A Gaussian Mixture Model for Error Distributions Used in Assessing RAIM Performance

C.A. Shively

Abstract:	Receiver Autonomous Integrity Monitoring (RAIM) is a method for mitigating the risk of a single satellite fault with performance characterized by a vertical protection level (VPL) as the sum of a threshold and integrity offset. Current RAIM design for future applications with vertical guidance has used a nominal error model to describe the fault-free satellite range errors when considered in the threshold, and a maximum error model to describe those same errors when considered in the integrity offset. This paper presents a Gaussian mixture model that combines both nominal and maximum models into a single model for use in both the threshold and integrity offset components of VPL. In the mixture model the nominal error probability density function (Pdf) applies with probability 1 – Pmax and the maximum error Pdf applies with probability Pmax. Continuity and integrity risk performance results are presented for an example geometry using current RAIM design operating on the mixture error model. For this example, the integrity risk requirement is always met regardless of the value of Pmax, but the continuity risk requirement is not met unless Pmax is essentially negligible. In order to design a RAIM tailored to the mixture model, the standard deviation of a single zero mean Gaussian distribution that bounds the mixture model is determined. The resulting mixture RAIM meets both integrity and continuity requirements for all values of Pmax as long as the value used in the design is at least 0.75. However, by using the overbound for the mixture model in both the integrity offset and also the threshold, the mixture RAIM has increased VPL values in comparison to current RAIM design. Therefore, mixture RAIM trades assurance that the continuity requirement is always met for possibly decreased availability of adequate satellite geometry.
Published in:	Proceedings of the 2012 International Technical Meeting of The Institute of Navigation January 30 - 1, 2012 Marriott Newport Beach Hotel & Spa Newport Beach, CA
Pages:	1590 - 1623
Cite this article:	Shively, C.A., "A Gaussian Mixture Model for Error Distributions Used in Assessing RAIM Performance," Proceedings of the 2012 International Technical Meeting of The Institute of Navigation, Newport Beach, CA, January 2012, pp. 1590-1623.
Full Paper:	ION Members/Non-Members: 1 Download Credit Sign In