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Exact Closed-Form Multitarget Bayes Filters
1Random Sets LLC, Eagan, MN 55122, USA. MahlerRonald@comcast.net.
Abstract:
The finite-set statistics (FISST) foundational approach to multitarget tracking and information fusion has inspired work by dozens of research groups in at least 20 nations; and FISST publications have been cited tens of thousands of times. This review paper addresses a recent and cutting-edge aspect of this research: exact closed-form-and, therefore, provably Bayes-optimal-approximations of the multitarget Bayes filter. The five proposed such filters-generalized labeled multi-Bernoulli (GLMB), labeled multi-Bernoulli mixture (LMBM), and three Poisson multi-Bernoulli mixture (PMBM) filter variants-are assessed in depth. This assessment includes a theoretically rigorous, but intuitive, statistical theory of "undetected targets", and concrete formulas for the posterior undetected-target densities for the "standard" multitarget measurement model.
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