Table of Contents
ISRN Signal Processing
Volume 2011, Article ID 148242, 11 pages
Research Article

Bayesian Change-Points Estimation Applied to GPS Signal Tracking

Laboratoire d'Informatique, Signaux et Images de la Côte d’Opale (LISIC), Université Lille Nord de France, Université du Littoral Côte d’Opale (ULCO) 50, rue Ferdinand Buisson BP 699, 62228 CALAIS Cedex, France

Received 24 February 2011; Accepted 20 April 2011

Academic Editors: G. Camps-Valls, C. S. Lin, and K. Sivakumar

Copyright © 2011 G. Stienne et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A hierarchical Bayesian model is applied to off-line segmentation of the GPS signal discriminator. The purpose of this work is to estimate the code delay of the receiving GPS CDMA code in order to retime the local receiver code and to estimate the pseudorange satellite receiver. The goal of our approach is to obtain a high-rate accurate positioning in the dynamic navigation case. We show that the behaviour of the coherent discriminator of a GPS pilot channel can be modelized by a piecewise stationary process. In our approach the discriminator behaviour in each stationary segment is approximated by a constant acceleration model, and the code delay at each end of the segments is known. The interest of this approach is that we use the coherent values of the discriminator in each segment to estimate the change instants of the process and to get in this case an accurate estimation of the code delays. In this context, a simultaneous estimation of the change instants is considered. We define the a posteriori distribution which integrates in its expression the signal change instants and the parameters of its statistical model. The proposed model leads after marginalization to a penalized contrast function that we minimize to estimate the discriminator change instants. The interest of the proposed model is that we can integrate in our estimate prior information on the roughly known values of the signal-to-noise ratio and relative speed satellite receiver. The potential of the proposed method is shown on experimentations realized on synthetic and real data for millisecond receiver localization.