Robust Kalman filtering with perturbation estimation process

An advanced Kalman filtering method is investigated by considering a perturbation estimation process in the standard Kalman filter, which reconstructs uncertainty with respect to the nominal state transition equation. The predictor and corrector are reformulated with the perturbation estimator, which has the intrinsic property of integrating innovations in the recursion of combined Kalman filter-perturbation estimator (CKF). The state/perturbation estimation error dynamics and the corresponding error covariance propagation equations are derived as well. A numerical example for mobile robot localization is shown to demonstrate the effectiveness of CKF.