Hypothesis Testing for Resolving Integer Ambiguity in GPS

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

Abstract:	In this paper, we present two statistical techniques appropriate for the ”validation” of integer ambiguities and the detection of cycle slips. The multiple hypothesis Wald sequential probability ratio test (SPRT) can find the conditional probability that each set of integer biases under consideration is the true bias condition. The multiple hypothesis Shiryayev SPRT determines the conditional probability that the integer biases have jumped from the nominal bias condition to each member of a collection of other bias conditions. Hence, the Wald SPRT is a method for validating the integer ambiguities during the initial ambiguity resolution, while the Shiryayev SPRT can be used to monitor for cycle slips. Each of these multiple hypothesis SPRTs (MHSPRTs) makes use of two measurement residuals. One is geometric combination of the carrier phase measurements, and the other is generated by differencing the carrier phase measurements with code measurements. Prior work on cycle slip monitoring has focused solely on the detection of the occurrence of a cycle slip in the fastest time, balanced against the probability of issuing a false alarm. Once a disruption has occurred, the ambiguity resolution process must restart from scratch. The Shiryayev SPRT bypasses this problem, as it announces the location of the biases after the jump, in addition to the time of the cycle slip. The calculations for the MHSPRTs are not linked to any particular distribution, unlike prior efforts. Only the probability density functions of the measurement residuals are required. Hence, the techniques can correctly compensate for non-Gaussian errors in measurement such as multipath. For each hypothesis under consideration, the MHSPRTs yield the probability of that hypothesis being the correct one. The ”state” of the MHSPRT recursions is the vector of all of these probabilities. Information from past measurements is embedded in this state. This recursive, probabilistic framework makes it very straightforward to add new hypotheses into the set of possible bias conditions while retaining information from prior measurements. Results from successful simulations and field experiments are presented, showing the efficacy of our techniques.
Published in:	Proceedings of the 14th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 2001) September 11 - 14, 2001 Salt Palace Convention Center Salt Lake City, UT
Pages:	1522 - 1531
Cite this article:	Updated citation: Published in NAVIGATION: Journal of the Institute of Navigation
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