Minimum Cauchy Kernel Loss Based Robust Cubature Kalman Filter and Its Low Complexity Cost Version With Application on INS/OD Integrated Navigation System

This article focuses on addressing the non-linear state estimations problem of measurement noise with non-Gaussian distribution, which is critical for the performance of the inertial navigation system (INS)/odometer (OD) integrated navigation system. Although many existing robust filters have been proposed to address the non-Gaussian issue, their performance is not quite ideal for non-Gaussian noise in real applications, such as impulsive and noises from multimodal distributions. Meanwhile, the computational complexity burden impedes the application of robust non-linear algorithms in INS/OD integrated navigation systems. This paper proposes a minimal Cauchy kernel Cubature Kalman filter (MCK-CKF) to address the non-Gaussian problem in general non-linear systems. In addition, a simplified MCK-CKF (SMCK-CKF) is proposed to reduce the computational cost in INS/OD integrated navigation system, meanwhile ensuring outstanding performance similar to MCK-CKF. First, we derive the MCK-CKF based on the new cost function, which is obtained by a combination of weighted least square (WLS) and MCK. Then, for the INS/OD integrated navigation non-linear system, which has a linear measurement equation, the SMCK-CKF is established by introducing the approximate method to calculate the matrix inversion in the combination of Kalman filter measurement updated and MCK-CKF framework. The computational complexity of the CKF/MCK-CKF/SMCK-CKF is analyzed and compared. The powerful robustness for tackling various forms of non-Gaussian interference of MCK-CKF is validated by simulation on a typical non-linearity system. Furthermore, the vehicle’s INS/OD integrated navigation experiment demonstrates that the MCK-CKF/SMCK-CKF have remarkable robustness, and the SMCK-CKF has outstanding time efficiency.