Multi-target Bayesian filter for propagating marginal distribution

• A multi-target Bayesian filter for propagating marginal distributions is derived.
• An implementation of the novel filter for linear and Gaussian models is proposed.
• Simulation results show that the proposed filter is better than the GM-PHD filter.

The Bayesian filter and its approximation, the probability hypothesis density (PHD) filter, propagate joint distribution of the multi-target state and the first-order moment of the joint distribution, respectively. However, these two filters fail to distinguish multiple distinct targets when these targets are closely spaced. To efficiently distinguish closely spaced targets according to a sequence of measurements, we (1) use the individual state distributions to model the uncertainties of individual target states caused by the target dynamic uncertainty and measurement uncertainty, (2) use the existence probabilities of individual targets to characterize the randomness of target appearance and disappearance, and (3) propose a novel multi-target Bayesian filter. Instead of maintaining the joint state distribution, the proposed filter jointly propagates the marginal distributions and existence probabilities of each target. An implementation of the proposed filter for linear and Gaussian models is also presented to deal with an unknown and variable number of targets. The simulation results demonstrate that the proposed filter is better at distinguishing distinct targets and tracking multiple targets than the Gaussian mixture PHD filter.