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Augmented LRFS-based Filter: Holistic Tracking of Group Objects

Chaoqun Yang, Xiaowei Liang, Zhiguo Shi, Heng Zhang, Xianghui Cao

TL;DR

The paper tackles group object tracking (GOT) by extending labeled random finite sets (LRFS) to augmented LRFSs that embed group information directly into object labels. It then derives an augmented LRFS-based multi-object Bayes filter, specifically an Agugmented LMB RFS, ensuring that group structure, object states, and identities are propagated and updated jointly. A group-information update step uses an adjacency-graph approach to partition Bernoulli items into groups and assign geometry centers, enabling simultaneous estimation of states, labels, and group structure. Numerical simulations demonstrate that the proposed framework yields improved tracking performance and accurate group-number estimation over traditional LMB methods, validating a holistic GOT approach with potential for partially resolvable GOT scenarios.

Abstract

This paper addresses the problem of group target tracking (GTT), wherein multiple closely spaced targets within a group pose a coordinated motion. To improve the tracking performance, the labeled random finite sets (LRFSs) theory is adopted, and this paper develops a new kind of LRFSs, i.e., augmented LRFSs, which introduces group information into the definition of LRFSs. Specifically, for each element in an LRFS, the kinetic states, track label, and the corresponding group information of its represented target are incorporated. Furthermore, by means of the labeled multi-Bernoulli (LMB) filter with the proposed augmented LRFSs, the group structure is iteratively propagated and updated during the tracking process, which achieves the simultaneously estimation of the kinetic states, track label, and the corresponding group information of multiple group targets, and further improves the GTT tracking performance. Finally, simulation experiments are provided, which well demonstrates the effectiveness of the labeled multi-Bernoulli filter with the proposed augmented LRFSs for GTT tracking.

Augmented LRFS-based Filter: Holistic Tracking of Group Objects

TL;DR

The paper tackles group object tracking (GOT) by extending labeled random finite sets (LRFS) to augmented LRFSs that embed group information directly into object labels. It then derives an augmented LRFS-based multi-object Bayes filter, specifically an Agugmented LMB RFS, ensuring that group structure, object states, and identities are propagated and updated jointly. A group-information update step uses an adjacency-graph approach to partition Bernoulli items into groups and assign geometry centers, enabling simultaneous estimation of states, labels, and group structure. Numerical simulations demonstrate that the proposed framework yields improved tracking performance and accurate group-number estimation over traditional LMB methods, validating a holistic GOT approach with potential for partially resolvable GOT scenarios.

Abstract

This paper addresses the problem of group target tracking (GTT), wherein multiple closely spaced targets within a group pose a coordinated motion. To improve the tracking performance, the labeled random finite sets (LRFSs) theory is adopted, and this paper develops a new kind of LRFSs, i.e., augmented LRFSs, which introduces group information into the definition of LRFSs. Specifically, for each element in an LRFS, the kinetic states, track label, and the corresponding group information of its represented target are incorporated. Furthermore, by means of the labeled multi-Bernoulli (LMB) filter with the proposed augmented LRFSs, the group structure is iteratively propagated and updated during the tracking process, which achieves the simultaneously estimation of the kinetic states, track label, and the corresponding group information of multiple group targets, and further improves the GTT tracking performance. Finally, simulation experiments are provided, which well demonstrates the effectiveness of the labeled multi-Bernoulli filter with the proposed augmented LRFSs for GTT tracking.
Paper Structure (22 sections, 6 theorems, 39 equations, 10 figures, 1 table)

This paper contains 22 sections, 6 theorems, 39 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. Proposed Augmented LRFS
  3. RFSs $\&$ LRFSs
  4. Augmented LRFS
  5. Agugmented LMB RFS
  6. Statistical Characteristic of Augmented LRFS
  7. Agugmented GLMB RFS
  8. System Model
  9. Dynamic Model
  10. Measurement Model
  11. The Objective of This Paper
  12. Augmented LRFS-based Filter for GOT Problem
  13. Multi-object Likelihood Function
  14. Multi-object Transition Kernel
  15. Augmented LRFS-based Filter
  16. ...and 7 more sections

Key Result

Proposition 1

An augmented LRFS with state space $\mathbb{X}$ and label space $\mathbb{L}$, i.e., $\mathsf{X}$ denoted in (alrf), essentially is an RFS on the space $\mathbb{X} \times \mathbb{L}$.

Figures (10)

  • Figure 1: The diagram of the dynamics of group structure, including group split, merge, die and rebuild.
  • Figure 2: The considered GOT scenario.
  • Figure 3: The entire schematic of the step of group information update.
  • Figure 4: An example for group information extraction, where T$i$ denotes the $i$-th object.
  • Figure 5: The trajectories of objects.
  • ...and 5 more figures

Theorems & Definitions (12)

  • Definition 1
  • Definition 2
  • Proposition 1
  • Proof 1
  • Proposition 2
  • Proof 2
  • Proposition 3
  • Proof 3
  • Lemma 1
  • Proof 4
  • ...and 2 more