Comparing 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 compares 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 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 spherically symmetric. Monte Carlo simulations suggest that, for moderate and large faults, the spherical overbound performs best, but for small faults, the cylindrical overbound performs best, at least in the case of a two-dimensional vector space.
Published in: NAVIGATION: Journal of the Institute of Navigation, Volume 65, Number 3
Pages: 363 - 376
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