Unifying the landmark developments in optimal bounding ellipsoid identification

Abstract : A quite general class of Optimal Bounding Ellipsoid (OBE) algorithms including all methods published to date, can be unified into a single framework called the Unified OBE (UOBE) algorithm. UOBE is based on generalized weighted recursive least squares in which very broad classes of 'forgetting factors' and data weights may be employed. Different instances of UOBE are distinguished by their weighting policies and the criteria used to determine their optimal values. A study of existing OBE algorithms, with a particular interest in the tradeoff between algorithm performance interpretability and convergence properties, is presented. Results suggest that an interpretable, converging UOBE algorithm will be found. In this context, a new UOBE technique, the set membership stochastic approximation (SM-SA) algorithm is introduced. SM-SA possesses interpretable optimization measures and known conditions under which its estimator will converge.

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