Robustness of the Filtered-X LMS Algorithm- Part II: Robustness Enhancement by Minimal Regularization for Norm Bounded Uncertainty
The relationship between the regularization methods proposed in the literature to increase the robustness of the filtered-X LMS (FXLMS) algorithm is discussed. It is shown that the existing methods are special cases of a more general robust FXLMS algorithm in which particular filters determine the t...
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| Veröffentlicht in: | IEEE transactions on signal processing 2007-08, Vol.55 (8), p.4038-4047 |
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| container_title | IEEE transactions on signal processing |
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| creator | Fraanje, R.. Elliott, S.J. Verhaegen, M.. |
| description | The relationship between the regularization methods proposed in the literature to increase the robustness of the filtered-X LMS (FXLMS) algorithm is discussed. It is shown that the existing methods are special cases of a more general robust FXLMS algorithm in which particular filters determine the type of regularization. Based on the analysis by Fraanje, Verhaegen, and Elliott [ldquorobustness of the filtered-X LMS algorithm - part I: necessary conditions for convergence and the asymptotic pseudospectrum of Toeplitz Matricesrdquo of this issue], regularization filters are designed that guarantee that the strictly positive real conditions for asymptotic convergence or noncritical behavior are just satisfied for all uncertain systems contained in a particular norm bounded set. |
| doi_str_mv | 10.1109/TSP.2007.896086 |
| format | Article |
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It is shown that the existing methods are special cases of a more general robust FXLMS algorithm in which particular filters determine the type of regularization. Based on the analysis by Fraanje, Verhaegen, and Elliott [ldquorobustness of the filtered-X LMS algorithm - part I: necessary conditions for convergence and the asymptotic pseudospectrum of Toeplitz Matricesrdquo of this issue], regularization filters are designed that guarantee that the strictly positive real conditions for asymptotic convergence or noncritical behavior are just satisfied for all uncertain systems contained in a particular norm bounded set.</description><identifier>ISSN: 1053-587X</identifier><identifier>EISSN: 1941-0476</identifier><identifier>DOI: 10.1109/TSP.2007.896086</identifier><identifier>CODEN: ITPRED</identifier><language>eng</language><publisher>New York, NY: IEEE</publisher><subject>Algorithms ; Applied sciences ; Asymptotic properties ; Convergence ; Cost function ; Effort weighting ; Error correction ; Exact sciences and technology ; filtered-x LMS (FXLMS) ; Filters ; Frequency ; Information, signal and communications theory ; leaky ; Least squares approximation ; Miscellaneous ; model uncertainty ; Norms ; output weighting ; Regularization ; Robust control ; Robustness ; Signal processing ; Telecommunications and information theory ; Uncertainty ; Weight control</subject><ispartof>IEEE transactions on signal processing, 2007-08, Vol.55 (8), p.4038-4047</ispartof><rights>2007 INIST-CNRS</rights><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2007</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c382t-8f37cd52bb462d5fa6f77b24631e0a368829816b99224010477c6fa0e0cdc7bd3</citedby><cites>FETCH-LOGICAL-c382t-8f37cd52bb462d5fa6f77b24631e0a368829816b99224010477c6fa0e0cdc7bd3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/4276970$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,780,784,796,27924,27925,54758</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/4276970$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=18951473$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Fraanje, R..</creatorcontrib><creatorcontrib>Elliott, S.J.</creatorcontrib><creatorcontrib>Verhaegen, M..</creatorcontrib><title>Robustness of the Filtered-X LMS Algorithm- Part II: Robustness Enhancement by Minimal Regularization for Norm Bounded Uncertainty</title><title>IEEE transactions on signal processing</title><addtitle>TSP</addtitle><description>The relationship between the regularization methods proposed in the literature to increase the robustness of the filtered-X LMS (FXLMS) algorithm is discussed. It is shown that the existing methods are special cases of a more general robust FXLMS algorithm in which particular filters determine the type of regularization. Based on the analysis by Fraanje, Verhaegen, and Elliott [ldquorobustness of the filtered-X LMS algorithm - part I: necessary conditions for convergence and the asymptotic pseudospectrum of Toeplitz Matricesrdquo of this issue], regularization filters are designed that guarantee that the strictly positive real conditions for asymptotic convergence or noncritical behavior are just satisfied for all uncertain systems contained in a particular norm bounded set.