# GOSPA and T-GOSPA quasi-metrics for evaluation of multi-object tracking algorithms

arXiv: https://arxiv.org/abs/2507.13706 · HTML: https://mlsanity.com/paper/2507.13706/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 55 references that are in the map.
- First posted on arXiv 18 Jul 2025.

## Builds on (most cited first, 17 of 17)

- [nuScenes: A multimodal dataset for autonomous driving](https://mlsanity.com/paper/1903.11027/) (2019)
- [HOTA: A Higher Order Metric for Evaluating Multi-Object Tracking](https://mlsanity.com/paper/2009.07736/) (2020)
- [Optimal Goal-Reaching Reinforcement Learning via Quasimetric Learning](https://mlsanity.com/paper/2304.01203/) (2023)
- [Generalized optimal sub-pattern assignment metric](https://mlsanity.com/paper/1601.05585/) (2016)
- [Poisson multi-Bernoulli mixture filter: direct derivation and implementation](https://mlsanity.com/paper/1703.04264/) (2017)
- [A metric on the space of finite sets of trajectories for evaluation of multi-target tracking algorithms](https://mlsanity.com/paper/1605.01177/) (2016)
- [On the Learning and Learnability of Quasimetrics](https://mlsanity.com/paper/2206.15478/) (2022)
- [Multiple target tracking based on sets of trajectories](https://mlsanity.com/paper/1605.08163/) (2016)
- [Trajectory Poisson multi-Bernoulli filters](https://mlsanity.com/paper/2003.12767/) (2020)
- [A metric for sets of trajectories that is practical and mathematically consistent](https://mlsanity.com/paper/1601.03094/) (2016)
- [A time-weighted metric for sets of trajectories to assess multi-object tracking algorithms](https://mlsanity.com/paper/2110.13444/) (2021)
- [Poisson Multi-Bernoulli Mixtures for Sets of Trajectories](https://mlsanity.com/paper/1912.08718/) (2019)
- [An efficient, variational approximation of the best fitting multi-Bernoulli filter](https://mlsanity.com/paper/1403.5022/) (2014)
- [Probabilistic GOSPA: A Metric for Performance Evaluation of Multi-Object Filters with Uncertainties](https://mlsanity.com/paper/2412.11482/) (2024)
- [From Target Tracking to Targeting Track -- Part I: A Metric for Spatio-Temporal Trajectory Evaluation](https://mlsanity.com/paper/2502.15842/) (2025)
- [Fast computation of the TGOSPA metric for multiple target tracking via unbalanced optimal transport](https://mlsanity.com/paper/2503.09449/) (2025)
- [Probabilistic Trajectory GOSPA: A Metric for Uncertainty-Aware Multi-Object Tracking Performance Evaluation](https://mlsanity.com/paper/2506.15148/) (2025)

## Abstract (arXiv)

This paper introduces two quasi-metrics for performance assessment of multi-object tracking (MOT) algorithms. One quasi-metric is an extension of the generalised optimal subpattern assignment (GOSPA) metric and measures the discrepancy between sets of objects. The other quasi-metric is an extension of the trajectory GOSPA (T-GOSPA) metric and measures the discrepancy between sets of trajectories. Similar to the GOSPA-based metrics, these quasi-metrics include costs for localisation error for properly detected objects, the number of false objects and the number of missed objects. The T-GOSPA quasi-metric also includes a track switching cost. Differently from the GOSPA and T-GOSPA metrics, the proposed quasi-metrics have the flexibility of penalising missed and false objects with different costs, and the localisation costs are not required to be symmetric. We also explain how to obtain similarity score functions based on these quasi-metrics. The performance of several Bayesian MOT algorithms is assessed with the T-GOSPA quasi-metric via simulations.