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Random finite sets (RFSs) are natural representations of multitarget states and observations that allow multisensor multitarget 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 multitarget 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 multitarget 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) multitarget 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 nonGaussian dynamics. Convergence results for these filters are also established.