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

TL;DR

This paper introduces Star-ID, a novel metric for evaluating continuous target trajectories over time, enabling more comprehensive assessment of tracking performance beyond point estimates.

Contribution

It proposes the spatiotemporal-aligned trajectory integral distance (Star-ID), the first metric for comparing full trajectory functions in the spatio-temporal domain.

Findings

Star-ID effectively distinguishes between aligned and unaligned trajectory segments.

The metric accurately captures false alarms, miss-detections, and localization errors.

Validation through theoretical analysis and numerical examples confirms its utility.

Abstract

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.