PHD and CPHD Filtering With Unknown Detection Probability

Abstract

A priori knowledge of target detection probability is of critical importance in the Gaussian mixture probability hypothesis density (PHD) and cardinalized PHD (CPHD) filters. In addition, these two filters require that the process noise and measurement noise of the state propagated in the recursion be Gaussian. These limitations may restrict the two filters application in real problems. To accommodate unknown target detection probability and nonnegative non-Gaussian parameters, this paper proposes a new implementation based on inverse gamma Gaussian mixtures, introducing a location independent feature whose posterior probability density and likelihood function are nonnegative non-Gaussian inverse gamma and gamma functions to determine detection probability incorporated into the recursions. The derivation of the merging inverse gamma components is also presented to prevent the unbounded increase of mixture components by minimizing the Kullback–Leibler divergence. First, a real heavy-clutter scenario is used to validate the effectiveness of the proposed filters in track initiation and target tracking without known detection probability. Then, simulations are presented to demonstrate that the proposed CPHD and PHD filters can achieve multitarget tracking performance similar to the standard counterparts with known target detection probability, and that they outperform the standard counterparts in scenarios with unknown and dynamically changing detection probability. The robustness of the proposed filters is tested in both real and simulation scenarios. It is also shown that the analytical and empirical computational complexities of the proposed filters are similar to those of their standard counterparts.