GPS Receivers and the Observables

Abstract

We saw in Chapter 3 that at a sufficiently large distance from a transmitter, the electromagnetic waves that it emits can be considered to be spherical. We can represent the electric field intensity of a spherical electromagnetic wave of frequency ω and wave number k at some distance r from the transmitter as

$$E = {{{E_0}} \over r}{e^{i(\user2{\omega }t - kr)}}.$$

(4.1)

The signal from a GPS satellite when it arrives at a receiver can be taken to be such a wave and if we replace r by ρ, we can represent the signal in simplified form as

$$y\, = \,A cos(\omega t\, - \,kp\, + \,\phi ')$$

(4.2)

where A is the signal amplitude, t is the elapsed time measured from the start of transmission from the satellite, is the distance travelled from the satellite to the receiver, and ϕ′ is a phase bias term which is the phase of the wave at the satellite at t = 0.