GPS Signal Processing
GPS is becoming more important and its widespread application is driving further research and development. This research has led to improved signal processing and has led to the use of the Fast Fourier Transform.
An overview of this analysis is as follows:
GPS - L1 C/A signal is represented by:
$ r(t) = A\cdot C(t - \tau )\cdot D(t - \tau) \cdot sin(w_{c}(t - \tau)t + \phi ) + n(t) $
Where:
$ w_{c} $ is the carrier frequency
A is the signal amplitude
C(t) is the C/A code
D(t) is the navigation message
$ \tau $ is the propagation delay
$ \phi $ is the initial phase offset
n(t) is the receiver noise
The Fast Fourier Transform (FFT) can be seen below as the correlation between the incoming and reference signal:
$ z(n) = \sum_{m = 0}^{N - 1} x(m)\cdot y(m + n) $
Using a combination of the DFT and the FFT above, the correlation of incoming signal and reference signal can be calculated.
