A formula for solution separation without subset solutions for advanced RAIM

Advanced RAIM (ARAIM) algorithms developed for aviation can be applied in situations where the probabilities of fault are arbitrarily high. However, with large probabilities, the user receiver needs to protect against a large number of fault modes (which results from the combination of simultaneous independent faults). In baseline ARAIM algorithms, the user receiver must compute a fault tolerant position solution for each fault mode (computed using the subset of the available measurements that would not be affected by the fault mode), or at least its error covariance. After showing how to use a solution separation algorithm without computing the fault tolerant position solutions, we present a technique to obtain upper bounds on the subset error covariance for a given subset size. This upper bound does not require the computation of every subset error covariance, and can be computed without additional matrix inversions. We evaluate the potential of this technique by examining a specific satellite geometry.