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Arithmetic Average Density Fusion -- Part III: Heterogeneous Unlabeled and Labeled RFS Filter Fusion

Tiancheng Li, Ruibo Yan, Kai Da, Hongqi Fan

TL;DR

The paper tackles scalable multisensor multitarget tracking when sensors employ heterogeneous RFS filters (unlabeled PHD, MB, and LMB). It proposes an approximate GM-PHD-AA fusion where only Gaussian-component weights are tuned via a coordinate-descent ISD-minimization to achieve PHD consensus across filters, enabling efficient, parallel fusion without label matching. Simulation results show significant PHD improvements in both homogeneous and heterogeneous settings, with MB/LMB gains limited by track-level label fusion challenges, highlighting the need for trackwise B2B association in future work. The work advances practical heterogeneous fusion by leveraging GM representations and an adaptive, low-cost weight-fitting mechanism, offering scalable performance boosts for real-world sensor networks.

Abstract

This paper proposes a heterogenous density fusion approach to scalable multisensor multitarget tracking where the inter-connected sensors run different types of random finite set (RFS) filters according to their respective capacity and need. These diverse RFS filters result in heterogenous multitarget densities that are to be fused with each other in a proper means for more robust and accurate detection and localization of the targets. Our approach is based on Gaussian mixture implementations where the local Gaussian components (L-GCs) are revised for PHD consensus, i.e., the corresponding unlabeled probability hypothesis densities (PHDs) of each filter best fit their average regardless of the specific type of the local densities. To this end, a computationally efficient, coordinate descent approach is proposed which only revises the weights of the L-GCs, keeping the other parameters unchanged. In particular, the PHD filter, the unlabeled and labeled multi-Bernoulli (MB/LMB) filters are considered. Simulations have demonstrated the effectiveness of the proposed approach for both homogeneous and heterogenous fusion of the PHD-MB-LMB filters in different configurations.

Arithmetic Average Density Fusion -- Part III: Heterogeneous Unlabeled and Labeled RFS Filter Fusion

TL;DR

The paper tackles scalable multisensor multitarget tracking when sensors employ heterogeneous RFS filters (unlabeled PHD, MB, and LMB). It proposes an approximate GM-PHD-AA fusion where only Gaussian-component weights are tuned via a coordinate-descent ISD-minimization to achieve PHD consensus across filters, enabling efficient, parallel fusion without label matching. Simulation results show significant PHD improvements in both homogeneous and heterogeneous settings, with MB/LMB gains limited by track-level label fusion challenges, highlighting the need for trackwise B2B association in future work. The work advances practical heterogeneous fusion by leveraging GM representations and an adaptive, low-cost weight-fitting mechanism, offering scalable performance boosts for real-world sensor networks.

Abstract

This paper proposes a heterogenous density fusion approach to scalable multisensor multitarget tracking where the inter-connected sensors run different types of random finite set (RFS) filters according to their respective capacity and need. These diverse RFS filters result in heterogenous multitarget densities that are to be fused with each other in a proper means for more robust and accurate detection and localization of the targets. Our approach is based on Gaussian mixture implementations where the local Gaussian components (L-GCs) are revised for PHD consensus, i.e., the corresponding unlabeled probability hypothesis densities (PHDs) of each filter best fit their average regardless of the specific type of the local densities. To this end, a computationally efficient, coordinate descent approach is proposed which only revises the weights of the L-GCs, keeping the other parameters unchanged. In particular, the PHD filter, the unlabeled and labeled multi-Bernoulli (MB/LMB) filters are considered. Simulations have demonstrated the effectiveness of the proposed approach for both homogeneous and heterogenous fusion of the PHD-MB-LMB filters in different configurations.
Paper Structure (26 sections, 1 theorem, 39 equations, 14 figures)

This paper contains 26 sections, 1 theorem, 39 equations, 14 figures.

Table of Contents

  1. Introduction
  2. Preliminaries: PHD, MB and LMB
  3. Basic MSMT Scenario
  4. RFS Modeling
  5. PHD of the Poisson, MB and LMB
  6. Poisson RFS
  7. MB
  8. LMB
  9. PHD-AA Consistency
  10. GM Representations of MB/LMB-PHD
  11. GM-PHD
  12. GM Representation of the MB PHD
  13. GM Representation of the LMB PHD
  14. GM-PHD Fit via Optimizing L-GC Weights
  15. Minimizing ISD of GMs via Reweighting
  16. ...and 11 more sections

Key Result

Lemma 1

Relaxing the non-negative constraint for the weights $\omega_{i,k}^{(j)}\geq 0$, eq:WeightISDfit can be solved by, $\forall i \in \mathcal{I}, j=1,...,J_{i,k}$, where $\Delta = {\left| {2 \bm{\Sigma}_{i,k}^{(j)} } \right|}^{1/2} { (2\pi )}^{d/2}$ and $\mathcal{J}_i^{-j} = \{1,..,J_{i,k}\} \setminus j$.

Figures (14)

  • Figure 1: A heterogenous RFS filter cooperation scenario based on unlabeled PHD-AA fusion
  • Figure 2: A MB filter reaches PHD consensus with a PHD filter
  • Figure 3: Four LMBs of the same unlabeled PHD but different labeled PHDs and different potential target-state-estimates.
  • Figure 4: ROI and target trajectories starting from $\circ$ and ending at $\triangle$
  • Figure 5: True tracks, measurements and target position estimates in one run by a local GM-PHD filter
  • ...and 9 more figures

Theorems & Definitions (5)

  • Remark 1
  • Lemma 1
  • proof
  • Remark 2
  • Remark 3