基于广义M估计的鲁棒容积卡尔曼滤波目标跟踪算法

为减小测量异常误差对非线性目标跟踪系统的影响, 提出了一种基于广义M估计的鲁棒容积卡尔曼滤波算法. 首先将非线性测量方程等价变换, 利用约束总体最小二乘准则构建广义M估计极值函数, 在不进行线性化近似的前提下将其引入到容积卡尔曼滤波求解框架中. 然后根据Mahalanobis距离构建异常误差判别量, 利用卡方分布的置信水平确定判决门限, 并建立改进的三段Huber权函数, 使其能够降低小异常误差权值, 剔除大异常误差. 理论分析表明, 该方法具有无需求导、跟踪精度高、实时性好等优点, 且无需已知异常误差的统计特性; 实验结果表明, 所提算法能够有效减小异常误差的影响, 在实际非线性物理系统中具有广阔的应用空间.

Robust cubature Kalman filter target tracking algorithm based on genernalized M-estiamtion

Target tracking has been introduced as a key point in the physical applications, such as passive sonar and chaotic communication etc. It is typically a nonlinear filtering problem to estimate the position and the velocity of a target from noise-corrupted measurements. Some approaches have been proposed for the problem, such as the extended Kalman filter, the unscented Kalman filter, and the cubature Kalman filter (CKF). However, they are effective only in the Gaussian and white assumption for the measurements. Actually, the measurements are easily polluted by the measurement outliers in practice. The measurement outliers may lead to inaccurate performance due to non-symmetrical or non-Gaussian property. In order to cope with the measurement outliers in nonlinear target tracking system, a robust filtering algorithm called the M-estimation based robust cubature Kalman filter (MR-CKF) is proposed for the target tracking problem. Firstly, the nonlinear measurement equation is transformed into an equivalently linear form according to the orthogonal vector, and then the Gaussian extremal function of the target tracking can be obtained by the constrained total least square (CTLS) criterion. By employing the Huber's robust score function, the Gaussian extremal function is further rendered into a robust extremal function, thus the generalized M-estimation can be introduced to the CKF without linearization approximation. The only difference between the Gaussian extremal function and the robust extremal function is the weight matrix, implying that the CKF solution framework does not change and the virtues of both the CKF and M-estimation can be fully utilized such as derivative-free, high accuracy and robust performance. Furthermore, an improved Huber equivalent weight function is designed for the MR-CKF based on the Mahalanobis distance. The outliers' judge threshold is determined according to the confidence level of Chi-square distribution and improper empirical value of the Huber's method can be avoided. In addition, the improved Huber weight function reduces weights of small outliers and removes large outliers, and this is more robust and reasonable than the Huber's method. Moreover, the statistical information of outliers is also not required. Theoretical analysis and numerical results show that the proposed filtering algorithm can improve the accuracy and robustness than the conventional robust algorithms.