Wigner-Hough/Randon Transform for GPS Post-Correlation Integration

Chun Yang, Mikel Miller, Thao Nguyen and Erik Blasch

Abstract:	This paper investigates the application of the Wigner- Hough transform (WHT) or Wigner-Radon transform (WRT) and their variants to GPS post-correlation integration. For an acquisition scheme wherein frequency search step is 500 Hz and code search step is a half chip, GPS despreading correlation is typically carried out over 1 millisecond. Such integration at the rate of 1 kHz can tolerate ±250 Hz errors in frequency and ±¼ chips in code phase in the sense of 3 dB loss of correlation power. In many applications, it is desired to integrate the 1 ms correlations over a rather long period of time so as to boost the signal strength while averaging out noise and interference. When the integration interval extends to and beyond 20 ms, the signs of data bits have to be considered. For even longer intervals, changes in signal frequency due to motion-induced Doppler and/or clock drift become important and have to be taken into account. Under a constant acceleration, the complex correlations are subject to a varying Doppler frequency, which behaves like a chirp signal (a linear frequency modulation or LFM). The Wigner-Ville distribution (WVD) is a well known method to estimate instantaneous frequency, which appears as a straight line in the time-frequency plane. The Hough transform (HT) is another well-known method to detect a line, which can be used to integrate the chirp signal power along the line. Similar to the HT, the Radon transform (RT) is another formulation that evaluates integrals along straight lines. However, the combination of the WVD and HT (called the Wigner- Hough transform) or the combination of the WVD and Radon transform (called the Wigner-Radon transform), cannot be applied directly to the despread correlations because of the presence of unknown data bits. A block-implemented WHT/WRT using the intra-block conjugate products is set forth in this paper, which can be used to estimate the initial frequency, chirping rate (frequency rate), and bit sync. Simulation results are presented to illustrate the operation and performance of the method.
Published in:	Proceedings of the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2007) September 25 - 28, 2007 Fort Worth Convention Center Fort Worth, TX
Pages:	2762 - 2771
Cite this article:	Yang, Chun, Miller, Mikel, Nguyen, Thao, Blasch, Erik, "Wigner-Hough/Randon Transform for GPS Post-Correlation Integration," Proceedings of the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2007), Fort Worth, TX, September 2007, pp. 2762-2771.
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