Title: Derivation of Spherical Overbounding for Quadratic Integrity Monitors with Non Gaussian Random Inputs
Author(s): Jason H. Rife
Published in: Proceedings of the 30th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2017)
September 25 - 29, 2017
Oregon Convention Center
Portland, Oregon
Pages: 2467 - 2476
Cite this article: Rife, Jason H., "Derivation of Spherical Overbounding for Quadratic Integrity Monitors with Non Gaussian Random Inputs," Proceedings of the 30th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2017), Portland, Oregon, September 2017, pp. 2467-2476.
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Abstract: Vector integrity monitors are commonly used for online verification of signal quality in safety-critical navigation systems. This paper derives a conservative bound on the missed-detection performance for a vector integrity monitor with a non-Gaussian noise probability density function (PDF). Specifically, the derivation concerns warping an arbitrary non-Gaussian PDF into a spherically symmetric Gaussian, and then approximating the volume of integration as a hypersphere. The end result is a relatively tight bound that is easily and efficiently evaluated using noncentral chi-square distribution functions, which are widely implemented in common numerical packages.