Ellipsoidal state-bounding-based set-membership estimation for linear system with unknown-but-bounded disturbances

This study proposes a fast and stable recursive ellipsoidal state-bounding-based set-membership estimation algorithm for the state estimation of linear system with unknown-but-bounded (UBB) disturbances. The proposed algorithm has a prediction-correction structure in time update and observation update, which is similar to Kalman filter. For both time update and observation update, there is a data-depending weighting factor. The observation weighting factor is acquired by minimising the upper bound on a Lyapunov function of the posteriori estimation error. It has been demonstrated that the estimation error of the proposed algorithm is input-to-state stable when the system is uniformly observable. With the property of selective observation update, the proposed algorithm not only improves the point estimation accuracy but also decreases the computation load of observation weighting factors and the volume of feasible ellipsoid sets. The efficiency of the proposed algorithm has been demonstrated by numerical simulations with different UBB disturbances.