Reducing and sharing computations for GPS signal processing

1. A method of processing a Global Positioning System (GPS) signal, comprising:

transforming a time domain GPS signal extending over a plurality of milliseconds to a frequency domain GPS signal, wherein the frequency domain GPS signal has a frequency bin spacing of an inverse of the plurality of milliseconds; and

correlating the frequency domain GPS signal with a frequency domain pseudorandom noise (PRN) signal at a plurality of frequencies, said correlating comprising:

performing a circular shift on the frequency domain GPS signal by an amount corresponding to one of the plurality of frequencies;

downsampling the shifted frequency domain GPS signal to produce a shifted and downsampled frequency domain GPS signal that has the same frequency bin spacing as a frequency bin spacing of the frequency domain PRN signal;

multiplying the shifted and downsampled frequency domain GPS signal by the frequency domain PRN signal to produce a frequency domain correlated signal; and

transforming the frequency domain correlated signal into a time domain correlated signal extending over a single millisecond.

2. The method of claim 1 , wherein:

said frequency domain PRN signal comprises a plurality of frequency domain PRN signals corresponding to a plurality of satellites; and

said correlating the frequency domain GPS signal with the PRN signal at the plurality of frequencies comprises correlating the frequency domain GPS signal with a plurality of frequencies for each of the PRN signals.

3. The method of claim 1 , wherein:

said transforming the time domain GPS signal to the frequency domain GPS signal comprises performing a fast Fourier transform (FFT) on the time domain GPS signal.

4. The method of claim 3 , wherein:

said performing the FFT on the time domain GPS signal comprises performing an 8K point FFT.

5. The method of claim 1 , further comprising:

performing a code phase adjustment on the correlated signal.

6. A receiver for processing a GPS signal, comprising:

a memory for storing a frequency domain GPS signal and a frequency domain pseudorandom noise (PRN) signal; and

a processor configured to:

transform a time domain GPS signal extending over a plurality of milliseconds to a frequency domain GPS signal and store the frequency domain GPS signal in the memory, wherein the frequency domain GPS signal has a frequency bin spacing of an inverse of the plurality of milliseconds; and

correlate the frequency domain signal with the PRN signal at a plurality of frequencies, said correlating comprising:

performing a circular shift on the frequency domain GPS signal by an amount corresponding to one of the plurality of frequencies;

downsampling the shifted frequency domain GPS signal to produce a shifted and downsampled frequency domain GPS signal that has the same frequency bin spacing as a frequency bin spacing of the stored frequency domain PRN signal;

multiplying the shifted and downsampled frequency domain GPS signal by the stored frequency domain PRN signal to produce a correlated frequency domain signal; and

transforming the correlated frequency domain signal into a correlated time domain signal extending over a single millisecond.

7. The receiver of claim 6 , wherein said processor is further configured to:

store a plurality of frequency domain PRN signals corresponding to a plurality of satellites; and

correlate the frequency domain GPS signal with a plurality of frequencies for each of the PRN signals.

8. The receiver of claim 6 , wherein said processor is further configured to:

transform the time domain GPS signal to the frequency domain GPS signal by performing a fast Fourier transform (FFT) on the time domain GPS signal.

9. The receiver of claim 8 , wherein:

said performing the FFT on the time domain GPS signal comprises performing an 8K point FFT.

10. The receiver of claim 6 , wherein said processor is further configured to:

perform an FFT on a time domain PRN signal to produce the frequency domain PRN signal.

11. The receiver of claim 6 , wherein said processor is further configured to:

perform a code phase adjustment on the correlated signal.

12. A method of processing a Global Positioning System (GPS) signal extending over a plurality of K milliseconds, wherein K is a positive integer, comprising:

producing a frequency domain representation of the GPS signal, the frequency domain GPS signal comprising a plurality of frequency bins having a bin frequency spacing of f b , wherein f b is an inverse of K milliseconds; and

correlating the GPS signal with a pseudorandom noise (PRN) signal at a plurality of M mixing frequencies with a mixing frequency spacing of f M =K×f b , said correlating comprising for each mixing frequency:

performing a circular shift on the frequency domain GPS signal by K×S samples, wherein S is an integer ranging from 0 to (M−1) to obtain a frequency domain shifted signal shifted by S×f M ;

downsampling the frequency domain shifted signal by K to produce a downsampled frequency domain shifted signal;

multiplying the downsampled frequency domain shifted signal with a frequency domain representation of the PRN signal to produce a frequency domain correlated signal; and

transforming the frequency domain correlated signal into a time domain signal extending over a single millisecond.

13. The method of claim 12 , wherein:

said PRN signal comprises a plurality of frequency domain PRN signals corresponding to a plurality of satellites; and

said correlating the GPS signal with the PRN signal at the plurality of M mixing frequencies comprises correlating the frequency domain GPS signal with a plurality of M mixing frequencies for each of the PRN signals.

14. The method of claim 12 , wherein:

said producing the frequency domain representation of the GPS signal comprises performing a fast Fourier transform (FFT) on a time domain representation of the GPS signal.

15. The method of claim 14 , wherein:

said performing the FFT on the time domain GPS signal comprises performing an 8 thousand point FFT.

16. The method of claim 12 , further comprising:

performing a code phase adjustment on the correlated signal.