Improved multi‐target multi‐Bernoulli filter with modelling of spurious targets

The cardinality‐balanced multi‐target multi‐Bernoulli (CBMeMBer) filter removes the positive bias from the data‐updated cardinality estimate in the multi‐target multi‐Bernoulli (MeMBer) filter. In this study, the relationship between the MeMBer corrector and the multi‐Bernoulli random finite set (RFS) distribution is analysed. By utilising this relationship, a filter that offers a new statistical framework for the MeMBer data update process is proposed. Thus, the multi‐Bernoulli RFS distribution is extended to model spurious targets arising from targets under the legacy track set with high probabilities of existence. Unlike the CBMeMBer filter, the proposed filter removes the bias observed in the MeMBer filter by distinguishing spurious targets from actual targets, and while doing this, it does not make any limiting assumption on the probability of target detection. In addition, the modelling of spurious targets allows the refinement of the existence probabilities of targets in light of measurements. As a result, the stability of the cardinality estimate is improved while removing the bias. The theoretical analysis performed on the joint detection and state estimation problem of a single target reveals the strengths and limitations of the proposed filter. In addition, numerical simulations are performed in a scenario involving targets with crossing trajectories to demonstrate the filter performance.