Amplitude-Aided PHD Filtering for Unresolved Swarm Tracking

This paper deals with tracking of swarm targets composed of groups of possibly unresolved, spatially dense, and similar individuals. Existing multi-target tracking methods focus on tracking each individual and maintaining its separate trajectory. However, given limited resolution of practical sensors, we argue that it is neither feasible nor necessary to allocate resources to perform such tracking. Instead, it is better to focus on tracking a swarm - such as its centroid, distribution of individuals, population size, and shape, thus providing a higher-level understanding of the swarm behavior and situational context. To this end, our analysis indicates that the probability hypothesis density (PHD) filter is a potential solution, although its existing variants are not well suited for swarm targets. We therefore propose an amplitude information-aided PHD (AIA-PHD) filter. By incorporating amplitude information, we develop a measurement equivalent decomposition. This decomposition establishes a one-to-one correspondence between individuals and pseudo-measurements, enabling the AIA-PHD filter to capture the spatial distribution of swarm targets more effectively via its intensity function. Furthermore, we develop a Gaussian mixture implementation of the proposed filter and present an algorithm for swarm tracking. Finally, the efficacy and robustness of the proposed filter are demonstrated in two representative and challenging scenarios: 1) eight swarms with over seven hundred individuals, and 2) two swarms undergoing splitting and merging.