Pseudorange

Pseudorange and time error estimation

A quartz oscillator is typically used in the receiver for timing, but quartz clocks generally have an accuracy worse than one part in a million. If uncorrected for a week, the deviation could be so large that the reported location would not be on Earth but beyond the Moon's orbit. Even after correction, a second later the clock may be unusable for positioning, as the error would amount to hundreds of meters for a typical quartz clock. However, because the receiver uses its clock to measure ranges to different satellites at nearly the same time, all measured ranges share the same error. Ranges with identical error are called pseudoranges. By obtaining the pseudorange of an additional fourth satellite, both the precise position and the time error can be estimated. The term 'pseudorange' reflects this contamination by an unknown receiver clock offset; GPS positioning is sometimes called trilateration but is more accurately described as pseudo-trilateration. Due to error propagation, neither the receiver position nor the clock offset is computed exactly; instead, they are estimated through a least squares adjustment procedure from geodesy. The imprecision is described by geometric dilution of precision (GDOP) quantities for x, y, z, and t. A clock with one-in-a-million accuracy introduces an error of one millionth of a second each second, which multiplied by the speed of light gives 300 meters. For a typical satellite constellation this error increases by about that amount, less if satellites are close together and more if they are near the horizon. Using only three satellites with such a clock, a stationary receiver would appear to be moving at over 300 meters per second (over 1000 km/h or 600 mph), and the receiver could not distinguish whether that speed came from clock error or actual movement.