pseudoranges

Pseudoranges are a fundamental measurement in satellite navigation systems, such as the Global Positioning System (GPS). They represent the apparent distance between a satellite and a receiver. This distance is calculated by multiplying the time it takes for a signal to travel from the satellite to the receiver by the speed of light. However, this calculated distance is not the true geometric range due to several factors.

The "pseudo" in pseudorange arises because the receiver's clock is not perfectly synchronized with the satellite's atomic clock. This clock offset introduces a significant error in the distance calculation. If the receiver's clock is ahead of the satellite's, the measured travel time will be shorter, leading to a shorter apparent distance. Conversely, if the receiver's clock is behind, the apparent distance will be longer.

Besides the clock bias, pseudoranges are also affected by other error sources. These include atmospheric delays (ionospheric and tropospheric), satellite clock errors, satellite orbital errors (ephemeris errors), multipath effects where signals bounce off surfaces, and receiver noise. To determine the precise position of a receiver, measurements from at least four satellites are required. These measurements, along with the pseudorange data, allow for the calculation of the receiver's three-dimensional position (latitude, longitude, and altitude) and the receiver's clock offset. By solving a system of equations, the receiver can correct for its own clock error and thus obtain its true location.