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

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. © 2018 Institute of Navigation

Applying sensor integrity concepts to detect intermittent bugs in aviation software

“…Overbounding is a common procedure used in aviation applications to conservatively model distributions for unknown fault modes. [29][30][31][32] As a starting point, it can be useful to assume that the distribution of the features is similar whether or not the bug is present, and that the bug simply acts to shift the mean of the feature-vector distribution. Given that the structure of the buggy and bug-free distributions may be different in the general case (as illustrated in Figure 4), this assumption that the bug only shifts the distribution mean without otherwise affecting distribution shape is clearly an approximation, one that should be revisited in future work.…”