On robust consistent Kalman filter for uncertain systems with application to PMSM systems

This paper addresses the state estimation problem for a class of uncertain systems with unknown nonlinear and time-varying dynamics as well as large disturbances. Actually, without exact model information about dynamics or disturbances, the Kalman filter (KF) or extended Kalman filter (EKF) struggles to obtain the covariance matrix (CM) of the state estimation error, which is quite important to ensure stability and evaluate estimation precision. To this end, this paper proposes a framework of robust consistent Kalman filter (RCKF) with provable boundedness of the CM of the state estimation error. Moreover, it is shown that the proposed method can ensure consistency, i.e., the upper bound of the CM of the state estimation error can be provided online. In particular, compared to the traditional consistent Kalman filter (CKF), the RCKF features a more robust design method, despite the large uncertainties exceeding the nominal upper bound. Finally, the proposed algorithm is applied to the state estimation problem of a permanent magnet synchronous motor (PMSM). The experimental results show a significant improvement in accuracy compared to the traditional CKF and other typical parameter estimation algorithms.