Sequential Monte Carlo methods for multi-target filtering with random finite sets

Random finite sets (RFSs) are natural representations of multi-target states and observations that allow multi-sensor multi-target filtering to fit in the unifying random set framework for data fusion. Although the foundation has been established in the form of finite set statistics (FISST), its relationship to conventional probability is not clear. Furthermore, optimal Bayesian multi-target filtering is not yet practical due to the inherent computational hurdle. Even the probability hypothesis density (PHD) filter, which propagates only the first moment (or PHD) instead of the full multi-target posterior, still involves multiple integrals with no closed forms in general. This article establishes the relationship between FISST and conventional probability that leads to the development of a sequential Monte Carlo (SMC) multi-target filter. In addition. an SMC implementation of the PHD filter is proposed and demonstrated on a number of simulated scenarios. Both of the proposed filters are suitable for problems involving nonlinear non-Gaussian dynamics. Convergence results for these filters are also established. © 2005 IEEE