In order to improve filtering accuracy and restrain the degradation of filtering performance caused by the heavy-tailed process and measurement noises in multi-target tracking, this paper proposes a robust Student’s t mixture probability hypothesis density (PHD) filter. In the proposed method, a Student’s t mixture is implemented to the PHD filter, which recursively propagates the intensity as a mixture of Student’s t components in PHD filtering framework. Furthermore, with the advantage of a designed judging and re-weighting mechanism, an M-estimation based dual-gating strategy is designed for the Student’s t mixture implementation to suppress the negative effect of the heavy-tailed noises. Our proposed approach not only utilizes the Student’s t distribution to match the real heavy-tailed non-Gaussian noise well, but also enhances the robustness of the Student’s t mixture based approach via the designed dual-gating strategy. The simulation results verify that the proposed algorithm can keep good filtering accuracy in the presence of the process and measurement outliers simultaneously.

In multi-target tracking, the outliers-corrupted process and measurement noises can reduce the performance of the probability hypothesis density (PHD) filter severely. To solve the problem, this paper proposed a novel PHD filter, called Student’s t mixture PHD (STM-PHD) filter. The proposed filter models the heavy-tailed process noise and measurement noise as a Student’s t distribution as well as approximates the multi-target intensity as a mixture of Student’s t components to be propagated in time. Then, a closed PHD recursion is obtained based on Student’s t approximation. Our approach can make full use of the heavy-tailed characteristic of a Student’s t distribution to handle the situations with heavy-tailed process and the measurement noises. The simulation results verify that the proposed filter can overcome the negative effect generated by outliers and maintain a good tracking accuracy in the simultaneous presence of process and measurement outliers.

To further improve the filtering accuracy in nonlinear estimation systems, a nonlinear filter, called the orthogonal simplex Chebyshev-Laguerre cubature Kalman filter (OSCL-CKF), is proposed. The filter is built within the cubature Kalman filter framework, which transforms the multidimensional, Gaussian weighted integral into a spherical-radial coordinate system. In the spherical integral, an orthogonal method is introduced to the third-degree spherical simplex rule, and then the nonlocal sampling effects can be reduced by tuning the high order interference terms. In the radial integral, the quadrature points and corresponding weights are determined according to the Chebyshev-Laguerre (CL) equation, which enables the nonlinear filter to improve the precision by the order of the CL polynomial. Numerical results show that the proposed filter outperforms the conventional algorithms.