The Dynamical Behavior of Detected vs. Undetected Targets

TL;DR

This paper critically examines the Poisson multi-Bernoulli mixture approach for detected versus undetected targets, proposing a new single-step recursive Bayes filter and verifying key formulas algebraically, challenging previous claims about parallel propagation.

Contribution

It introduces a novel single-step MRBF for U/D targets and verifies key formulas algebraically, clarifying the limitations of PMBM filters for separate target propagation.

Findings

PMBM approach cannot be rigorously formulated with existing MRBF methods

A new single-step MRBF can partially salvage the approach

Algebraic verification of U/D formulas confirms previous results

Abstract

This paper is a sequel of the 2019 paper [5]. It demonstrates the following: a) the Poisson multi-Bernoulli mixture (PMBM) approach to detected vs. undetected (U/D) targets cannot be rigorously formulated using either the two-step or single-step multitarget recursive Bayes filter (MRBF); b) it can, however, be partially salvaged using a novel single-step MRBF; c) probability hypothesis density (PHD) filters can be derived for both the original "S-U/D" approach in [5] and the novel "D-U/D" approach; d) important U/D formulas in [5] can be verified using purely algebraic methods rather than the intricate statistical analysis employed in that paper; and e) the claim, that PMBM filters can propagate detected and undetected targets separately in parallel, is doubtful.