From Target Tracking to Targeting Track -- Part I: A Metric for Spatio-Temporal Trajectory Evaluation
This addresses a gap in performance evaluation for target tracking systems, though it appears incremental as it builds on existing trajectory concepts.
The paper tackles the lack of metrics for evaluating trajectory functions of time (FoT) in target tracking by proposing the spatiotemporal-aligned trajectory integral distance (Star-ID), which aligns estimated and actual trajectories to account for errors like false alarms and miss-detections, validated through theoretical analysis and numerical examples.
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.