Gating for multitarget tracking with the Gaussian Mixture PHD and CPHD filters

In this paper we investigate the problem of jointly estimating a time varying number of targets and their locations from sets of noisy range measurements received at fixed sensors with known location in presence of association uncertainty. To do so we use a recent generalization of the Bayesian approach to the multitarget problem that go under the names of Probability Hypothesis Density (PHD) filter and Cardinalized PHD filter (CPHD). While the PHD and CPHD recursions are proved to admit closed-form solution in the form of a Gaussian Mixture (GM) in the case of linear systems, because of the nonlinearity between observations and state model existing in the formulation of the filters for the problem at hand, we employ the new Cubature Kalman Filter (CKF). To lower the computational complexity for the proposed CKF-GM-PHD and CKF-GM-CPHD filters we propose a novel weighted gating strategy which exploits the GM implementation of the filters. The results revel that for both filters the proposed gating strategy yields a considerable save in computational complexity without any significant degradation in performance.