A Metric for Multi-Target Continuous-Time Trajectory Evaluation

Existing target trackers, as well as the corresponding evaluation metrics, are based on discrete-time point-state estimates. An emerging approach to target tracking is to estimate the continuous-time trajectories that are given by a state function of time and contain more information than discrete-time point estimates, for which a proper metric is still missing. In this study, a fundamental metric called the integral multi-target trajectory assignment (IMTA) distance that is suitable for evaluating the continuous-time curve trajectories is proposed. Based on optimal matching between the estimated and ground-truth trajectories, the localization distance consists of the integral for the time-consistent trajectory parts and the penalty for the trajectory time-inconsistent parts. Furthermore, the cardinality error is also defined to account for the false alarm and mis-detection in the level of a whole trajectory. Theoretical analysis and numerical examples are presented to demonstrate the performance of the proposed metric.