Maximum Correntropy Unscented Kalman Filter for Spacecraft Relative State Estimation

A new algorithm called maximum correntropy unscented Kalman filter (MCUKF) is proposed and applied to relative state estimation in space communication networks. As is well known, the unscented Kalman filter (UKF) provides an efficient tool to solve the non-linear state estimate problem. However, the UKF usually plays well in Gaussian noises. Its performance may deteriorate substantially in the presence of non-Gaussian noises, especially when the measurements are disturbed by some heavy-tailed impulsive noises. By making use of the maximum correntropy criterion (MCC), the proposed algorithm can enhance the robustness of UKF against impulsive noises. In the MCUKF, the unscented transformation (UT) is applied to obtain a predicted state estimation and covariance matrix, and a nonlinear regression method with the MCC cost is then used to reformulate the measurement information. Finally, the UT is adopted to the measurement equation to obtain the filter state and covariance matrix. Illustrative examples demonstrate the superior performance of the new algorithm.