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A centralized multisensor unscented joint probabilistic data association algorithm, CMSUJPDA, is proposed for the multisensor multitarget tracking problem of the nonlinear system in clutter. In the algorithm, UKF is used for the propagation of state distribution in the nonlinear system at first. Then the association of measurements to track is implemented according to the method of JPDA. Based on this, the CMSUJPDA algorithm is derived by use of the idea of sequential MSJPDA. Due to higher order of accuracy of UKF than EKF, the association probabilities and state estimates in our algorithm are not affected by the linearization error. Hence compared with MSJPDA/EKF, the accuracy and robustness of CMSUJPDA are more favorable. Finally simulation results show the superiority of the proposed algorithm.