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Asymptotically Optimal Smoothing of Stochastic Approximation Estimates for Regression Parameter Tracking
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2001 (English)Report (Other academic)
Abstract [en]

The sequence of estimates formed by the LMS algorithm for a standard linear regression estimation problem are 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 amatrix updating will lead to smoothed estimates with optimal tracking properties, also in the case the true parameters are 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 simplified algorithm, SLAMS, which is based on averages and requires much less computations.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2001. , 16 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 2360
Keyword [en]
Recursive methods, Accelerated convergence
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-55805ISRN: LiTH-ISY-R-2360OAI: oai:DiVA.org:liu-55805DiVA: diva2:316526
Available from: 2010-04-30 Created: 2010-04-30 Last updated: 2014-09-08Bibliographically approved

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Ljung, Lennart

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CiteExportLink to record
Permanent link

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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf