  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 \delta-generalised labelled multi-Bernoulli
(\delta-GLMB) filter, showing that a \delta-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.
