This paper presents an improved approach for guaranteed state estimation combining set-membership estimation techniques based on zonotopes and ellipsoids, applied on linear discrete-time systems with unknown but bounded perturbations and noises. The proposed approach starts with a zonotopic approximation and continues with an ellipsoidal approximation; this allows to manage the trade-off between the accuracy of the zonotopic estimation and the reduced complexity of the ellipsoidal estimation. A new criterion based on the P -radius of a zonotope is proposed to make the transition from the zonotopic estimation to the ellipsoidal estimation. An illustrative example is analyzed to show the advantages of the proposed approach.
This paper proposes a new ellipsoid-based guaranteed state estimation approach for linear discrete-time systems with bounded perturbations and bounded measurement noise. This approach is based on the minimization of the radius of the ellipsoidal state estimation set. Firstly, the ellipsoidal state estimation is computed by off-line solving a Linear Matrix Inequality optimization problem. Secondly, a new online method is developed in order to improve the accuracy of the estimation but it leads to an increase of the online computation load. A new scaling technique is proposed to reduce the computation time, while keeping a good accuracy of the state estimation. An illustrative example is analyzed in order to show the advantages of the proposed approach.
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