Analysis of the hierarchical LMS algorithm
We analyze the hierarchical least mean-square (HLMS) algorithm, providing expressions for its steady-state mean-square error (MSE). We find conditions for the hierarchical structure to be equivalent to the optimal (full-length) Wiener solution. When these conditions are not satisfied, we show that H...
Saved in:
| Published in | IEEE signal processing letters Vol. 10; no. 3; pp. 78 - 81 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
New York
IEEE
01.03.2003
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1070-9908 1558-2361 |
| DOI | 10.1109/LSP.2002.807863 |
Cover
| Abstract | We analyze the hierarchical least mean-square (HLMS) algorithm, providing expressions for its steady-state mean-square error (MSE). We find conditions for the hierarchical structure to be equivalent to the optimal (full-length) Wiener solution. When these conditions are not satisfied, we show that HLMS will compute biased estimates. Our analysis also shows that even when these conditions hold, the MSE obtained using HLMS may be much larger than that obtained using LMS, since the potentially large MSEs at the subfilters in the first hierarchical level directly affect the output MSE. |
|---|---|
| AbstractList | We analyze the hierarchical least mean-square (HLMS) algorithm, providing expressions for its steady-state mean-square error (MSE). We find conditions for the hierarchical structure to be equivalent to the optimal (full-length) Wiener solution. When these conditions are not satisfied, we show that HLMS will compute biased estimates. Our analysis also shows that even when these conditions hold, the MSE obtained using HLMS may be much larger than that obtained using LMS, since the potentially large MSEs at the subfilters in the first hierarchical level directly affect the output MSE. |
| Author | Nascimento, V.H. |
| Author_xml | – sequence: 1 givenname: V.H. surname: Nascimento fullname: Nascimento, V.H. organization: Electron. Syst. Eng. Dept., Univ. de Sao Paulo, Brazil |
| BookMark | eNp9kM9LwzAUx4NMcJuePXgpHhSEbi9J0ybHMfwFFYXpOaRpajO6ZibdYf-9HRWEHXZ678Hn-x7vM0Gj1rUGoWsMM4xBzPPVx4wAkBmHjKf0DI0xYzwmNMWjvocMYiGAX6BJCGsA4JizMXpYtKrZBxsiV0VdbaLaGq-8rq1WTZS_rSLVfDtvu3pzic4r1QRz9Ven6Ovp8XP5Eufvz6_LRR5rmoguLksiygJoJYjBpNCKGk6oLnjZT4xnnBWaUAOmqhKCFaZFWZESa16kQtCS0im6H_ZuvfvZmdDJjQ3aNI1qjdsFKSATKUs49OTdSZLwJMmEYD14ewSu3c73nwfJeYIJS0XSQ_MB0t6F4E0lt95ulN9LDPKgWPaK5UGxHBT3CXaU0LZTnXVt55VtTuRuhpw1xvxfwZyAAPoL2kyIeg |
| CODEN | ISPLEM |
| CitedBy_id | crossref_primary_10_1109_TSP_2005_850347 crossref_primary_10_1016_j_dsp_2016_03_004 crossref_primary_10_1049_ip_vis_20050139 crossref_primary_10_1016_j_dsp_2025_105031 crossref_primary_10_1016_j_compeleceng_2012_06_008 crossref_primary_10_1109_JSEN_2015_2504106 crossref_primary_10_1109_TCSII_2005_858494 |
| Cites_doi | 10.1017/cbo9780511810817 10.1109/97.969446 10.1109/4234.913147 10.1002/j.1538-7305.1979.tb03332.x 10.1007/978-1-4419-8660-3 |
| ContentType | Journal Article |
| Copyright | Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2003 |
| Copyright_xml | – notice: Copyright The Institute of Electrical and Electronics Engineers, Inc. (IEEE) 2003 |
| DBID | RIA RIE AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D F28 FR3 |
