Bounding Integrity Risk and False Alert Probability Over Exposure Time Intervals

This paper investigates the impact of the autocorrelations of monitor test statistics on navigation integrity and continuity. General analytical methods are rigorously developed to evaluate the actual integrity risk and false alert probability over the exposure interval. Prior to this work, the probabilities computed based on one-sample test have been widely applied in aviation navigation. However, it will be shown that using the one-sample probability may lead to overly optimistic results, because the actual risk can be significantly higher, especially for false alert. The new methods are applied to an example problem of advanced receiver autonomous integrity monitoring. To quantify integrity, a simple but conservative upper bound is derived. As for continuity, both analytical and experimental results show that the actual false alert probability is two orders of magnitude higher than previously thought, due to the time-correlation effects. A feasible solution to mitigate this impact is provided, without degrading navigation availability.