Results on the Optimal Detection Statistic for Integrity Monitoring

Juan Blanch, Todd Walter, Per Enge

Abstract:	One of the most stringent requirements of positioning systems for aviation is integrity. The provision of integrity is the main function of Satellite-based Augmentation systems (like the Wide Area Augmentation System and EGNOS), Ground Based Augmentation Systems, and Receiver Autonomous Integrity Monitoring (RAIM). All these systems have different threat models, different nominal error models, and different constraints, but they all attempt to do the same thing: maximize the availability while maintaining integrity. Despite this common problem structure, there is a wide variety of integrity algorithms, even within the case of RAIM alone. In this paper, we focus on the choice of the detection statistics, and attempt to determine the optimal statistic given a threat model. There are three contributions in this paper. First, we cast the search of the optimal detection region as a mini-max problem. Second, we use the Neyman-Pearson lemma to limit the search of the detection regions to a class of regions parameterized by a bias. Finally, we have shown that in the case of one threat, even multi-dimensional, the optimal detection statistic is the solution separation, that is, the difference between the all-in-view solution and the solution obtained by assuming that the threat might be present.
Published in:	Proceedings of the 2013 International Technical Meeting of The Institute of Navigation January 29 - 27, 2013 Catamaran Resort Hotel San Diego, California
Pages:	262 - 273
Cite this article:	Blanch, Juan, Walter, Todd, Enge, Per, "Results on the Optimal Detection Statistic for Integrity Monitoring," Proceedings of the 2013 International Technical Meeting of The Institute of Navigation, San Diego, California, January 2013, pp. 262-273.
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