Maximum Correntropy Quaternion Kalman Filter

To solve the estimation problem in three-dimensional space, the quaternion Kalman filter (QKF) is developed for quaternion-valued signals using the well-known minimum mean square error (MMSE) criterion under the Gaussian assumption. However, when the system is disturbed by some non-Gaussian impulsive noises, the performance of QKF will be degraded significantly. To address this issue, this paper first develops a new QKF, called the maximum correntropy quaternion Kalman filter (MCQKF) by using the robust maximum correntropy criterion (MCC) instead of the MMSE criterion to improve the robustness of QKF against non-Gaussian impulsive noises. The proposed MCQKF is also an online algorithm in a recursive form, in which the posterior estimates are updated by a quaternion iterative equation (QIE). Then a sufficient condition to guarantee the existence and uniqueness of the fixed point of QIE is provided to ensure the convergence of the proposed quaternion algorithms. Furthermore, a variable kernel width strategy is proposed to avoid the selection problem of kernel width, generating another variable kernel width MCQKF (VKWMCQKF). In addition, the computational complexity of MCQKF is given. Finally, simulations on two examples validate the high filtering accuracy and strong robustness of the proposed quaternion algorithms in the presence of non-Gaussian noise.