Integrity Monitoring Using Bayes' Rule

Stephen Bancroft and Susan S. Chen

Abstract:	This paper uses Bayes’ Rule and a Bayes’ Risk strategy adopted from game theory [l] to provide early detection, identification and compensation of a measurement bias in an overdetermined set of equations. One intended application of these results is Receiver Autonomous Integrity Monitoring (RAIM) of the satellites in a GPS navigation system. However, the techniques can be applied to any system whose system state is observed with an overdetermined set of measurements. For a single axis (measurement) fault, the probability of bias detection and fault isolation is related to the system GDOP through determinants of order 1 and 2 respectively, extracted from an orthogonal projection operator Q. (Detecting and isolating faults along two axes will involve determinants of submatrices of order 2 and 4 extracted from Q, etc.) A new means for computing all relevant GDOPs is provided, working in the requirements (measurement) space rather than the solution (state) space. The Bayes’ Risk strategy is summarixed in an algorithm that lends itself to efficient computer implementation. Proofs of some of the stated results are moderately involved and therefore will be published in a forthcoming paper.
Published in:	Proceedings of the 4th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1991) September 11 - 13, 1991 Albuquerque, NM
Pages:	781 - 788
Cite this article:	Bancroft, Stephen, Chen, Susan S., "Integrity Monitoring Using Bayes' Rule," Proceedings of the 4th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GPS 1991), Albuquerque, NM, September 1991, pp. 781-788.
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