Systems, methods, and media for calculating an overbound distribution, from a base mixture distribution, that can be used with a solution-separation raim algorithm

Abstract

An overbound distribution is calculated from a base mixture distribution. For a bounded region, the base distribution is lower-bound at an evaluation point with a second-order polynomial of the base distribution and upper-bound at the evaluation point with a first-order polynomial of a single distribution with a standard deviation value calculated from the base distribution. If the step size from the evaluation point to an intersection of the lower and upper bounds is less than a threshold, the standard deviation value can be iteratively increased until the step size exceeds the threshold. The process is performed for additional portions of the base distribution up to a critical value to determine a final adjusted standard deviation value for the single distribution that is tightly bound to the base distribution and that can be used by a solution algorithm to determine a solution (used to seed filter states for a navigation filter).