The Global Positioning System (GPS)

Posted on Jul 29, 2007 By : Mizake Laziaf
The Global Positioning System (GPS) is currently the only fully functional Global Navigation Satellite System (GNSS). Utilizing a constellation of at least 24 medium Earth orbit satellites that transmit precise microwave signals, the system enables a GPS receiver to determine its location, speed and direction.

Civilian GPS receiver in a marine application(Photo:Nachoman-au)

GPS has become a widely used aid to navigation worldwide, and a useful tool for map-making, land surveying, commerce, and scientific uses. GPS also provides a precise time reference used in many applications including scientific study of earthquakes, and synchronization of telecommunications networks.

Simplified method of GPS operation

A GPS receiver calculates its position by measuring the distance between itself and three or more GPS satellites. Measuring the time delay between transmission and reception of each GPS microwave signal gives the distance to each satellite, since the signal travels at a known speed. The signals also carry information about the satellites' location. By determining the position of, and distance to, at least three satellites, the receiver can compute its position using trilateration.

Calculating Coordinate positions from GPS

The coordinates are calculated according to the World Geodetic System WGS84 coordinate system. To calculate its position, a receiver needs to know the precise time. The satellites are equipped with extremely accurate atomic clocks, and the receiver uses an internal crystal oscillator-based clock that is continually updated using the signals from the satellites.

The receiver identifies each satellite's signal by its distinct C/A code pattern, then measures the time delay for each satellite. To do this, the receiver produces an identical C/A sequence using the same seed number as the satellite. By lining up the two sequences, the receiver can measure the delay and calculate the distance to the satellite, called the pseudorang.

he orbital position data from the Navigation Message is then used to calculate the satellite's precise position. Knowing the position and the distance of a satellite indicates that the receiver is located somewhere on the surface of an imaginary sphere centered on that satellite and whose radius is the distance to it. When four satellites are measured simultaneously, the intersection of the four imaginary spheres reveals the location of the receiver. Receivers known to be near sea level can substitute the sphere of the planet for one satellite by using their altitude. Often, these spheres will overlap slightly instead of meeting at one point, so the receiver will yield a mathematically most-probable position (and often indicate the uncertainty).

Overlapping pseudoranges, represented as curves,
are modified to yield the probable position (Photo:Richtom80)

Calculating a position with the P(Y) signal is generally similar in concept, assuming one can decrypt it. The encryption is essentially a safety mechanism: if a signal can be successfully decrypted, it is reasonable to assume it is a real signal being sent by a GPS satellite. In comparison, civil receivers are highly vulnerable to spoofing since correctly formatted C/A signals can be generated using readily available signal generators. RAIM features do not protect against spoofing, since RAIM only checks the signals from a navigational perspective.

GPS Accuracy and its error sources

The position calculated by a GPS receiver requires the current time, the position of the satellite and the measured delay of the received signal. The position accuracy is primarily dependent on the satellite position and signal delay.

To measure the delay, the receiver compares the bit sequence received from the satellite with an internally generated version. By comparing the rising and trailing edges of the bit transitions, modern electronics can measure signal offset to within about 1% of a bit time, or approximately 10 nanoseconds for the C/A code. Since GPS signals propagate nearly at the speed of light, this represents an error of about 3 meters. This is the minimum error possible using only the GPS C/A signal.

Position accuracy can be improved by using the higher-chiprate P(Y) signal. Assuming the same 1% bit time accuracy, the high frequency P(Y) signal results in an accuracy of about 30 centimeters.

Electronics errors are one of several accuracy-degrading effects outlined in the table below. When taken together, autonomous civilian GPS horizontal position fixes are typically accurate to about 15 meters (50 ft). These effects also reduce the more precise P(Y) code's accuracy.

Sources of User Equivalent Range
Errors (UERE)
Source Effect
Ionospheric effects ± 5 meter
Ephemeris errors ± 2.5 meter
Satellite clock errors ± 2 meter
Multipath distortion ± 1 meter
Tropospheric effects ± 0.5 meter
Numerical errors ± 1 meter or less

Atmospheric effects to GPS Signals

Inconsistencies of atmospheric conditions affect the speed of the GPS signals as they pass through the Earth's atmosphere and ionosphere. Correcting these errors is a significant challenge to improving GPS position accuracy. These effects are smallest when the satellite is directly overhead and become greater for satellites nearer the horizon since the signal is affected for a longer time. Once the receiver's approximate location is known, a mathematical model can be used to estimate and compensate for these errors.

Because ionospheric delay affects the speed of microwave signals differently based on frequency—a characteristic known as dispersion—both frequency bands can be used to help reduce this error. Some military and expensive survey-grade civilian receivers compare the different delays in the L1 and L2 frequencies to measure atmospheric dispersion, and apply a more precise correction. This can be done in civilian receivers without decrypting the P(Y) signal carried on L2, by tracking the carrier wave instead of the modulated code. To facilitate this on lower cost receivers, a new civilian code signal on L2, called L2C, was added to the Block IIR-M satellites, which was first launched in 2005. It allows a direct comparison of the L1 and L2 signals using the coded signal instead of the carrier wave.

The effects of the ionosphere generally change slowly, and can be averaged over time. The effects for any particular geographical area can be easily calculated by comparing the GPS-measured position to a known surveyed location. This correction is also valid for other receivers in the same general location. Several systems send this information over radio or other links to allow L1 only receivers to make ionospheric corrections. The ionospheric data are transmitted via satellite in Satellite Based Augmentation Systems such as WAAS, which transmits it on the GPS frequency using a special pseudo-random number (PRN), so only one antenna and receiver are required.

Humidity also causes a variable delay, resulting in errors similar to ionospheric delay, but occurring in the troposphere. This effect is both more localized and changes more quickly than ionospheric effects and is not frequency dependent. These traits making precise measurement and compensation of humidity errors more difficult than ionospheric effects.

Changes in altitude also change the amount of delay due to the signal passing through less of the atmosphere at higher elevations. Since the GPS receiver computes its approximate altitude, this error is relatively simple to correct.

Multipath effects to GPS Signals

GPS signals can also be affected by multipath issues, where the radio signals reflect off surrounding terrain; buildings, canyon walls, hard ground, etc. These delayed signals can cause inaccuracy. A variety of techniques, most notably narrow correlator spacing, have been developed to mitigate multipath errors. For long delay multipath, the receiver itself can recognize the wayward signal and discard it. To address shorter delay multipath from the signal reflecting off the ground, specialized antennas may be used. Short delay reflections are harder to filter out since they are only slightly delayed, causing effects almost indistinguishable from routine fluctuations in atmospheric delay.

Multipath effects are much less severe in moving vehicles. When the GPS antenna is moving, the false solutions using reflected signals quickly fail to converge and only the direct signals result in stable solutions.

Ephemeris and clock errors

The navigation message from a satellite is sent out only every 12.5 minutes. In reality, the data contained in these messages tend to be "out of date" by an even larger amount. Consider the case when a GPS satellite is boosted back into a proper orbit; for some time following the maneuver, the receiver's calculation of the satellite's position will be incorrect until it receives another ephemeris update. The onboard clocks are extremely accurate, but they do suffer from some clock drift. This problem tends to be very small, but may add up to 2 meters (6 ft) of inaccuracy.

This class of error is more "stable" than ionospheric problems and tends to change over days or weeks rather than minutes. This makes correction fairly simple by sending out a more accurate almanac on a separate channel. (Wikipedia, the free encyclopedia)

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