Geometric Approximations of Heavy-Tail Effects for Chi-Square Integrity Monitors

Jason H. Rife and John Scott Parker

Peer Reviewed

Abstract:	This paper considers the verification of integrity monitors used commonly in safety-of-life navigation systems. The paper introduces three conservative bounds (also known as overbounds) that can be used to compute missed-detection performance for nominally chi-square integrity monitors subject to random noise with non-Gaussian heavy tails. The three proposed overbounds rely on simple geometric shapes – cones, cylinders, and spheres – to ensure that missed-detection probability can be computed conservatively, reliably, and efficiently. The overbounds provide conservative estimates of missed-detection performance even when the exact form of the noise distribution is not known, so long as the noise CDF is radially symmetric and bounded above and below. Monte Carlo simulations suggest that the spherical overbound performs best for faults inducing a bias of moderate or large magnitude. The cylindrical overbound performs best when the fault-induced bias is small in magnitude.
Published in:	Proceedings of the 2017 International Technical Meeting of The Institute of Navigation January 30 - 2, 2017 Hyatt Regency Monterey Monterey, California
Pages:	536 - 561
Cite this article:	Rife, Jason H., Parker, John Scott, "Geometric Approximations of Heavy-Tail Effects for Chi-Square Integrity Monitors," Proceedings of the 2017 International Technical Meeting of The Institute of Navigation, Monterey, California, January 2017, pp. 536-561. https://doi.org/10.33012/2017.14875
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