Labeled Random Finite Sets With Moment Approximation

The probability hypothesis density (PHD) filter was proposed as a practical approximation of the multitarget Bayes filter. The cardinalized PHD (CPHD) filter improves on the PHD filter by propagating cardinality distribution. However, both the PHD and CPHD filters have limitations in dealing with missed detections, extracting target state in their particle implementations, and maintaining track continuity. In this paper, based on the labeled random finite set theory, r-labeled PHD and CPHD (r-LPHD/LCPHD) filtering approaches, in which the PHD components are separated and uniquely identified by a tag r, are proposed. Based on the information from the r-LPHD/LCPHD filtering processes, new δ-generalized labeled PHD and CPHD filtering approaches are proposed to address the issues in the r-LPHD/LCPHD filters, which are similar to the issues in the standard PHD/CPHD filters. The two proposed methods interact with each other and inherit the advantages of the δ-generalized labeled multi-Bernoulli filter, with substantial savings in computation resources.