A Probabilistic Approach to Derivation of Geometrical Criteria for Evaluating GPS RAIM Detection Availability

Jizhang Sang and Kurt Kubik

Abstract:	Receiver Autonomous Integrity Monitoring (RAIM) is a vehicle self-contained method to monitor GPS navigation integrity. As the availability of the RAIM function is strongly dependent on satellite geometry, many investigations concentrated on geometry criteria for evaluating RAIM availability. Approximate Radial- error Protection (ARP) ceilings have been widely used in evaluation of the GPS RAIM availability. This paper gives a rigorous probabilistic approach to derivation of the geometrical criteria for evaluating the GPS RAIM availability, based on the concept of the power of statistical testing. This test power represents the minimum detection probability. From the assumption of a bias in individual measurement, a test statistic relating the satellite geometry with the navigation radial error is obtained. Then, the probability density function of this test statistic is derived by applying the probability density function of non-central chi-square variable. Finally, iterative computations are carried out to obtain the geometrical criteria for achieving the required test power. The derivation is based on the weighted least-squares method, and can be easily expanded to derive the RAIM geometrical criteria for different alarm limits and test power. The relationship between our criteria and existing ARP ceiling values is also presented.
Published in:	Proceedings of the 1997 National Technical Meeting of The Institute of Navigation January 14 - 16, 1997 Loews Santa Monica Hotel Santa Monica, CA
Pages:	511 - 517
Cite this article:	Sang, Jizhang, Kubik, Kurt, "A Probabilistic Approach to Derivation of Geometrical Criteria for Evaluating GPS RAIM Detection Availability," Proceedings of the 1997 National Technical Meeting of The Institute of Navigation, Santa Monica, CA, January 1997, pp. 511-517.
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