Multi-Bernoulli filter and hybrid multi-Bernoulli CPHD filter for superpositional sensors

Superpositional sensor model can characterize the observations in many different applications such as radio frequency tomography, acoustic sensor network based tracking and wireless communications. In this paper we present two filters based on the random finite set (RFS) theory the multi-Bernoulli filter and its variant the hybrid multi-Bernoulli CPHD filter for superpositional sensors. We provide derivations for the filter update equations which are based on propagating the conditional probability hypothesis density (PHD). The conditional PHD is defined for the individual Bernoulli components of the multiBernoulli RFS and for the independent and identically distributed cluster (IIDC) RFS. Computationally tractable update equations are derived by assuming the sensor noise to be Gaussian. The filters are used for multitarget tracking in simulated radio frequency (RF) tomography application.