Set-Membership State Estimation with Optimal Bounding Ellipsoids1

| This paper presents a set-membership state estimation scheme for linear systems with unknown but bounded inputs and noise. The approach is to compute 100% conndence regions for the state vector in the form of optimal ellipsoidal sets in the state-space. The proposed algorithm entails greatly reduced computational complexity in comparison to other state estimation schemes (e.g., Schweppe's algorithm 1, 2] and the celebrated Kalman lter 3, 4]) due to a signiicant reduction in the order of the matrix inversion involved. As a result, the new algorithm can be expected to circumvent the well-known problem of numerical instability observed in the Kalman lter. Our scheme also features the capability to selectively update the state estimates as opposed to conventional techniques that require continual updating. More interestingly , simulations show mean-square error performance of the proposed algorithm to be almost identical to the Kalman lter, which is known to be optimal in Gaussian noise.