Abstract:PHD filtering is a common and effective multiple object tracking (MOT) algorithm used in scenarios where the number of objects and their states are unknown. In scenarios where each object can generate multiple measurements per scan, some PHD filters can estimate the extent of the objects as well as their kinematic properties. Most of these approaches are, however, not able to inherently estimate trajectories and rely on ad-hoc methods, such as different labeling schemes, to build trajectories from the state estimates. This paper presents a Gamma Gaussian inverse Wishart mixture PHD filter that can directly estimate sets of trajectories of extended targets by expanding previous research on tracking sets of trajectories for point source objects to handle extended objects. The new filter is compared to an existing extended PHD filter that uses a labeling scheme to build trajectories, and it is shown that the new filter can estimate object trajectories more reliably.