Overbounding Risk for Quadratic Monitors With Arbitrary Noise Distributions
Jason H. Rife · IEEE Transactions on Aerospace and Electronic Systems · 2018
This paper derives equations to bound missed-detection and false-alarm probabilities for a quadratic monitor subject to vector noise with an uncertain, non-Gaussian probability density function (PDF). The bounding equation offers utility for the verification of safety-of-life navigation systems, in terms of both robustness and computational efficiency. Robustness is achieved in that the noise PDF need not be known precisely, so long as the PDF can be appropriately bracketed. Computational efficiency is achieved by transforming non-Gaussian PDFs into a Gaussian form that contributes to fast, repeated evaluations across a great many fault scenarios.