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Predetection fusion can be indispensable for multisensor/multitarget tracking using large networks of low quality sensors. Previously we derived both the "optimal" generalized likelihood ratio test (GLRT) and a more practicable contact-sifting variant. Unfortunately, the gaps between the two in terms both of computation time and performance are not inconsiderable. In this paper we propose an approach, based on random finite sets (RFS) and implemented by Markov chain Monte Carlo (MCMC) simulation, that offers a good balance between run time and metrics for the tracking results.