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Convergence analysis of the quasi‐OBE algorithm and related performance issues

‘Quasi‐OBE’ (QOBE) is an adaptive set identification and filtering algorithm which is based on the principles of optimal bounding ellipsoid processing, but which has other geometric and classic least‐squares interpretations which greatly enhance its application potential. In particular, because of its unusual optimization criterion, the ellipsoidal membership set associated with QOBE is more likely to retain (i.e. to move in the parameter space with) the system model's ‘true parameters, ’ say θ*, when those parameters are time varying. Moreover, in the unlikely event that θ* moves outside the set, the integrity of the point‐set estimation remains intact, and the estimator provably converges under known conditions. The consistency of the set estimation can be restored at any time using typical ‘rescue procedures’ if desired. Understanding convergence performance is very critical to successful QOBE application. Convergence analysis of both the central point estimate and measures of the hyperellipsoidal membership set is presented. The main results give conditions for point estimate convergence, and show that set convergence to a point is not possible. Implications of these convergence results for practical application are discussed. Copyright © 2007 John Wiley & Sons, Ltd.