Poisson multi-Bernoulli conjugate prior for multiple extended object estimation

This paper presents a Poisson multi-Bernoulli mixture (PMBM) conjugate prior for multiple extended object estimation. A Poisson point process is used to describe the existence of yet undetected targets, while a multi-Bernoulli mixture describes the distribution of the targets that have been detected. The conjugacy property allows the posterior PMBM density to be computed exactly, meaning that given enough computational power the PMBM filter is correct. However, in practice, the data association problem requires approximations. The update and the prediction of the PMBM density parameters are presented and are given interpretations, and a simple linear Gaussian implementation is presented along with methods to handle the data association problem. A simulation study shows that the extended target PMBM filter outperforms the extended target cardinalized probability hypothesis density (CPHD) filter in scenarios where the expected number of detections per target per time step is low.