Bounded Error Estimation: Set-Theoretic and Least-Squares Formulations

An Optimal Bounding Ellipsoid (OBE) algorithm with asymptotic convergence properties and a selective update capability is developed in this paper. Interesting geometrical insights into the updating rule are found. This algorithm is shown to be robust with respect to certain model violations. Convergence of the algorithm can be established even when the assumption of bounding ellipsoids breaks down due to incorrect initialization. A least-squares formulation is developed next for systems with bounded noise. The recursive estimation procedure of this approach is shown to be identical to that of the proposed OBE algorithm. Fundamental connections between these two approaches are also shown. These results are shown to imply enhanced tracking performance of the algorithm. Simulation results, tested on real channel data, show excellent performance inspite of highly reduced updating. Moreover , the algorithm is shown to render superior tracking capability, as expected.