  This paper shows that the Poisson multi-Bernoulli mixture (PMBM) density is a
multi-target conjugate prior for general target-generated measurement
distributions and arbitrary clutter distributions. That is, for this
multi-target measurement model and the standard multi-target dynamic model with
Poisson birth model, the predicted and filtering densities are PMBMs. We derive
the corresponding PMBM filtering recursion. Based on this result, we implement
a PMBM filter for point-target measurement models and negative binomial clutter
density in which data association hypotheses with high weights are chosen via
Gibbs sampling. We also implement an extended target PMBM filter with clutter
that is the union of Poisson-distributed clutter and a finite number of
independent clutter sources. Simulation results show the benefits of the
proposed filters to deal with non-standard clutter.
