# From Target Tracking to Targeting Track -- Part I: A Metric for Spatio-Temporal Trajectory Evaluation

arXiv: https://arxiv.org/abs/2502.15842 · HTML: https://mlsanity.com/paper/2502.15842/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 54 references that are in the map.
- First posted on arXiv 20 Feb 2025.

## Builds on (most cited first, 13 of 13)

- [Generalized optimal sub-pattern assignment metric](https://mlsanity.com/paper/1601.05585/) (2016)
- [A metric on the space of finite sets of trajectories for evaluation of multi-target tracking algorithms](https://mlsanity.com/paper/1605.01177/) (2016)
- [How Trustworthy are Performance Evaluations for Basic Vision Tasks?](https://mlsanity.com/paper/2008.03533/) (2020)
- [Multiple target tracking based on sets of trajectories](https://mlsanity.com/paper/1605.08163/) (2016)
- [Continuous-Time State Estimation Methods in Robotics: A Survey](https://mlsanity.com/paper/2411.03951/) (2024)
- [An Uncertainty-Aware Performance Measure for Multi-Object Tracking](https://mlsanity.com/paper/2108.04619/) (2021)
- [Spatio-Temporal Trajectory Similarity Measures: A Comprehensive Survey and Quantitative Study](https://mlsanity.com/paper/2303.05012/) (2023)
- [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)
- [Joint Smoothing, Tracking, and Forecasting Based on Continuous-Time Target Trajectory Fitting](https://mlsanity.com/paper/1708.02196/) (2017)
- [From Target Tracking to Targeting Track: A Data-Driven Yet Analytical Approach to Joint Target Detection and Tracking](https://mlsanity.com/paper/2104.11122/) (2021)
- [Graph GOSPA metric: a metric to measure the discrepancy between graphs of different sizes](https://mlsanity.com/paper/2311.07596/) (2023)
- [Track Coalescence and Repulsion in Multitarget Tracking: An Analysis of MHT, JPDA, and Belief Propagation Methods](https://mlsanity.com/paper/2308.06326/) (2023)

## Built on by (most cited first, 2 of 2)

- [From Target Tracking to Targeting Track -- Part III: Stochastic Process Modeling and Online Learning](https://mlsanity.com/paper/2503.05799/) (2025)
- [GOSPA and T-GOSPA quasi-metrics for evaluation of multi-object tracking algorithms](https://mlsanity.com/paper/2507.13706/) (2025)

## Abstract (arXiv)

In the realm of target tracking, performance evaluation plays a pivotal role in the design, comparison, and analytics of trackers. Compared with the traditional trajectory composed of a set of point-estimates obtained by a tracker in the measurement time-series, the trajectory that our series of studies including this paper pursued is given by a curve function of time (FoT). The trajectory FoT provides complete information of the movement of the target over time and can be used to infer the state corresponding to arbitrary time, not only at the measurement time. However, there are no metrics available for comparing and evaluating the trajectory FoT. To address this lacuna, we propose a metric denominated as the spatiotemporal-aligned trajectory integral distance (Star-ID). The StarID associates and aligns the estimated and actual trajectories in the spatio-temporal domain and distinguishes between the time-aligned and unaligned segments in calculating the spatial divergence including false alarm, miss-detection and localization errors. The effectiveness of the proposed distance metric and the time-averaged version is validated through theoretical analysis and numerical examples of a single target or multiple targets.