{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T03:40:36Z","timestamp":1776397236298,"version":"3.51.2"},"reference-count":22,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,9,2]],"date-time":"2025-09-02T00:00:00Z","timestamp":1756771200000},"content-version":"vor","delay-in-days":244,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62101362"],"award-info":[{"award-number":["62101362"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>The affine projection\u2013like (APL) algorithm has garnered significant attention due to its low steady\u2010state mean\u2010square deviation and simplicity. However, its performance is limited by a fixed step\u2010size, which forces a trade\u2010off between fast convergence and low steady\u2010state error. To overcome this limitation, this paper introduces two novel variants of the APL algorithm: the convex combination affine projection\u2013like (CC\u2010APL) and the combined step\u2010size affine projection\u2013like (CSS\u2010APL) algorithms. The CC\u2010APL algorithm leverages a convex combination of adaptive filters with different step\u2010sizes, allowing for dynamic adjustment between convergence speed and accuracy. The CSS\u2010APL algorithm optimizes performance by integrating multiple step\u2010sizes directly into the adaptation process. Both algorithms are designed to enhance the balance between convergence rate and steady\u2010state mean\u2010square deviation, addressing a key drawback of the traditional APL. Simulation results demonstrate that the proposed algorithms significantly improve performance compared to the conventional APL algorithm, especially in scenarios requiring both fast adaptation and low mean\u2010square deviation.<\/jats:p>","DOI":"10.1155\/jama\/1787885","type":"journal-article","created":{"date-parts":[[2025,9,2]],"date-time":"2025-09-02T16:19:34Z","timestamp":1756829974000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Improving Performance of Affine Projection\u2013Like Algorithm Using Two Combination Methods"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-1012-4389","authenticated-orcid":false,"given":"Yinxia","family":"Dong","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zongsheng","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xudong","family":"He","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Baoquan","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fengkun","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hui","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linlan","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,9,2]]},"reference":[{"key":"e_1_2_12_1_2","volume-title":"Adaptive Filter Theory","author":"Haykin S.","year":"2002"},{"key":"e_1_2_12_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/ecja.4400670503"},{"key":"e_1_2_12_3_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2014.2304665"},{"key":"e_1_2_12_4_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSP.2005.863126"},{"key":"e_1_2_12_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/ICASSP.2012.6288684"},{"key":"e_1_2_12_6_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCSII.2021.3068857"},{"key":"e_1_2_12_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.aeue.2015.07.009"},{"key":"e_1_2_12_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2013.05.014"},{"key":"e_1_2_12_9_2","doi-asserted-by":"publisher","DOI":"10.1109\/ICDSP.2011.6004882"},{"key":"e_1_2_12_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCE.2010.5606296"},{"key":"e_1_2_12_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.apacoust.2021.108175"},{"key":"e_1_2_12_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/s12652-017-0570-9"},{"key":"e_1_2_12_13_2","first-page":"1269","volume-title":"Proceedings of 2011 19th European Signal Processing Conference","author":"Arenas-Garc\u00eda J.","year":"2011"},{"key":"e_1_2_12_14_2","doi-asserted-by":"publisher","DOI":"10.1109\/TASL.2010.2045185"},{"key":"e_1_2_12_15_2","doi-asserted-by":"publisher","DOI":"10.1109\/TCSII.2015.2505067"},{"key":"e_1_2_12_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2017.01.009"},{"key":"e_1_2_12_17_2","doi-asserted-by":"publisher","DOI":"10.3390\/electronics13224436"},{"key":"e_1_2_12_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2017.06.007"},{"key":"e_1_2_12_19_2","doi-asserted-by":"publisher","DOI":"10.3390\/electronics13214319"},{"key":"e_1_2_12_20_2","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2016.2532340"},{"key":"e_1_2_12_21_2","first-page":"82","article-title":"Low Cost Variable Step-Size LMS With Maximum Similarity to the Affine Projection Algorithm","volume":"5","author":"Ferrer M.","year":"2024","journal-title":"IEEE Open Journal of Signal Processing"},{"key":"e_1_2_12_22_2","unstructured":"Azpicueta-RuizL. A. ZellerM. Figueiras-VidalA. R. Arenas-Garc\u00edaJ. andKellermannW. Improved Acoustic Echo Cancellation for Low SNR Based on Blockwise Combination of Filters Presented at the 20th Int. Congr Acoust 2010 https:\/\/www.acoustics.asn.au\/conference_proceedings\/ICA2010\/cdrom-ICA2010\/papers\/p218.pdf."}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/1787885","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1155\/jama\/1787885","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/jama\/1787885","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T02:41:23Z","timestamp":1776393683000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/jama\/1787885"}},"subtitle":[],"editor":[{"given":"Arpan","family":"Hazra","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2025,1]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2025,1]]}},"alternative-id":["10.1155\/jama\/1787885"],"URL":"https:\/\/doi.org\/10.1155\/jama\/1787885","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,1]]},"assertion":[{"value":"2024-01-05","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-07-25","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-09-02","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"1787885"}}