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Numerically Stable Ellipsoidal State Bounding Algorithm

Chai Wei,Sun Xianfang(School of Automation Science and Electrical Engineering, Beijing University of Aeronautics and Astronautics,Beijing 100083,China)  
A numerically stable recursive set membership state estimation algorithm for linear discrete-time systems with unknown but bounded noises is proposed,where ellipsoidal sets are adopted to describe the state uncertainties and to bound the process and observation noises.With the purpose of getting high numerical stability,singular value decomposition is used in the propagation of the shape-defining matrix of the ellipsoid.Besides,a subminimal-volume ellipsoid containing the intersection of the time-updated ellipsoid and the ellipsoidal set of state values consistent with the current observation and noise bounds is computed to circumvent inverse of ill-conditioned matrix.Monte Carlo simulations are performed on a digital computer for different models to demonstrate the effectiveness of the proposed algorithm.The simulation results show that the proposed algorithm not only matches the performance of the optimal algorithm closely in terms of mean ellipsoid volumes and mean square errors,but also keeps shape-defining matrix positive definite consistently.
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