Zoom, Pruning, and Partial FFT for GPS Signal Tracking

Chun Yang

Abstract:	The circular property of FFT-implemented correlation has been used for GPS code acquisition by virtue of its fast calculation of the entire correlation function over all code phases. Recently, the equivalence between the spectrum translation and the complex exponential multiplication (in-phase and quadrature phase rotation in the time-domain) has been introduced for Doppler removal as a natural insertion in the above FFT-implemented correlation procedure. This thus enables the frequency- domain GPS signal acquisition. The full-blow FFT and IFFT, though necessary for search over a large time and frequency uncertainty zone in the acquisition mode, is an overkill in the tracking mode, where the Doppler frequency and code delay are known with good certainty. However, to continue enjoying the frequency-domain benefits of digital downconversion to baseband and narrowband jam suppression, modifications have to be made, which is the subject of this paper. By introducing feedback of the acquired or estimated Doppler and code phase, the frequency-domain tracking loops are thus formed. In the incoming signal path, the use of zoom FFT only calculates those spectral contents covering the effective signal bandwidth plus Doppler spread. In the reverse path, only the correlation values at those code phases around the detected peak are calculated (a partial IFFT). If a finer resolution is required to produce the correlation function for such purpose as multipath estimation and mitigation, frequency-domain zero padding can be effected. When the inverse transform is taken, those calculation branches corresponding to the padded zeros can be eliminated (pruning FFT). These techniques reduce unnecessary computation, thus making the frequency-domain implementation of tracking loops viable. The proposed techniques are tested on recorded real GPS data and the processing results are presented in the paper to illustrate the functionality and performance of the techniques.
Published in:	Proceedings of the 2001 National Technical Meeting of The Institute of Navigation January 22 - 24, 2001 Westin Long Beach Hotel Long Beach, CA
Pages:	839 - 849
Cite this article:	Yang, Chun, "Zoom, Pruning, and Partial FFT for GPS Signal Tracking," Proceedings of the 2001 National Technical Meeting of The Institute of Navigation, Long Beach, CA, January 2001, pp. 839-849.
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