Abstract
The 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 the Radon-Nikodym derivative and the 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.
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