Gaussian-mixture probability hypothesis density filter for multiple extended targets

A multiple extended-target Gaussian-mixture probability hypothesis density (RHM-GMPHD) filter, which provides the kinematic state and the extension state of extended targets, is proposed to address the difficultly estimated extension state. The pseudo-measurement likelihood function describing the relationship between kinematic state and extension state of extended target and measurements is constructed via the random hypersurface model(RHM) for convex-star extended target and sensor measurement function. Then the predicted state is considered, the update of extend target filter is derived to recursively estimate the kinematic state and extension state for extended targets. Moreover, the Jaccard distance is presented to evaluate the performance of the estimate extension state. Compared with the joint probabilistic data association(JPDA) and GMPHD filter, RHM-GMPHD provides the extension state and enhances the precision of the estimate number and the estimate kinematic state. Simulations indicate that the root-mean-square error of centroid from RHM-GMPHD gets 1/3 of that from JPDA or 1/2 of that from GMPHD. The estimation number of extended targets approaches the true value, and Jaccard distance gets usually less than 0.2.