Random Finite Sets and Sequential Multi-target Tra

Random finite set provides a rigorous foundation for optimal Bayes multi-target filtering. The major hurdle faced in Bayes multi-target filtering is the inherent computational intractability. 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 this paper, we highlight the relationship between Radon-Nikodym derivative and set derivative of random finite sets that enables a Sequential Monte Carlo (SMC) implementation of the optimal multitarget filter. In addition, a generalised SMC method to implement the PHD filter is also presented. The SMC PHD filter has an attractive feature-its computational complexity is independent of the (time-varying) number of targets.