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Tracking before detection using partial orders and optimization

Michael Robinson, Michael Stein, Henry S. Owen

TL;DR

This work addresses multi-object tracking under coarse, topological constraints by modeling targets with set-valued dynamics on a topological space and linking observations through a constraint function $C$. The authors develop a tracklet poset $TP_{C}(\mathcal{U})$ and a weighted, batch optimization to extract tracks, inspired by Ford–Fulkerson while enforcing timeline disjointness. They prove sampling-rate-based performance bounds (search-region size and loss of custody) and demonstrate the method on air-traffic ADS-B data and indoor sonar, showing improved track custody and reduced misidentification compared to a Kalman-filter baseline, especially when using a tailored weighting scheme. The approach is robust to feature-poor targets and offers a principled, algorithmic alternative to probabilistic tracking in cluttered or observation-poor environments with practical implications for offline batch analysis.

Abstract

This article addresses the problem of multi-object tracking by using a non-deterministic model of target behaviors with hard constraints. To capture the evolution of target features as well as their locations, we permit objects to lie in a general topological target configuration space, rather than a Euclidean space. We obtain tracker performance bounds based on sample rates, and derive a flexible, agnostic tracking algorithm. We demonstrate our algorithm on two scenarios involving laboratory and field data.

Tracking before detection using partial orders and optimization

TL;DR

This work addresses multi-object tracking under coarse, topological constraints by modeling targets with set-valued dynamics on a topological space and linking observations through a constraint function . The authors develop a tracklet poset and a weighted, batch optimization to extract tracks, inspired by Ford–Fulkerson while enforcing timeline disjointness. They prove sampling-rate-based performance bounds (search-region size and loss of custody) and demonstrate the method on air-traffic ADS-B data and indoor sonar, showing improved track custody and reduced misidentification compared to a Kalman-filter baseline, especially when using a tailored weighting scheme. The approach is robust to feature-poor targets and offers a principled, algorithmic alternative to probabilistic tracking in cluttered or observation-poor environments with practical implications for offline batch analysis.

Abstract

This article addresses the problem of multi-object tracking by using a non-deterministic model of target behaviors with hard constraints. To capture the evolution of target features as well as their locations, we permit objects to lie in a general topological target configuration space, rather than a Euclidean space. We obtain tracker performance bounds based on sample rates, and derive a flexible, agnostic tracking algorithm. We demonstrate our algorithm on two scenarios involving laboratory and field data.
Paper Structure (19 sections, 10 theorems, 24 equations, 12 figures, 1 algorithm)

This paper contains 19 sections, 10 theorems, 24 equations, 12 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Historical discussion
  3. Contributions
  4. Outline of the paper
  5. Constraints and the tracklet poset
  6. Controlling search region size
  7. Target separation
  8. Maintaining custody of timelines
  9. Tracking process flow
  10. Local weighting optimization
  11. Results
  12. Monitoring air traffic
  13. Designing the constraint function
  14. Sample rates for disambiguation
  15. Statistical performance overview
  16. ...and 4 more sections

Key Result

Proposition 8

If $\mathcal{U}$ is a refinement of $\mathcal{V}$ (each $U \in \mathcal{U}$ is a subset of some $V \in \mathcal{V}$) then this induces an order preserving function $TP_C(\mathcal{U}) \to TP_C(\mathcal{V})$.

Figures (12)

  • Figure 1: The timeline and some upsets for Example \ref{['eg:single_target']}
  • Figure 2: Two timelines, observations of them, and their associated tracklet posets. At left, there is aliasing because observations touch both timelines. At right, the observations separate the two timelines, but two different sets of maximal chains exist.
  • Figure 3: Too sparse observations result in misleading tracklet posets
  • Figure 4: A view of the air traffic data with no subsampling, colored by target identity.
  • Figure 5: Distribution of previous and subsequent detections centered on a given detection, aggregated over all targets in the density 4, subsample 4 dataset. The vertical axis of the plot is time offset, while the horizontal axes are latitude and longitude. Vertical displacement is not shown.
  • ...and 7 more figures

Theorems & Definitions (35)

  • Definition 1
  • Definition 2
  • Remark 3
  • Definition 4
  • Remark 5
  • Remark 6
  • Example 7
  • Proposition 8
  • proof
  • Definition 9
  • ...and 25 more