Particle filter processing of out-of-sequence measurements: Exact Bayesian solution

This paper considers the problem of out-of-sequence measurement (OOSM) processing when the filtering technique used at the tracker is a particle filter (PF). First, the exact Bayesian algorithm for updating with OOSMs is derived. Then, the PF implementation of the exact Bayesian algorithm, called A-PF, is developed. Since A-PF is rooted in exact Bayesian inference, if the number of particles is sufficiently large, A-PF is the one (and the only one) that is able to achieve the optimal performance obtained from the in-sequence processing. This is confirmed by the simulation results. Also, it is shown that the performance of A-PF is always superior to previous (heuristic) PF-based algorithms with the same number of particles.