School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China.
School of Electronic and Information Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China; School of Software Engineering, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China.
ISA Trans. 2018 Sep;80:195-202. doi: 10.1016/j.isatra.2018.05.001. Epub 2018 May 31.
For a nonlinear system, the cubature Kalman filter (CKF) and its square-root version are useful methods to solve the state estimation problems, and both can obtain good performance in Gaussian noises. However, their performances often degrade significantly in the face of non-Gaussian noises, particularly when the measurements are contaminated by some heavy-tailed impulsive noises. By utilizing the maximum correntropy criterion (MCC) to improve the robust performance instead of traditional minimum mean square error (MMSE) criterion, a new square-root nonlinear filter is proposed in this study, named as the maximum correntropy square-root cubature Kalman filter (MCSCKF). The new filter not only retains the advantage of square-root cubature Kalman filter (SCKF), but also exhibits robust performance against heavy-tailed non-Gaussian noises. A judgment condition that avoids numerical problem is also given. The results of two illustrative examples, especially the SINS/GPS integrated systems, demonstrate the desirable performance of the proposed filter.
对于非线性系统，容积卡尔曼滤波器（CKF）及其平方根版本是解决状态估计问题的有用方法，它们在高斯噪声下都能获得良好的性能。然而，在面对非高斯噪声时，它们的性能往往会显著下降，特别是当测量值受到一些重尾脉冲噪声污染时。本文利用最大相关熵准则（MCC）来提高稳健性能，而不是传统的最小均方误差（MMSE）准则，提出了一种新的平方根非线性滤波器，称为最大相关熵平方根容积卡尔曼滤波器（MCSCKF）。新滤波器不仅保留了平方根容积卡尔曼滤波器（SCKF）的优势，而且对重尾非高斯噪声具有稳健性能。还给出了一个避免数值问题的判断条件。两个说明性示例的结果，特别是 SINS/GPS 集成系统的结果，证明了所提出滤波器的良好性能。
