Bayes‐optimal tracking of two statistically correlated targets in general clutter

Abstract

The Bernoulli filter is a very general, computationally feasible Bayes-optimal approach for tracking a single disappearing and reappearing target, using a single sensor whose observations are corrupted by missed detections and a known, general point-clutter process. This paper shows how to generalise it to the dyadic labelled random finite set (DLRFS) filter—that is, a very general, computationally feasible Bayes-optimal approach for tracking two disappearing and reappearing and possibly correlated targets, using a single sensor whose observations are corrupted by missed detections and a known, general clutter process. It is further shown that, like the Bernoulli filter, the DLRFS filter is an exact special case of the labelled multitarget recursive Bayes filter (LMRBF)—and thus that, given the target and sensor models, there cannot be a theoretically better tracking filter. The paper also describes the relationship between the DLRFS filter and the (unlabelled) Gauss–Poisson filter of Singh, Vo, Baddeley, and Zuyev.