Robust Kalman filtering with perturbation estimation process for uncertain systems

Abstract

A robust Kalman filtering method is suggested by adopting a perturbation estimation process which is to reconstruct total uncertainty with respect to the nominal state equation of a physical system. The predictor and corrector of the discrete Kalman filter are reformulated with the perturbation estimator. In succession, the state and perturbation estimation error dynamics and the covariance propagation equations are derived. In the sequel, the recursive algorithm of combined discrete Kalman filter and perturbation estimator is obtained. The proposed robust Kalman filter has the property of integrating innovations and the adaptation capability to the time-varying uncertainties. An example of application to a mobile robot is shown to validate the performance of the proposed scheme.