</description><subject>Algorithms</subject><subject>Applied sciences</subject><subject>Asymptotic properties</subject><subject>Convergence</subject><subject>Cost function</subject><subject>Effort weighting</subject><subject>Error correction</subject><subject>Exact sciences and technology</subject><subject>filtered-x LMS (FXLMS)</subject><subject>Filters</subject><subject>Frequency</subject><subject>Information, signal and communications theory</subject><subject>leaky</subject><subject>Least squares approximation</subject><subject>Miscellaneous</subject><subject>model uncertainty</subject><subject>Norms</subject><subject>output weighting</subject><subject>Regularization</subject><subject>Robust control</subject><subject>Robustness</subject><subject>Signal processing</subject><subject>Telecommunications and information theory</subject><subject>Uncertainty</subject><subject>Weight control</subject><issn>1053-587X</issn><issn>1941-0476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNp9kc1rFTEUxYMoWJ-uXbgJgqWbec3X5MNdLa0-eNXSD-guZGaSvpSZpCaZxXPpX27KK1q6cHUv3N85cM8B4D1GS4yROry6PF8ShMRSKo4kfwH2sGK4QUzwl3VHLW1aKW5egzc53yGEGVN8D_y-iN2cS7A5w-hg2Vh46sdikx2aG7g-u4RH421MvmymBp6bVOBq9Rk-EZ2EjQm9nWwosNvCMx_8ZEZ4YW_n0ST_yxQfA3Qxwe8xTfBLnMNgB3hdNakYH8r2LXjlzJjtu8e5ANenJ1fH35r1j6-r46N101NJSiMdFf3Qkq5jnAytM9wJ0RHGKbbIUC4lURLzTilCGML1b9FzZ5BF_dCLbqALsL_zvU_x52xz0ZPPvR1HE2ycs6ZMYYpqTgtw8F8Qc4GpbDHBFf34DL2Lcwr1DS05a6mQSFXocAf1KeacrNP3qYaUthoj_dCdrt3ph-70rruq-PRoa3JvRpdqxD7_k0nVYiZo5T7sOG-t_XtmRHAlEP0DMd2hyA</recordid><startdate>20070801</startdate><enddate>20070801</enddate><creator>Fraanje, R..</creator><creator>Elliott, S.J.</creator><creator>Verhaegen, M..</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>F28</scope><scope>FR3</scope></search><sort><creationdate>20070801</creationdate><title>Robustness of the Filtered-X LMS Algorithm- Part II: Robustness Enhancement by Minimal Regularization for Norm Bounded Uncertainty</title><author>Fraanje, R.. ; Elliott, S.J. ; Verhaegen, M..</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c382t-8f37cd52bb462d5fa6f77b24631e0a368829816b99224010477c6fa0e0cdc7bd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Algorithms</topic><topic>Applied sciences</topic><topic>Asymptotic properties</topic><topic>Convergence</topic><topic>Cost function</topic><topic>Effort weighting</topic><topic>Error correction</topic><topic>Exact sciences and technology</topic><topic>filtered-x LMS (FXLMS)</topic><topic>Filters</topic><topic>Frequency</topic><topic>Information, signal and communications theory</topic><topic>leaky</topic><topic>Least squares approximation</topic><topic>Miscellaneous</topic><topic>model uncertainty</topic><topic>Norms</topic><topic>output weighting</topic><topic>Regularization</topic><topic>Robust control</topic><topic>Robustness</topic><topic>Signal processing</topic><topic>Telecommunications and information theory</topic><topic>Uncertainty</topic><topic>Weight control</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Fraanje, R..</creatorcontrib><creatorcontrib>Elliott, S.J.</creatorcontrib><creatorcontrib>Verhaegen, M..</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library Online</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><jtitle>IEEE transactions on signal processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Fraanje, R..</au><au>Elliott, S.J.</au><au>Verhaegen, M..</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Robustness of the Filtered-X LMS Algorithm- Part II: Robustness Enhancement by Minimal Regularization for Norm Bounded Uncertainty</atitle><jtitle>IEEE transactions on signal processing</jtitle><stitle>TSP</stitle><date>2007-08-01</date><risdate>2007</risdate><volume>55</volume><issue>8</issue><spage>4038</spage><epage>4047</epage><pages>4038-4047</pages><issn>1053-587X</issn><eissn>1941-0476</eissn><coden>ITPRED</coden><abstract>The relationship between the regularization methods proposed in the literature to increase the robustness of the filtered-X LMS (FXLMS) algorithm is discussed. It is shown that the existing methods are special cases of a more general robust FXLMS algorithm in which particular filters determine the type of regularization. Based on the analysis by Fraanje, Verhaegen, and Elliott [ldquorobustness of the filtered-X LMS algorithm - part I: necessary conditions for convergence and the asymptotic pseudospectrum of Toeplitz Matricesrdquo of this issue], regularization filters are designed that guarantee that the strictly positive real conditions for asymptotic convergence or noncritical behavior are just satisfied for all uncertain systems contained in a particular norm bounded set.</abstract><cop>New York, NY</cop><pub>IEEE</pub><doi>10.1109/TSP.2007.896086</doi><tpages>10</tpages></addata></record> |
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| ispartof | IEEE transactions on signal processing, 2007-08, Vol.55 (8), p.4038-4047 |
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| source | IEEE Electronic Library Online |
| subjects | Algorithms Applied sciences Asymptotic properties Convergence Cost function Effort weighting Error correction Exact sciences and technology filtered-x LMS (FXLMS) Filters Frequency Information, signal and communications theory leaky Least squares approximation Miscellaneous model uncertainty Norms output weighting Regularization Robust control Robustness Signal processing Telecommunications and information theory Uncertainty Weight control |
| title | Robustness of the Filtered-X LMS Algorithm- Part II: Robustness Enhancement by Minimal Regularization for Norm Bounded Uncertainty |
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