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Asymptotically Optimal Smoothing of Averaged LMS Estimates for Regression Parameter Tracking
Institute of Control Sciences, Russia.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2002 (English)In: Automatica, ISSN 0005-1098, Vol. 38, no 8, 1287-1293 p.Article in journal (Refereed) Published
Abstract [en]

The sequence of estimates formed by the LMS algorithm for a standard linear regression estimation problem is considered. It is known since earlier that smoothing these estimates by simple averaging will lead to, asymptotically, the recursive least-squares algorithm. In this paper, it is first shown that smoothing the LMS estimates using a matrix updating will lead to smoothed estimates with optimal tracking properties, also in case the true parameters are slowly changing as a random walk. The choice of smoothing matrix should be tailored to the properties of the random walk. Second, it is shown that the same accuracy can be obtained also for a modified algorithm, SLAMS, which is based on averages and requires much less computations.

Place, publisher, year, edition, pages
Elsevier, 2002. Vol. 38, no 8, 1287-1293 p.
Keyword [en]
Asymptotic MSE, Linear regression, LMS, Parameter tracking, Slow random walk, Smoothing
National Category
Control Engineering
URN: urn:nbn:se:liu:diva-46936DOI: 10.1016/S0005-1098(02)00028-6OAI: diva2:267832

© 2002 Elsevier Science Ltd. All rights reserved.

Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2013-07-17

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