Multitarget Tracking with the Cubature Kalman Probability Hypothesis Density Filter

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 anchor nodes in presence of association uncertainty and clutter measurements. To do so we use the Probability Hypothesis Density (PHD) filter, a recent approximation to the generalized Bayesian formulation of the multitarget tracking (MTT) problem in which both targets states X-k and measurements Y-k at the generic time k are modeled as Random Finite Sets (RFS). A closed-form solution to the PHD recursion for linear Gaussian systems exists in the form of a Gaussian Mixture (GM), however, due to the nonlinearity existing between observations and state model in the scenario under consideration, we propose to incorporate the Cubature Kalman Filter (CKF) inside the GM-PHD filter. The performance for the proposed CKF-GM-PHD filter is compared against the linearized (EKF-based) version of the PHD recursion. The results show that the CKF-based solution is far more robust than the other solutions both in terms of cardinality as well as in terms of location estimates.