  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.
