The GPS satellite transmits two microwave carrier signals the L1 and the L2. Three binary codes shift the L1 and L2 carrier phase. The P-Code modulates both the L1 and L2 carrier phases. The Navigation Message is a 50 Hz signal which describes the GPS satellite orbits, clock corrections from the control system. The pseudo random code transmitted by the satellites is used to determine the pseudo-range, which is a measure of the range or distance between the satellites and the GPS reciever.
Position is determined by multiple pseudo range mesurements during a single observation.
In theory the pseudo range is the time offset between the satellite and the reciever multiplied by the speed of light. Four satellites are need to accurately characterize a position. An equation which relates the pseudo range to these biases is as follows The goal is to model mathematically or difference out the terms on the righthand side of this equation so that the sum of the remaining terms is the measurement value on the lefthand side. A far more precise way to obtain position data is to use the phase of the recieved carrier with respect to the phase of a carrier generated by an oscillator in the GPS reciever. The carrier generated by the GPS reciever has a constant frequency, whereas the recieved carrier is changing in frequency during to the Doppler shift induced by the relative motion of the satellite and the GPS reciever.