Hypothesis Testing for Resolving Integer Ambiguity in GPS

Jonathan D. Wolfe, Walton R. Williamson, and Jason L. Speyer

Peer Reviewed

Abstract: This paper presents statistical techniques for validating integer ambiguities and detecting cycle slips. The multiple-hypothesis Wald sequential probability ratio test (SPRT) validates the choice of initial integer ambiguities by finding the conditional probability that each set of integer biases under consideration is the true bias condition. The multiple-hypothesis Shiryayev SPRT monitors for cycle slips by determining the conditional probability that the integer biases have jumped from the nominal bias condition to each member of a collection of other bias conditions. Both tests use a geometric combination of the carrier-phase measurements and the difference between the carrier-phase measurements and code measurements as measurement residuals. Because the SPRT calculations operate on the probability density functions of these measurement residuals, they can correctly compensate for non-Gaussian measurement errors, such as multipath. The efficacy of our techniques is demonstrated by results from simulations and field experiments.
Published in: NAVIGATION: Journal of the Institute of Navigation, Volume 50, Number 1
Pages: 45 - 56
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