receiver should now be located at the intersection of four spheres, one around each satellite, with a radius equal to the time delay between the satellite and the receiver multiplied by the speed of the radio signals. Because the receiver does not have a very precise clock it cannot compute the time delays. However, it can measure with high precision the differences between the times when the various messages were received. This yields 3 hyperboloids of revolution of two sheets, whose intersection point gives the precise location of the receiver. This is why at least four satellites are needed: fewer than 4 satellites yield 2 hyperboloids, whose intersection is a curve; it is impossible to know where the receiver is located along the curve without supplemental information, such as elevation. If elevation information is already known, only signals from three satellites are needed (the point is then defined as the intersection of two hyperboloids and an ellipsoid representing the Earth at this altitude).

Related Topics:
Sphere - Hyperboloid

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When there are n > 4 satellites, the n-1 hyperboloids should, assuming a perfect model and measurements, intersect on a single point. In reality, the surfaces rarely intersect, because of various errors. The question of finding the point P can be reformulated into finding its three coordinates as well as n numbers ri such that for all i, PSi-ri is close to zero, and the various ri-rj are close to C.Δij where C is the speed of light and Δij are the time differences between signals i and j. For instance, a least squares method may be used to find an optimal solution. In practice, GPS calculations are more complex (repeat measurements, etc.).

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There are several causes: The initial local time is a guess due to the relatively imprecise clock of the receiver, the radio signals move more slowly as they pass through the ionosphere, and the receiver may be moving. To counteract these variables, the receiver then applies an offset to the local time (and therefore to the spheres' radii) so that the spheres finally do intersect in one point. Once the receiver is roughly localized, most receivers mathematically correct for the ionospheric delay, which is least when the satellite is directly overhead and becomes greater toward the horizon, as more of the ionosphere is traversed by the satellite signal. Since it is common for the receiver to be moving, some receivers attempt to fit the spheres to a directed line segment.

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The receiver contains a mathematical model to account for these influences, and the satellites also broadcast some related information which helps the receiver in estimating the correct speed of propagation. High-end receiver/antenna systems make use of both L1 and L2 frequencies to aid in the determination of atmospheric delays. Because certain delay sources, such as the ionosphere, affect the speed of radio waves based on their frequencies, dual frequency receivers can actually measure the effects on the signals.

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In order to measure the time delay between satellite and receiver, the satellite sends a repeating 1,023 bit long pseudo random sequence; the receiver knows the seed of the sequence, constructs an identical sequence and shifts it until the two sequences match.

Related Topics:
Bit - Pseudo random sequence

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Different satellites use different sequences, which lets them all broadcast on the same frequencies while still allowing receivers to distinguish between satellites. This is an application of Code Division Multiple Access, or CDMA.

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Several frequencies make up the GPS electromagnetic spectrum:

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• L1 (1575.42MHz):
  Carries a publicly usable coarse-acquisition (C/A) code as well as an encrypted precision P(Y) code.
• L2 (1227.60MHz):
  Usually carries only the P(Y) code. The encryption keys required to directly use the P(Y) code are tightly controlled by the U.S. government and are generally provided only for military use. The keys are changed on a daily basis. In spite of not having the P(Y) code encryption key, several high-end GPS receiver manufacturers have developed techniques for utilizing this signal (in a round-about manner) to increase accuracy and remove error caused by the ionosphere.
• L3 (1381.05MHz):
  Carries the signal for the GPS constellation's alternative role of detecting missile/rocket launches (supplementing Defense Support Program satellites), nuclear detonations, and other high-energy infrared events.
• L4 (1841.40MHz):
  Being studied for additional ionospheric correction.
• L5 (1176.45MHz):
  Proposed for use as a civilian safety-of-life signal.

A minor detail is that the atomic clocks on the satellites are set to "GPS time", which is the number of seconds since midnight, January 6, 1980. It is ahead of UTC because it does not follow leap seconds. Receivers thus apply a clock correction factor (which is periodically transmitted along with the other data), and optionally adjust for a local time zone in order to display the correct time. The clocks on the satellites are also affected by both special and general relativity, which causes them to run at a slightly slower rate than do clocks on the Earth's surface. This amounts to a discrepancy of around 38 microseconds per day, which is corrected by electronics on each satellite. This offset is a dramatic proof of the theory of relativity in a real-world system, as it is exactly that predicted by the theory, within the limits of accuracy of measurement.

Related Topics:
January 6 - 1980 - UTC - Leap second - Special - General relativity

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The inspiration for the GPS system came when the Soviets launched the first Sputnik in 1957. A team of U.S. scientists led by Dr. Richard B. Kershner were monitoring Sputnik's radio transmissions. They discovered that, due to the Doppler effect, the frequency of the signal being transmitted by Sputnik was higher as the satellite approached, and lower as it continued away from them. They realized that since they knew their exact location on the globe, they could pinpoint where the satellite was along its orbit by measuring the Doppler distortion. It was only a small leap of logic to realize that the converse was also true; if the satellite's position was known then they could identify their own position on Earth.

Related Topics:
Soviets - Sputnik - 1957 - Richard B. Kershner - Doppler effect

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Sources of GPS measurement errors

Ideally, GPS receivers would easily be able to convert the C/A and P(Y)-code measurements into accurate positions. However, a system with such complexity leaves many openings for errors to affect the measurements. The following are several causes of error in GPS measurements.

