Pseudorange

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The pseudorange (from pseudo and range) is a first-approximation measurement for the distance between a satellite and a navigation satellite receiver - for instance Global Positioning System (GPS) receivers.

To determine its position, a satellite navigation receiver will determine the ranges to (at least) three satellites as well as their positions at time of transmitting. Knowing the satellites' orbital parameters, these positions can be calculated for any point in time. The pseudoranges are then the time the signal has taken from there to the receiver, multiplied by the speed of light.

To measure this time, the relationship between the internal receiver time (typically derived from an inexpensive quartz oscillator) and GPS time must be known. This is done by introducing the receiver clock offset Δt into the positional computation, requiring one extra satellite signal. With four signals, solutions for the receiver's position along the x-, y-, z- and Δt- axes can be computed.

The reason we speak of pseudo-ranges rather than ranges, is precisely this "contamination" with unknown receiver clock offset. GPS positioning is sometimes referred to as trilateration, but would be more accurately referred to as pseudo-trilateration.

Following the laws of error propagation, neither the receiver position nor the clock offset are computed exactly, but rather estimated through a least squares adjustment procedure known from geodesy. To describe this imprecision, so-called GDOP quantities have been defined: Geometric Dilution of Precision (x,y,z,t).