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The Smooth Trajectory Estimator for LMB Filters

Hoa Van Nguyen, Tran Thien Dat Nguyen, Changbeom Shim, Marzhar Anuar

TL;DR

This work addresses multi-object tracking with fluctuating object counts by enhancing the LMB filter with trajectory smoothing. It exploits the GLMB structure to retain the best association map during GLMB→LMB conversion and performs forward single-object filtering followed by RTS smoothing to recover complete labelled trajectories across their histories, maintaining the first-moment consistency with the GLMB. Empirical results in linear and nonlinear scenarios show STE-LMB delivers substantial gains in cardinality accuracy and OSPA metrics with only a small overhead (under $3.5\%$ of runtime). The approach reduces track fragmentation and label switching, and the authors publish public code to promote adoption in MOT tasks.

Abstract

This paper proposes a smooth-trajectory estimator for the labelled multi-Bernoulli (LMB) filter by exploiting the special structure of the generalised labelled multi-Bernoulli (GLMB) filter. We devise a simple and intuitive approach to store the best association map when approximating the GLMB random finite set (RFS) to the LMB RFS. In particular, we construct a smooth-trajectory estimator (i.e., an estimator over the entire trajectories of labelled estimates) for the LMB filter based on the history of the best association map and all of the measurements up to the current time. Experimental results under two challenging scenarios demonstrate significant tracking accuracy improvements with negligible additional computational time compared to the conventional LMB filter. The source code is publicly available at https://tinyurl.com/ste-lmb, aimed at promoting advancements in MOT algorithms.

The Smooth Trajectory Estimator for LMB Filters

TL;DR

This work addresses multi-object tracking with fluctuating object counts by enhancing the LMB filter with trajectory smoothing. It exploits the GLMB structure to retain the best association map during GLMB→LMB conversion and performs forward single-object filtering followed by RTS smoothing to recover complete labelled trajectories across their histories, maintaining the first-moment consistency with the GLMB. Empirical results in linear and nonlinear scenarios show STE-LMB delivers substantial gains in cardinality accuracy and OSPA metrics with only a small overhead (under of runtime). The approach reduces track fragmentation and label switching, and the authors publish public code to promote adoption in MOT tasks.

Abstract

This paper proposes a smooth-trajectory estimator for the labelled multi-Bernoulli (LMB) filter by exploiting the special structure of the generalised labelled multi-Bernoulli (GLMB) filter. We devise a simple and intuitive approach to store the best association map when approximating the GLMB random finite set (RFS) to the LMB RFS. In particular, we construct a smooth-trajectory estimator (i.e., an estimator over the entire trajectories of labelled estimates) for the LMB filter based on the history of the best association map and all of the measurements up to the current time. Experimental results under two challenging scenarios demonstrate significant tracking accuracy improvements with negligible additional computational time compared to the conventional LMB filter. The source code is publicly available at https://tinyurl.com/ste-lmb, aimed at promoting advancements in MOT algorithms.
Paper Structure (12 sections, 16 equations, 5 figures, 1 algorithm)

This paper contains 12 sections, 16 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Notations
  4. Labelled Random Finite Sets
  5. Generalised Labelled Multi-Bernoulli (GLMB) Filter
  6. The Proposed Method
  7. LMB Filtering Recursion
  8. Smooth Trajectory Estimator for LMB Filter
  9. Experiments
  10. Scenario 1 - Linear
  11. Scenario 2 - Non-Linear
  12. Conclusion

Figures (5)

  • Figure 1: Scenario 1 (Linear): Truth vs Estimates using a) LMB filter, and b) STE-LMB filter.
  • Figure 2: Scenario 1 (Linear) - performance comparison results averaged over $100$ Monte Carlo trials: a) Carnality estimation, b) OSPA distance, and c) OSPA(2) distance.
  • Figure 3: Scenario 2 (Non-Linear): Truth vs Estimates using a) LMB filter, and b) STE-LMB filter.
  • Figure 4: Scenario 2 (Non-Linear) - performance comparison results averaged over $100$ Monte Carlo trials: a) Carnality estimation, b) OSPA distance, and c) OSPA(2) distance.
  • Figure 5: Percentage of the smooth trajectory estimator's computational time in relation to the total filtering time averaged over $100$ Monte Carlo trials.