Explicit filtering equations for labelled random finite sets
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Copyright © 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
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We decompose a probability density function (PDF) of a labelled random finite set (RFS) into a probability mass function over a set of labels and a PDF on a vector-valued multitarget state given the labels. Using this decomposition, we write the Bayesian filtering recursion for labelled RFSs in an explicit form. The resulting formulas are of conceptual and practical interest in the RFS approach to multiple target tracking, especially, for track-before-detect particle filter implementations.
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