From target tracking to targeting track — part I: a metric for spatio-temporal trajectory evaluation

In the realm of target tracking, performance evaluation plays a pivotal role in the design, comparison, and analysis of trackers. Compared with the traditional trajectory composed of a finite set of point estimates obtained by a tracker at the discrete measurement time instants, the trajectory that our series of studies pursued is given by a curve function of time (FoT). This approach takes root in modeling the states of the target in times series as a stochastic process (SP) and the trajectory FoT (T-FoT) represents the deterministic part of this SP. The T-FoT provides the 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 T-FoT. To address this lacuna, this paper, as the first part of a series of companion papers, proposes a metric denominated as the spatio-temporal-aligned trajectory integral distance (Star-ID). The Star-ID associates and aligns the estimated and actual trajectories in the spatio-temporal domain and distinguishes between the time-aligned and unaligned segments in calculating false alarm, miss-detection and localization errors. The effectiveness of the Star-ID and its time-averaged measure is validated through theoretical analysis, sanity test and simulation of single target or multiple target tracking.