Performance Studies on a \ Quasi - OBE " Algorithm for Real - time

|A novel algorithm is studied for the iden-tiication of linear-in-parameters models. This technique is dubbed \Quasi-OBE" (QOBE) because it is based on the principles of optimal bounding ellip-soid (OBE) identiication, but has other geometric and classic least-squares interpretations that enhance its interpretability and application potential. Convergence behavior of both the central point estimate and measures of the hyperellipsoidal membership-set will be discussed in general terms, particularly in comparison with several conventional OBE algorithms. The QOBE algorithm uses highly-selective updating and exhibits excellent tracking ability in time-varying environments. I. Formulation and background Optimal bounding ellipsoid (OBE) algorithms 1]{{3], 6], 7] are becoming increasingly popular in signal processing , system identiication, control, and communication problems as alternatives to conventional least-square-error (LSE) identiiers. For detailed discussion on the advantages and properties of OBE algorithms, refer 1], 2], 4]. Recently, a novel algorithm was introduced in 5] that shares most of the motivating principles and algorithmic structure with the OBE algorithms, but which has novel interpretations and operational properties that make it uniquely diierent. We shall refer to this algorithm as quasi-OBE (QOBE) to connote both the similarities and diierences. The purpose of the present work is to generally examine the convergence properties of QOBE and to provide some insights into its operation in practical applications. The OBE and QOBE algorithms are used to identify a linear-in-parameters model y t = T x t + " t (1) in which 2 < m is the unknown \true" parameter vector to be identiied; fx t g is a sequence of measurable vectors of dimension m; and f" t g is an error sequence. These algorithms are based on the premise that f" t g has a point-wise energy bound that is known a priori , " 2 t 2 t ; for all t: (2) At each t, these bounds imply two hyperstrips in parameter space, say H + t = fjy t = T x t + t g and H ? t = fjy t = T x t ? t g, between which must lie. The intersection of these strips forms a polytope in < m , which is a subset of a hyperellipsoidal set at time t given by t def = n j (? t) T C t (? t) < t o : (3) The ellipsoid center, t , and matrix P t def = C ?1 t are …