Poisson multi-Bernoulli conjugate prior for estimation of both detected and undetected extended objects

Preprint, 2016

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 prediction and update equations are presented for the standard transition density and measurement likelihood. Both the prediction and the update preserve the PMBM form of the density, and in this sense the PMBM density is a conjugate prior. However, the unknown data associations lead to an intractably large number of terms in the PMBM density, and approximations are necessary for tractability. A gamma Gaussian inverse Wishart 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 PHD, CPHD and LMB filters.