  Multi-Bernoulli mixture (MBM) filter is one of the exact closed-form
multi-target Bayes filters in the random finite sets (RFS) framework, which
utilizes multi-Bernoulli mixture density as the multi-target conjugate prior.
This filter is the variant of Poisson multi-Bernoulli mixture filter when the
birth process is changed to a multi-Bernoulli RFS or a multi-Bernoulli mixture
RFS from a Poisson RFS. On the other hand, labeled multi-Bernoulli mixture
filter evolves to MBM filter when the label is discarded. In this letter, we
provide a complete derivation of MBM filter where the derivation of update step
does not use the probability generating functional. We also describe the
sequential Monte Carlo implementation and adopt Gibbs sampling for truncating
the MBM filtering density. Numerical simulation with a nonlinear measurement
model shows that MBM filter outperforms the classical probability hypothesis
density filter.
