Poisson multi-Bernoulli mixture filter: direct derivation and implementation
This work addresses multi-target tracking for applications like surveillance, but it is incremental as it builds on existing PMBM and δ-GLMB filters.
The paper tackles the problem of multi-target tracking by deriving the Poisson multi-Bernoulli mixture (PMBM) filter without using complex mathematical tools, and shows it outperforms other filters in a challenging scenario.
We provide a derivation of the Poisson multi-Bernoulli mixture (PMBM) filter for multi-target tracking with the standard point target measurements without using probability generating functionals or functional derivatives. We also establish the connection with the δ-generalised labelled multi-Bernoulli (δ-GLMB) filter, showing that a δ-GLMB density represents a multi-Bernoulli mixture with labelled targets so it 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.