On point processes in multitarget tracking

TL;DR

This paper critically examines the foundations of point process methods in multitarget tracking, revealing that non-RFS approaches are flawed, and clarifies the relationship between FISST and other purported frameworks, exposing misattributions and errors.

Contribution

It demonstrates that non-RFS point processes are incorrect for multitarget tracking and clarifies that the so-called point process approach is essentially a rephrasing of FISST with misattributions.

Findings

Non-RFS point processes are phenomenologically incorrect for multitarget tracking.

Most equations and concepts in JAIF appeared originally in FISST publications.

FISST is not due to Moyal and the point process approach is a rephrasing of FISST.

Abstract

The finite-set statistics (FISST) approach to multitarget tracking was introduced in the mid-1990s. Its current extended form dates from 2001. In 2008, an "elementary" alternative to FISST was proposed, based on "finite point processes" rather than RFS's. This was accompanied by single-sensor and multisensor versions of a claimed generalization of the PHD filter, the "iFilter." Then in 2013 in the Journal of Advances in Information Fusion (JAIF) and elsewhere, the same author went on to claim that the FISST p.g.fl./functional derivative approach is actually "due to" (a "corollary" of) a 50-year-old pure-mathematics paper by Moyal; and described a "point process" p.g.fl./functional derivative approach to multitarget tracking supposedly based on it. In this paper it is shown that: (1)non-RFS point processes are a phenomenologically erroneous foundation for multitarget tracking; (2) nearly every equation, concept, discussion, derivation, and methodology in the JAIF paper originally appeared in FISST publications, without being so attributed; (3) FISST cannot possibly be "due to Moyal"; (4) the "point process" approach described in JAIF differs from FISST only in regard to terminology and notation, and thus in this sense appears to be an obscured, phenomenologically erroneous, and improperly attributed copy of FISST. It is also shown that the derivations of the single-sensor and multisensory iFilter appear to have had major errors, as did a subsequent recasting of the multisensor iFilter as a "traffic mapping filter."