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Clocks

Both GPS satellites and receivers are prone to timing errors. Ground stations throughout the world monitor the satellites to ensure that their atomic clocks are kept synchronized. Receiver clock errors depend upon the oscillator provided within the unit. However, they can be calculated and then eliminated once the receiver is tracking at least four satellites.

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Ionosphere

The Ionosphere is one of the leading causes of GPS error. The speed of light varies due to atmospheric conditions. As a result, errors greater than 10 metres may arise. To compensate for these errors, the second frequency band L2 was provided. By comparing the phase difference between the L1 and L2 signals, the error caused by the ionosphere can be calculated and eliminated.

Related Topics:
Ionosphere - Metre

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Multipath

The antenna receives not only direct GPS signals, but also multipath signals: reflections of the radio signals off the ground and/or surrounding structures (buildings, canyon walls, etc). For long delay multipath signals, the receiver itself can filter the signals out. A variety of receiver techniques, most notably Narrow Correlator spacing, have been developed to mitigate multipath error contributions to pseudorange measurements. For shorter delay multipath signals that result from reflections from the ground, special antenna features may be used such as a ground plane, or a choke ring antenna. Shorter multipath signals from ground reflections can often be very close to the direct signals, and can greatly reduce precision.

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Selective Availability

In the past, the civilian signal was degraded, and a more accurate Precise Positioning Service was available only to the United States military, its allies and a few others, mostly government users. However, on May 1, 2000, then US President Bill Clinton announced that this "Selective Availability" would be turned off, allowing all users to enjoy nearly the same level of access, with a precision of position determination of less than 20 meters.

Related Topics:
May 1 - 2000 - Bill Clinton

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Techniques to improve GPS accuracy

The accuracy of GPS can be improved in a number of ways:

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• Using a network of fixed ground based reference stations. 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. This method is called Differential GPS or DGPS. DGPS was especially useful when GPS was still degraded (via the "Selective Availability" described above), since DGPS could nevertheless provide 5–10 metre accuracy. The 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.
• Exploitation of DGPS for Guidance Enhancement (EDGE) is an effort to integrate DGPS into precision guided munitions such as the Joint Direct Attack Munition (JDAM).
• The Wide Area Augmentation System (WAAS). This uses a series of ground reference stations to calculate GPS correction messages, which are uploaded to a series of additional satellites in geosynchronous orbit for transmission to GPS receivers, including information on ionospheric delays, individual satellite clock drift, and suchlike. Although only a few WAAS satellites are currently available as of 2004, it is hoped that eventually WAAS will provide sufficient reliability and accuracy that it can be used for critical applications such as GPS-based instrument approaches in aviation (landing an airplane in conditions of little or no visibility). The current WAAS system only works for North America (where the reference stations are located), and due to the satellite location the system is only generally usable in the eastern and western coastal regions. However, variants of the WAAS system are being developed in Europe (EGNOS, the Euro Geostationary Navigation Overlay Service), and Japan (MSAS, the Multi-Functional Satellite Augmentation System), which are virtually identical to WAAS.
• A Local-Area Augmentation System (LAAS). This is similar to WAAS, in that similar correction data are used. But in this case, the correction data are transmitted from a local source, typically at an airport or another location where accurate positioning is needed. These correction data are typically useful for only about a thirty to fifty kilometre radius around the transmitter.
• A Carrier-Phase Enhancement (CPGPS). This technique utilizes the 1.575 GHz L1 carrier wave to act as a sort of clock signal, resolving ambiguity caused by variations in the location of the pulse transition (logic 1-0 or 0-1) of the C/A PRN signal. The problem arises from the fact that the transition from 0-1 or 1-0 on the C/A signal is not instantaneous, it takes a finite amount of time, and thus the correlation (satellite-receiver sequence matching) operation is imperfect. A successful correlation could be defined in a number of various places along the rising/falling edge of the pulse, which imparts timing errors. CPGPS solves this problem by using the L1 carrier, which has a period 1/1000 that of the C/A bit width, to define the transition point instead. The phase difference error in the normal GPS amounts to a 2-3 m ambiguity. CPGPS working to within 1% of perfect transition matching can achieve 3 mm ambiguity; in reality, CPGPS coupled with DGPS normally realizes 20-30 cm accuracy.
• Wide Area GPS Enhancement (WAGE) is an attempt to improve GPS accuracy by providing more accurate satellite clock and ephemeris (orbital) data to specially-equipped receivers.
• Relative Kinematic Positioning (RKP) is another approach for a precise GPS-based positioning system. In this approach, accurate determination of range signal can be resolved to an accuracy of less than 10 centimetres. This is done by resolving the number of cycles in which the signal is transmitted and received by the receiver. This can be accomplished 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).
• Many automobile GPS systems combine the GPS unit with a gyroscope and speedometer pickup, allowing the computer to maintain a continuous navigation solution by dead reckoning when buildings, terrain, or tunnels block the satellite signals. This is similar in principle to the combination of GPS and inertial navigation used in ships and aircraft, but less accurate and less expensive because it only fills in for short periods.