Abstract
Given appropriate persistency of excitation, the ellipsoidal seta associated with optimal bounding ellipsoid (OBE) algorithms with an interpretable optimization (volume) criterion, converge to a point under the condition that the model disturbance process visit the error bounds infinitely often. The spectral properties of the disturbance are not primary in the convergence behavior of OBE algorithms, rendering these identifiers distinctly different from the structurally similar RLS. Rigorous proof of the sufficiency of the "infinite visitation" property is given for both independent and correlated noise. In the colored noise case, it is shown that a mixing condition on the observations will assure convergence if the OBE algorithm is slightly modified. Examples of simulations are used to illustrate the theoretical developments.
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