Bitmead, Robert R.Anderson, Brian D.O.Ng, Tung Sang2025-07-082025-07-080005-1098ORCID:/0000-0002-1493-4774/work/174739892https://hdl.handle.net/1885/733766277A convergence rate estimate is derived for the homogeneous gradient-based adaptive linear estimator algorithm. This estimate involves the eigenvalues of the regression vector covariance matrix, yielding a useful measure for the choice of input signals for adaptive parameter estimation. The connection between this criterion and those more familiar from nonadaptive system identification is made and comparisons are drawn between the two areas.One of the analytical problems of examining adaptive linear parameter estimation algorithms is that, in applications involving noises, time variations * Received 14 December 1984; revised 18 September 1985.T he original version of this paper was presented at the IFAC World Congress on a Bridge BetweenC ontrol Sciencea nd Technology, in Budapest, Hungary, July 1984. The Published Proceedings of this I FAC Meetingm ay be ordered from Pergamon Press Limited, Headington Hill Hall, Oxford OX30BW, U.K. This paper was recommendedf or publication in revisedf orm by AssociateE ditor R. Vinter under the direction of Editor P. C. Parks. This work was supported by the Radio Research Board of Australia. t Department of Systems Engineering, Research School of Physical Sciences, Australian National University, Canberra, Australia. :~Department of Electrical Engineering, University of Wollongong, Wollongong, NSW, Australia.7enAdaptive systemsaveraging theoryconvergenceparameter estimationrecursive algorithmsstochastic systems198610.1016/0005-1098(86)90079-80022681541