| DOI | 10.1109/LSP.2002.807863 |
| DatabaseName | IEEE All-Society Periodicals Package (ASPP) 1998–Present IEEE Electronic Library (IEL) CrossRef Computer and Information Systems Abstracts Electronics & Communications Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional ANTE: Abstracts in New Technology & Engineering Engineering Research Database |
| DatabaseTitle | CrossRef Technology Research Database Computer and Information Systems Abstracts – Academic Electronics & Communications Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional Engineering Research Database ANTE: Abstracts in New Technology & Engineering |
| DatabaseTitleList | Technology Research Database Computer and Information Systems Abstracts |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://proxy.k.utb.cz/login?url=https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering |
| EISSN | 1558-2361 |
| EndPage | 81 |
| ExternalDocumentID | 2428165061 10_1109_LSP_2002_807863 1182090 |
| Genre | orig-research |
| GroupedDBID | -~X .DC 0R~ 29I 3EH 4.4 5GY 5VS 6IK 85S 97E AAJGR AARMG AASAJ AAWTH AAYJJ ABAZT ABFSI ABQJQ ABVLG ACGFO ACGFS ACIWK AENEX AETIX AGQYO AGSQL AHBIQ AI. AIBXA AKJIK AKQYR ALLEH ALMA_UNASSIGNED_HOLDINGS ATWAV BEFXN BFFAM BGNUA BKEBE BPEOZ CS3 DU5 E.L EBS EJD F5P HZ~ H~9 ICLAB IFIPE IFJZH IPLJI JAVBF LAI M43 O9- OCL P2P RIA RIE RNS TAE TN5 VH1 AAYXX CITATION 7SC 7SP 8FD JQ2 L7M L~C L~D RIG F28 FR3 |
| ID | FETCH-LOGICAL-c349t-dd29db03f92e12bca3e823cb8d12b58785bc23e0eff421a13bdf2d1c8b6993d33 |
| IEDL.DBID | RIE |
| ISSN | 1070-9908 |
| IngestDate | Sat Sep 27 20:13:29 EDT 2025 Sun Sep 28 12:32:39 EDT 2025 Mon Jun 30 05:39:08 EDT 2025 Wed Oct 01 06:37:14 EDT 2025 Thu Apr 24 23:03:36 EDT 2025 Tue Aug 26 16:38:28 EDT 2025 |
| IsDoiOpenAccess | false |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Language | English |
| License | https://ieeexplore.ieee.org/Xplorehelp/downloads/license-information/IEEE.html |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c349t-dd29db03f92e12bca3e823cb8d12b58785bc23e0eff421a13bdf2d1c8b6993d33 |
| Notes | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 content type line 23 |
| PQID | 884125694 |
| PQPubID | 23500 |
| PageCount | 4 |
| ParticipantIDs | proquest_journals_884125694 proquest_miscellaneous_28447995 crossref_primary_10_1109_LSP_2002_807863 proquest_miscellaneous_907965480 crossref_citationtrail_10_1109_LSP_2002_807863 ieee_primary_1182090 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2003-03-01 |
| PublicationDateYYYYMMDD | 2003-03-01 |
| PublicationDate_xml | – month: 03 year: 2003 text: 2003-03-01 day: 01 |
| PublicationDecade | 2000 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | IEEE signal processing letters |
| PublicationTitleAbbrev | LSP |
| PublicationYear | 2003 |
| Publisher | IEEE The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Publisher_xml | – name: IEEE – name: The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| References | ref7 ref3 Haykin (ref2) 1996 ref6 ref5 ref1 Kailath (ref4) 2000 |
| References_xml | – ident: ref3 doi: 10.1017/cbo9780511810817 – volume-title: Adaptive Filter Theory year: 1996 ident: ref2 – ident: ref6 doi: 10.1109/97.969446 – volume-title: Linear Estimation year: 2000 ident: ref4 – ident: ref7 doi: 10.1109/4234.913147 – ident: ref5 doi: 10.1002/j.1538-7305.1979.tb03332.x – ident: ref1 doi: 10.1007/978-1-4419-8660-3 |
