RAIM with Optimal Integrity and Continuity Allocations Under Multiple Failures

Among the receiver autonomous integrity monitoring (RAIM) algorithms treating multiple failures, multiple hypothesis solution separation algorithms (MHSS) - a type of solution separation algorithm - offer several advantages: First, the link between threat model, upper bound on the position error - the protection level and probability of hazardously misleading information is an easy and straightforward one; second, the calculation of the protection level does not involve complex steps. One of the critical steps in this algorithm is the allocation of the integrity and continuity budgets among the failure modes, as it determines the overall performance of the algorithm. After describing the baseline MHSS approach, we present an algorithm that simultaneously allocates the integrity and continuity budget among the failure modes to obtain the minimum protection level per satellite geometry. Then, we show how slope-based RAIM and solution separation RAIM are related through a little-known formula, which both unifies and highlights the differences between the two approaches. Finally, we apply the algorithm to evaluate the performance of RAIM for vertical guidance for a dual constellation, and find that even with a very large prior probability of satellite failure, vertical guidance can be achieved worldwide with high availability.