The PHD filter for extended target tracking with estimable extent shape parameters of varying size

In extended target tracking, targets potentially produce more than one measurement per time step. In recent random finite set (RFS) approaches, the set of measurements obtained from an extended target is modelled as a point process. In this paper, we expand on the RFS approach to extended target tracking by considering a hierarchical point process representation of multiple extended target, more specifically a Poisson cluster process. This allows us to impose a geometric shape, in particular an ellipse, on each extended target. The set of target states, which are characterised by the kinematic variables and the shape parameters, represents the higher level (parent) process and the set of points on the boundary, from which measurements are generated, represents the lower level (daughter) process. We describe the PHD filter for multiple extended targets, whose extents vary in size, that estimates the shape parameters of the targets jointly with their positions and velocities. The main contribution of this paper is the practical implementation we propose, based on a particle-system representation for the targets' shape and a Gaussian mixture formulation for the kinematic state per particle. The method is demonstrated on simulated data for multiple elliptical shaped extended targets.