Adaptive Gating for Multitarget Tracking With Gaussian Mixture Filters

In this correspondence, we use a generalization of the Bayesian approach to the multitarget problem that goes under the name of cardinalized probability hypothesis density (CPHD) filter to jointly estimate a time varying number of targets and their locations from sets of noisy range measurements. While in the case of Gaussian linear models a closed-form solution for the CPHD recursion exists in the form of a Gaussian mixture (GM), the more general case of nonlinear systems suboptimal solutions becomes necessary. Due to the Gaussianity assumption in the the GM-CPHD filter, we propose to integrate the square-root cubature Kalman filter (S-CKF) into the GM-CPHD recursion. A novel weighted gating strategy, which exploits the GM implementation of the proposed S-CKF-GM-CPHD filter, is offered to lower the computational time by adaptively increasing the gate sizes in proportion to the likelihood of the single GM components. The results reveal that the proposed gating yields considerable savings in processing requirements compared to no gating, without any significant degradation in performance. In addition, although the run time improvement achieved with elliptical or adaptive gating is equivalent, the latter does not degrade the results.