Multi-object particle filter revisited

Instead of the filtering density, we are interested in the entire posterior density that describes the random set of object trajectories. So far only Markov Chain Monte Carlo (MCMC) technique have been proposed to approximate the posterior distribution of the set of trajectories. Using labeled random finite set we show how the classical multi-object particle filter (a direct generalisation of the standard particle filter to the multi-object case) can be used to recursively compute posterior distribution of the set of trajectories. The result is a generic Bayesian multi-object tracker that does not require re-computing the posterior at every time step nor running a long Markov chain, and is much more efficient than the MCMC approximations.