AbstractA general class of optimal bounding elipsoid (OBE) algorithms, including all methods published to date, is unified into a single framework called theunified 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 for determining optimal weight values.A study of existing OBE algorithms, with a particular interest in the trade‐off 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, theset membership stochastic approximation (SM‐SA)algorithm, is introduced. SM‐SA possesses interpretable optimization measures and known conditions under which its pointestimator