# Q 4.1 Give an overview of the global positioning system (GPS).

The Global Positioning System (GPS) is a global satellite navigation system, developed by the US government for the Department of Defense. It is essentially a military system, available to civilians with a lower accuracy. Position fix is obtained in passive receivers by the triangulation method, wherein estimated ranges from four satellites are used to derive the position and altitude of a point. Ranges from three satellites can provide latitude and longitude of a point on the Earth; the addition of a fourth satellite can provide a user’s altitude and correct receiver clock error. The system can also be used to derive the velocity of a user. Moreover, receivers can extract precise time information originating from onboard atomic clocks, which have a drift rate of 1 s per 70,000 years. There are two rubidium and two cesium clocks aboard each first generation satellite.

Each satellite transmits two pseudo-random codes for the receivers to derive range of the satellite. These codes are transmitted on two frequency bands, L1 (1575.42 MHz) and L2 (1227.6 MHz). The encrypted Precise-Code (P-Code) meant for US military operation is available on both frequencies, and the unencrypted coarse acquisition code (C/A-code), for public, is transmitted only in L1 band, where it is combined with P-Code in phase quadrature. Codes have low cross-correlation, allowing transmissions from each satellite on the same frequency with little mutual interference. Spread spectrum modulation used for transmissions provides resistance to multipath and immunity to interference. The C/A code, operating at 1.023 Mbps, is a 1023-bit pseudo-random code repeating each milli-second, and the P-code, operating at 10.023 Mbps, has a cycle of 267 days but is reset every seven days. Each code is combined with a navigation message comprising the status of the satellite, time synchronization information for transferring from coarse to fine code, clock correction, satellite ephemeris, propagation delay corrections, approximate ephemeris and status of the constellation. The nominal constellation comprises 21 satellites with three in-orbit spares. Satellites are dispersed across the globe in circular orbits for global coverage at an altitude of about 20,200 km (orbital period of about 12 hours).

The range is estimated as the product of time taken for a signal to travel from satellite to receiver. For accurate range estimate, each user clock must be synchronized to the satellite clock. The problem of correcting clock error uncertainty is resolved by estimating the range from a fourth satellite. The travel time of the signal is estimated by measuring the time shift between identical codes generated at the satellite and the receiver. The code generated at the receiver is time shifted until a maximum correlation is achieved between transmit and receive codes; the time-shift provides an approximate range or ‘pseudo’ range which includes numerous errors. Note that the user must have knowledge of code to be able to use the system; this feature permits the military to use the higher accuracy P-Code securely.

The true range is estimated from the pseudo-range by solving a set of four simultaneous equations called navigation equation populated by pseudo-range measurements.

The solution can be explained qualitatively by observing that the receiver lies at the intersection of three sphere of radius Rpi, Rpj and Rpk where subscripts i, j and k represent distances from satellites i, j and k respectively.

The speed with which position is calculated can be improved by using only three measurements, and traded off against accuracy and receiver complexity. User velocity can be extracted from Doppler information or as a time derivative of travelled distance. The interested reader should refer the rich literature on the subject for a detailed exposition. Please refer to the relevant NASA sites for up-to-date information.

Useful sites

http://www.gps.gov (Retrieved July 2015)

https://www.nasa.gov/audience/foreducators/topnav/materials/listbytype/How_Do_Global_Positioning_Systems.html (Retrieved July 2015)