Poisson Multi-Bernoulli Mixture Filter: Direct Derivation and Implementation

We provide a derivation of the Poisson multi-Bernoulli mixture (PMBM) filter for multitarget tracking with the standard point target measurements without using probability generating functionals or functional derivatives. We also establish the connection with the δ-generalized labeled multi-Bernoulli (δ-GLMB) filter, showing that a δ-GLMB density represents a multi-Bernoulli mixture with labeled targets soit can be seen as a special case of PMBM. In addition, we propose an implementation for linear/Gaussian dynamic and measurement models and how to efficiently obtain typical estimators in the literature from the PMBM. The PMBM filter is shown to outperform other filters in the literature in a challenging scenario.