A cardinality preserving multitarget multi-Bernoulli RFS tracker

This paper proposes a novel multitarget multi-Bernoulli (MeMBer) random finite set (RFS) posterior density recursion that preserves the cardinality probability mass function (pmf) upon update. The proposed recursion propagates the posterior density of a MeMBer RFS that is parameterized by target existence probabilities and marginal densities, that are assumed independent. At update, the exact posterior is derived via marginalization over a set of global (measurement dependent) hypotheses. However, it is shown that the independent existence probability assumption is violated in the exact posterior. In order to alleviate this problem, an approach inspired by the recently proposed set-joint probabilistic data association (SJPDA) filter is proposed to modify the exact posterior to another density within the same RFS family that contains independent existence probabilities. Furthermore, this approach is designed to preserve the cardinality pmf, without affecting mean optimal subpattern assignment (MOSPA) results. The proposed recursion is general, i.e., it does not make any assumptions about target distribution models. Furthermore, it is proved that when the number of existing targets is not more than two, the described modification of the posterior can always be made. Future work entails the extension of the proof by relaxing the constraint on the number of targets.