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The direction of arrival (DOA) tracking problem based on an angle sensor is an important topic in many fields. In this paper, a nonlinear filter named the feedback M-estimation based robust cubature Kalman filter (FMR-CKF) is proposed to deal with measurement outliers from the angle sensor. The filter designs a new equivalent weight function with the Mahalanobis distance to combine the cubature Kalman filter (CKF) with the M-estimation method. Moreover, by embedding a feedback strategy which consists of a splitting and merging procedure, the proper sub-filter (the standard CKF or the robust CKF) can be chosen in each time index. Hence, the probability of the outliers’ misjudgment can be reduced. Numerical experiments show that the FMR-CKF performs better than the CKF and conventional robust filters in terms of accuracy and robustness with good computational efficiency. Additionally, the filter can be extended to the nonlinear applications using other types of sensors.

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.

Bearings-only tracking only adopts measurements from angle sensors to realize target tracking, thus, the accuracy of the state prediction has a significant influence on the final results of filtering. There exist unpredictable approximation errors in the process of filtering due to state propagation, discretization, linearization or other adverse effects. The idea of online covariance adaption is proposed in this work, where the post covariance information is proved to be effective for the covariance adaption. With theoretical deduction, the relationship between the posterior covariance and the priori covariance is investigated; the priori covariance is modified online based on the feedback rule of covariance updating. The general framework integrates the continuous-discrete cubature Kalman filtering and the feedback rule of covariance updating. Numerical results illustrated that the proposed method has advantages over decreasing unpredictable errors and improving the computational accuracy and efficiency.