Adaptive Quaternion State Estimation for 3-D and 4-D Signals With Weighted Maximum Correntropy: A Widely Linear Approach

To address the quaternion state estimation problem, the widely linear quaternion Kalman filter (WL-QKF) has been developed for improper quaternion signals using the minimum mean square error (MMSE) criterion under the Gaussian noise assumption. However, the performance of WL-QKF is significantly degraded when the quaternion system is disturbed by non-Gaussian noises. Hence, this article proposes a widely linear weighted maximum correntropy quaternion Kalman filter (WL-WMCQKF) to improve the robustness of WL-QKF against non-Gaussian noises. For the improper quaternion signal, to capture its complete second-order statistical information, augmented second-order statistics are first employed. Then, the WL-WMCQKF uses the weighted maximum correntropy criterion (WMCC) instead of the MMSE criterion to improve its robustness. Additionally, a weighted maximum correntropy quaternion extended Kalman filter (WMCQEKF) is developed for the quaternion nonlinear model using the quaternion Taylor series expansion. Moreover, an adaptive kernel width strategy is presented to avoid the selection issue of kernel width. Thus, two adaptive kernel width algorithms for WL-WMCQKF and WMCQEKF are proposed simultaneously. Finally, simulations on two examples validate the strong robustness and high filtering accuracy of the proposed quaternion state estimation algorithms in the presence of non-Gaussian noises.