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Ronald Mahler

Publications and source records attributed to Ronald Mahler.

8 recordsLinked to original sources
arXiv2025

Generalized Labeled Multi-Bernoulli Filters and Multitarget-Correlation Models

The generalized labeled multi-Bernoulli (GLMB) filter is a theoretically rigorous Bayes-optimal multitarget tracking algorithm with computationally tractable implementations, based on labeled random finite set (LRFS) theory. It presumes that multitarget populations can be approximated using GLMB multitarget probability density functions (p.d.f.'s), which consist of weighted hypotheses regarding the current target-states. A special case of the GLMB p.d.f.-the LMB p.d.f.-presumes that the targets are statistically independent. This paper demonstrates that a) GLMB p.d.f.'s can be interpreted as straightforward generalizations of LMB p.d.f.'s to statistically correlated target populations, given an implicit presumption of "simple labeled correlation" (SLC) models of multitarget correlation; b) the GLMB filter can be reformulated as a SLC-GLMB filter; and c) SLC models seem primarily appropriate for target clusters consisting of small numbers of closely-spaced targets.

stat.ME↗
arXiv2025

The Dynamical Behavior of Detected vs. Undetected Targets

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.

stat.ME↗
arXiv2023

Labeled random finite sets vs. trajectory random finite sets

The paper [12] discussed two approaches for multitarget tracking (MTT): the generalized labeled multi-Bernoulli (GLMB) filter and three Poisson multi-Bernoulli mixture (PMBM) filters. The paper [13] discussed two frameworks for multitarget trajectory representation--labeled random finite set (LRFS) and set of trajectories (SoT)--and the merging of SoT and PMBM into trajectory PMBM (TPMBM) theory. This paper summarizes and augments the main findings of [12], [13]--specifcally, why SoT, PMBM, and TPMBM are physically and mathematically erroneous.

eess.SY↗
arXiv2018

On point processes in multitarget tracking

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."

stat.OT↗
arXiv2017

Measurement-to-Track Association and Finite-Set Statistics

This is a shortened, clarified, and mathematically more rigorous version of the original arXiv version. Its first four findings remain unchanged from the original: 1) measurement-to-track associations (MTAs) in multitarget tracking (MTT) are heuristic and physically erroneous multitarget state models; 2) MTAs occur in the labeled random finite set (LRFS) approach only as purely mathematical abstractions that do not occur singly; 3) the labeled random finite set (LRFS) approach is not a mathematically obfuscated replication of multi-hypothesis tracking (MHT); and 4) the conventional interpretation of MHT is more consistent with classical than Bayesian statistics. This version goes beyond the original in including the following additional main finding: 5) a generalized, RFS-like interpretation results in a correct Bayesian formulation of MHT, based on MTA likelihood functions and MTA Markov transitions/.

stat.ME↗
arXiv2015

The Cauchy-Schwarz divergence for Poisson point processes

In this paper, we extend the notion of Cauchy-Schwarz divergence to point processes and establish that the Cauchy-Schwarz divergence between the probability densities of two Poisson point processes is half the squared $\mathbf{L^{2}}$-distance between their intensity functions. Extension of this result to mixtures of Poisson point processes and, in the case where the intensity functions are Gaussian mixtures, closed form expressions for the Cauchy-Schwarz divergence are presented. Our result also implies that the Bhattachryaa distance between the probability distributions of two Poisson point processes is equal to the square of the Hellinger distance between their intensity measures. We illustrate the result via a sensor management application where the system states are modeled as point processes.

cs.IT↗