A Set-membership Smoother for State Estimation in Disturbances of Unknown Distribution

A novel set-membership-based smoothing method for state estimation using the optimal bounding ellipsoid (OBE) algorithms is presented. OBE filters have been proven to be effective in state estimation problems with unknown but bounded errors. Compared with filtering methods, smoothing methods provide a much more accurate and reliable state estimate because observations beyond the current estimation time are used. The new method is a Rauch-Tung-Striebel (RTS)-type smoother which employs both forward and backward passes to estimate the system state. The forward pass is performed using the OBE filter, while the backward pass maintains the fundamental spirit of OBE algorithm in the backward direction. The minimum-volume and minimum-trace bounding ellipsoids containing the feasible state set are derived from this algorithm. Simulation results show the performance of the proposed smoother is superior to both the traditional OBE filter and Kalman filter for state estimation.