# A metric on the space of finite sets of trajectories for evaluation of multi-target tracking algorithms

arXiv: https://arxiv.org/abs/1605.01177 · HTML: https://mlsanity.com/paper/1605.01177/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2016.

## Built on by (most cited first, 17 of 17)

- [A time-weighted metric for sets of trajectories to assess multi-object tracking algorithms](https://mlsanity.com/paper/2110.13444/) (2021)
- [Graph GOSPA metric: a metric to measure the discrepancy between graphs of different sizes](https://mlsanity.com/paper/2311.07596/) (2023)
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- [Trajectory Poisson multi-Bernoulli mixture filter for traffic monitoring using a drone](https://mlsanity.com/paper/2306.16890/) (2023)
- [TGOSPA Metric Parameters Selection and Evaluation for Visual Multi-object Tracking](https://mlsanity.com/paper/2412.08321/) (2024)
- [From Target Tracking to Targeting Track -- Part I: A Metric for Spatio-Temporal Trajectory Evaluation](https://mlsanity.com/paper/2502.15842/) (2025)
- [Continuous-discrete multiple target tracking with out-of-sequence measurements](https://mlsanity.com/paper/2106.04898/) (2021)
- [Fast computation of the TGOSPA metric for multiple target tracking via unbalanced optimal transport](https://mlsanity.com/paper/2503.09449/) (2025)
- [SelectTSL: Prompt-Guided Selective Target Sound Localization in Complex Scenarios](https://mlsanity.com/paper/2607.02343/) (2026)
- [Extended Object Tracking Using Sets Of Trajectories with a PHD Filter](https://mlsanity.com/paper/2109.01019/) (2021)
- [Deep Fusion of Multi-Object Densities Using Transformer](https://mlsanity.com/paper/2209.08857/) (2022)
- [Attention-Bayesian Hybrid Approach to Modular Multiple Particle Tracking](https://mlsanity.com/paper/2506.09441/) (2025)
- [A family of graph GOSPA metrics for graphs with different sizes](https://mlsanity.com/paper/2506.17316/) (2025)
- [GOSPA and T-GOSPA quasi-metrics for evaluation of multi-object tracking algorithms](https://mlsanity.com/paper/2507.13706/) (2025)
- [Model-based Multi-object Visual Tracking: Identification and Standard Model Limitations](https://mlsanity.com/paper/2508.13647/) (2025)
- [Beyond Chamfer Distance: Granular Order-aware Evaluation Metric For Online Mapping](https://mlsanity.com/paper/2605.22578/) (2026)
- [Causal neural set filtering for online multi-target tracking](https://mlsanity.com/paper/2609.16054/) (2026)

## Abstract (arXiv)

In this paper, we propose a metric on the space of finite sets of trajectories for assessing multi-target tracking algorithms in a mathematically sound way. The main use of the metric is to compare estimates of trajectories from different algorithms with the ground truth of trajectories. The proposed metric includes intuitive costs associated to localization error for properly detected targets, missed and false targets and track switches at each time step. The metric computation is based on solving a multi-dimensional assignment problem. We also propose a lower bound for the metric, which is also a metric for sets of trajectories and is computable in polynomial time using linear programming. We also extend the proposed metrics on sets of trajectories to random finite sets of trajectories.