Latest revision as of 10:07, 22 September 2009

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 the incoming and reference signal can be calculated.

Information found in paper:

Lachapelle, G., M. E. Cannon, and C. Ma. Implementation of a Software GPS Receiver. 
      Thesis. Department of Geomatics Engineering, University of Calgary, 2004. Print.

Implementation of a Software GPS Receiver

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