Multi-Bernoulli filter for superpositional sensors

The superpositional sensor model encompasses an important class of sensors such as acoustic sensors and radio-frequency sensors used for multi-target tracking. Recently, random finite set based moment filters such as PHD and CPHD filters have been developed for superpositional sensors. In this paper we derive multi-Bernoulli filter equations for superpositional sensors. The multi-Bernoulli update is derived by defining a conditional PHD for each component of the multi-Bernoulli random finite set and then following an approach similar to that used in deriving the CPHD filter update equation for superpositional sensors. The cardinality distribution is also updated along with the conditional PHD.