Marginal multi-Bernoulli filters (extended version)

Random finite sets (RFSs) has been a fruitful area of research in recent years, yielding new approximate methods for multiple target tracking such as the probability hypothesis density (PHD), cardinalised PHD (CPHD), and multiple target multi-Bernoulli (MeMBer) filters. These new approaches have largely been based on approximations that side-step the need for measurement-to-track association in order to maintain tractability. In this paper, we derive a conjugate prior form for the full Bayes RFS filter under commonly invoked assumptions. We observe that data association is implicitly present in the form, and obtain alternative algorithms by approximating the discrete distribution of joint association events utilising a recently developed, high quality approximation of marginal association probabilities. The two resulting algorithms maintain a hybrid MeMBer/Poisson distribution of objects, but form Bernoulli components differently to the conventional MeMBer filter. The track-oriented marginal MeMBer/Poisson (TOM-MeMBer/P) is shown to be closely related to a variant of the popular joint integrated probabilistic data association (JIPDA) algorithm. The measurement oriented MeMBer/P (MOM-MeMer/P) adopts the structure of the MeMBer filter (collecting all hypotheses utilising a given measurement into a single multi-Bernoulli component), but uses marginal association probabilities to provide a significant improvement to performance in low probability of detection cases. We demonstrate both the performance and tractability of the filters in a challenging scenario involving multiple targets in close proximity.