| SSID | ssj0008185 |
| Score | 1.7375958 |
| Snippet | We analyze the hierarchical least mean-square (HLMS) algorithm, providing expressions for its steady-state mean-square error (MSE). We find conditions for the... |
| SourceID | proquest crossref ieee |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 78 |
| SubjectTerms | Algorithm design and analysis Algorithms Computational efficiency Convergence Councils Equivalence Error analysis Estimates Filters Least squares approximation Least squares methods Mathematical models Optimization Robustness Signal processing Steady-state Stochastic systems |
| Title | Analysis of the hierarchical LMS algorithm |
| URI | https://ieeexplore.ieee.org/document/1182090 https://www.proquest.com/docview/884125694 https://www.proquest.com/docview/28447995 https://www.proquest.com/docview/907965480 |
| Volume | 10 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVIEE databaseName: IEEE Electronic Library (IEL) customDbUrl: eissn: 1558-2361 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0008185 issn: 1070-9908 databaseCode: RIE dateStart: 19940101 isFulltext: true titleUrlDefault: https://ieeexplore.ieee.org/ providerName: IEEE |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1LT8MwDLaAExx4DcR49sABIVraJkuTI0IghBhCGkjcquYFiLGirbvw63HSbrwlbq3qtpYTx18S5zPAvuJZ5sqGhLFBb6Ik06FgxoQFQpGEZrRgnme2e80u7ujlfed-Bo6mZ2GMMT75zETu0u_l61KN3VLZsQPDscAJ-mzGWX1WazrqusBT5xfGIY6wvKHxSWJxfNW78bkIkeNWZ-RLBPIlVX6Mwz64nC9Bd6JWnVPyHI0rGam3b4yN_9V7GRYblBmc1N1iBWbMYBUWPnEPtuBwQkcSlDZAFBi4oth-WwFbLbjq9oKi_1AOn6rHlzW4Oz-7Pb0Im8IJoSJUVKHWqdAyJlakJkmlKojhKVGSa7zr8Ix3pEqJiY21NE2KhEhtU50oLhnCFU3IOswNyoHZgCArcAplORcWm866dSJBEskk7WiL36ZtiCbGzFXDKu6KW_RzP7uIRY7Wd7Uu07y2fhsOpi-81oQaf4u2nC0_xGoztmFr0lp543CjnHOKUI0JVGhv-hQ9xW1_FANTjkc5BmLq6O_aEPwhIeJMMEeAt_n7n7dg3ufy-RS0bZirhmOzg5ikkru-M74DDtvbSA |
| linkProvider | IEEE |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV1LT4QwEJ4YPagH38Z1fXDwYIwg0ALt0RjNqrvGRE28EfpSoy7GZS_-eqeFXd-JNwgDTKadztd2-g3AjmRZZsuG-KFGb6IkUz5PtfYLhCIRzWiROp7Z3kXauaFnt8ntBOyPz8JorV3ymQ7spdvLV6Uc2qWyAwuGQ44T9KmEUprUp7XG464NPXWGYejjGMsaIp8o5Afdq0uXjRBYdvWUfIlBrqjKj5HYhZeTeeiNFKuzSh6DYSUC-faNs_G_mi_AXIMzvcO6YyzChO4vwewn9sFl2BsRknil8RAHerYstttYwHbzur0rr3i6K18fqvvnFbg5Ob4-6vhN6QRfEsorX6mYKxESw2MdxUIWRLOYSMEU3iUsY4mQMdGhNobGURERoUysIslEioBFEbIKk_2yr9fAywqcRBnGuMHGM3aliJNIpIImyuC3aQuCkTFz2fCK2_IWT7mbX4Q8R-vbapdxXlu_BbvjF15qSo2_RZetLT_EajO2oD1qrbxxuUHOGEWwlnJUaHv8FH3FboAUfV0OBzmGYmoJ8Frg_SHBw4ynlgJv_fc_b8N057rXzbunF-dtmHGZfS4hbQMmq9eh3kSEUokt1zHfAbNw3pU |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Analysis+of+the+hierarchical+LMS+algorithm&rft.jtitle=IEEE+signal+processing+letters&rft.au=Nascimento%2C+V.H.&rft.date=2003-03-01&rft.issn=1070-9908&rft.eissn=1558-2361&rft.volume=10&rft.issue=3&rft.spage=78&rft.epage=81&rft_id=info:doi/10.1109%2FLSP.2002.807863&rft.externalDBID=n%2Fa&rft.externalDocID=10_1109_LSP_2002_807863 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1070-9908&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1070-9908&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1070-9908&client=summon |