School of Automation Science and Electrical Engineering, Beihang University, No. 37 Xueyuan Road, Haidian District, Beijing 100083, China.
Science and Technology on Aircraft Control Laboratory, Beihang University, No. 37 Xueyuan Road, Haidian District, Beijing 100083, China.
Sensors (Basel). 2022 Feb 21;22(4):1683. doi: 10.3390/s22041683.
The state estimation problem is ubiquitous in many fields, and the common state estimation method is the Kalman filter. However, the Kalman filter is based on the mean square error criterion, which can only capture the second-order statistics of the noise and is sensitive to large outliers. In many areas of engineering, the noise may be non-Gaussian and outliers may arise naturally. Therefore, the performance of the Kalman filter may deteriorate significantly in non-Gaussian noise environments. To improve the accuracy of the state estimation in this case, a novel filter named Student's kernel-based maximum correntropy Kalman filter is proposed in this paper. In addition, considering that the fixed-point iteration method is used to solve the optimal estimated state in the filtering algorithm, the convergence of the algorithm is also analyzed. Finally, comparative simulations are conducted and the results demonstrate that with the proper parameters of the kernel function, the proposed filter outperforms the other conventional filters, such as the Kalman filter, Huber-based filter, and maximum correntropy Kalman filter.
状态估计问题在许多领域都普遍存在，常用的状态估计方法是卡尔曼滤波器。然而，卡尔曼滤波器基于均方误差准则，只能捕获噪声的二阶统计量，对大的离群值敏感。在工程的许多领域中，噪声可能是非高斯的，并且离群值可能自然出现。因此，在非高斯噪声环境中，卡尔曼滤波器的性能可能会显著恶化。为了提高在这种情况下的状态估计精度，本文提出了一种新的滤波器，名为基于学生核的最大互信息卡尔曼滤波器。此外，考虑到在滤波算法中使用定点迭代法来求解最优估计状态，还对算法的收敛性进行了分析。最后，进行了对比仿真，结果表明，在核函数的适当参数下，所提出的滤波器优于其他传统滤波器，如卡尔曼滤波器、基于 Huber 的滤波器和最大互信息卡尔曼滤波器。
