Singularity Detection Technique for GPS Cycle Slip in Wavelets Domain

M. Elhabiby, A. El-Ghazouly, N. El-Sheimy

Abstract:	Cycle slip is a sudden jump in the carrier phase observables by an integer number of cycles which occurs between two epochs if the satellite signal can’t reach the antenna (Figure 1). Cycle slips are caused by the loss of lock of the phase lock loops, which may be due signal blockage or high troposphere activities, etc. Cycle slip can be seen as a singularity in the GPS data, which needs to be detected and removed. A method that excels in finding and identifying these singularities is the Continuous Wavelets Transform (CWT), because of its capability of decomposing a signal into elementary base functions that are well localized in both time and frequency domains. In this paper a new cycle slip detection and removal technique is demonstrated base on wavelets multiresolution analysis. The propagation of singularities between the wavelets levels of decomposition is different from the propagation of noise. This characteristic is used to identify the singularities by computing and linking the local maxima of the wavelets coefficients at different levels of decompositions. The characterization of singularities from the decay of the wavelets transform enables us to have a precise meaning to discontinuity. Therefore, the decay of the wavelets coefficient is computed between levels of decomposition by Lipschitz exponent to characterize the regularity of the signal.
Published in:	Proceedings of the 22nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2009) September 22 - 25, 2009 Savannah International Convention Center Savannah, GA
Pages:	1999 - 2007
Cite this article:	Elhabiby, M., El-Ghazouly, A., El-Sheimy, N., "Singularity Detection Technique for GPS Cycle Slip in Wavelets Domain," Proceedings of the 22nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS 2009), Savannah, GA, September 2009, pp. 1999-2007.
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