{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T06:15:59Z","timestamp":1783059359280,"version":"3.54.6"},"reference-count":36,"publisher":"Elsevier BV","issue":"10","license":[{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"funder":[{"DOI":"10.13039\/100012542","name":"Sichuan Provincial Science and Technology Support Program","doi-asserted-by":"publisher","award":["2026YFHZ0262"],"award-info":[{"award-number":["2026YFHZ0262"]}],"id":[{"id":"10.13039\/100012542","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62471412"],"award-info":[{"award-number":["62471412"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of the Franklin Institute"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1016\/j.jfranklin.2026.108748","type":"journal-article","created":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T23:55:57Z","timestamp":1778889357000},"page":"108748","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"title":["Low-complexity decorrelation affine projection algorithms: Formulations and applications"],"prefix":"10.1016","volume":"363","author":[{"given":"Lin","family":"Luo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3790-0945","authenticated-orcid":false,"given":"Yi","family":"Yu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuyu","family":"Zhu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hongsen","family":"He","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rodrigo C.","family":"de Lamare","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.jfranklin.2026.108748_bib0001","series-title":"Fundamentals of adaptive filtering","author":"Sayed","year":"2003"},{"issue":"11","key":"10.1016\/j.jfranklin.2026.108748_bib0002","doi-asserted-by":"crossref","first-page":"4242","DOI":"10.1109\/TCSI.2019.2917011","article-title":"Convergence Analysis of Deficient-Length Frequency-Domain Adaptive Filters","volume":"66","author":"Yang","year":"2019","journal-title":"IEEE Trans. Circuits Syst. I Regular Pap."},{"key":"10.1016\/j.jfranklin.2026.108748_bib0003","first-page":"1","article-title":"Neural Momentum-Enhanced LMS for Linear Acoustic Echo Cancellation","author":"Yu","year":"2025","journal-title":"IEEE Trans. Audio Speech Language Process."},{"key":"10.1016\/j.jfranklin.2026.108748_bib0004","doi-asserted-by":"crossref","first-page":"1949","DOI":"10.1109\/TASLPRO.2025.3561576","article-title":"Subband Adaptive Filtering Based on the Squared Sine Error Criterion: Analysis and Applications","volume":"33","author":"Gong","year":"2025","journal-title":"IEEE Trans. Audio Speech Language Process."},{"issue":"2","key":"10.1016\/j.jfranklin.2026.108748_bib0005","doi-asserted-by":"crossref","first-page":"782","DOI":"10.1109\/TCSI.2018.2868662","article-title":"Variable Threshold-Based Selective Updating Algorithms in Feed-Forward Active Noise Control Systems","volume":"66","author":"Aslam","year":"2019","journal-title":"IEEE Trans. Circuits Syst. I Regular Pap."},{"key":"10.1016\/j.jfranklin.2026.108748_bib0006","doi-asserted-by":"crossref","first-page":"3908","DOI":"10.1109\/TASLPRO.2025.3611274","article-title":"Active Impulsive Noise Control With Adaptive Robust Kernels","volume":"33","author":"Zhou","year":"2025","journal-title":"IEEE Trans. Audio Speech Language Process."},{"issue":"7","key":"10.1016\/j.jfranklin.2026.108748_bib0007","doi-asserted-by":"crossref","first-page":"3436","DOI":"10.1109\/TCSI.2025.3562481","article-title":"Robust Fractional-Order-Based Von Mises Subband Adaptive Filtering for Feedback Cancellation in Hearing Aids","volume":"72","author":"Devi R","year":"2025","journal-title":"IEEE Trans. Circuits Syst. I Regular Pap."},{"key":"10.1016\/j.jfranklin.2026.108748_bib0008","first-page":"1","article-title":"A Family of Robust Generalized Adaptive Filters and Application for Time-Series Prediction","author":"Peng","year":"2025","journal-title":"IEEE Trans. Circuits Syst. I Regular Pap."},{"issue":"5","key":"10.1016\/j.jfranklin.2026.108748_bib0009","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1002\/ecja.4400670503","article-title":"An adaptive filtering algorithm using an orthogonal projection to an affine subspace and its properties","volume":"67","author":"Ozeki","year":"1984","journal-title":"Electron. Commun. Japan (Part I: Commun.)"},{"key":"10.1016\/j.jfranklin.2026.108748_bib0010","series-title":"International Conference on Acoustics, Speech, and Signal Processing","first-page":"3023","article-title":"The fast affine projection algorithm","volume":"5","author":"Gay","year":"1995"},{"key":"10.1016\/j.jfranklin.2026.108748_bib0011","series-title":"IEEE Workshop on Signal Processing Systems","first-page":"109","article-title":"The Gauss-Seidel fast affine projection algorithm","author":"Albu","year":"2002"},{"key":"10.1016\/j.jfranklin.2026.108748_bib0012","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1109\/LSP.2008.2001111","article-title":"Low-complexity implementation of the affine projection algorithm","volume":"15","author":"Zakharov","year":"2008","journal-title":"IEEE Signal Process. Lett."},{"issue":"5","key":"10.1016\/j.jfranklin.2026.108748_bib0013","doi-asserted-by":"crossref","first-page":"2017","DOI":"10.1109\/TSP.2011.2113346","article-title":"Pseudo affine projection algorithms revisited: robustness and stability analysis","volume":"59","author":"Rupp","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"10.1016\/j.jfranklin.2026.108748_bib0014","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/j.dsp.2018.09.004","article-title":"A comparative survey of fast affine projection algorithms","volume":"83","author":"Yang","year":"2018","journal-title":"Digital Signal Process."},{"key":"10.1016\/j.jfranklin.2026.108748_bib0015","doi-asserted-by":"crossref","first-page":"6621","DOI":"10.1109\/TSP.2020.3039595","article-title":"Low-complexity decorrelation NLMS algorithms: Performance analysis and AEC application","volume":"68","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Signal Process."},{"key":"10.1016\/j.jfranklin.2026.108748_bib0016","doi-asserted-by":"crossref","first-page":"5940","DOI":"10.1109\/TSP.2020.3029884","article-title":"Variable step-size widely linear complex-valued affine projection algorithm and performance analysis","volume":"68","author":"Shi","year":"2020","journal-title":"IEEE Trans. Signal Process."},{"key":"10.1016\/j.jfranklin.2026.108748_bib0017","doi-asserted-by":"crossref","DOI":"10.1016\/j.sigpro.2024.109442","article-title":"A variable diagonal-matrix-step-size APA robust to impulsive noises","volume":"220","author":"Park","year":"2024","journal-title":"Signal Process."},{"issue":"22","key":"10.1016\/j.jfranklin.2026.108748_bib0018","doi-asserted-by":"crossref","first-page":"3698","DOI":"10.3390\/electronics11223698","article-title":"Switching mechanism on the order of affine projection algorithm","volume":"11","author":"Niu","year":"2022","journal-title":"Electronics"},{"key":"10.1016\/j.jfranklin.2026.108748_bib0019","doi-asserted-by":"crossref","DOI":"10.1016\/j.dsp.2025.105198","article-title":"Minimum error entropy with affine projection algorithm for robust adaptive filtering","volume":"163","author":"Zhang","year":"2025","journal-title":"Digital Signal Process."},{"key":"10.1016\/j.jfranklin.2026.108748_bib0020","article-title":"An \u03b1-sigmoid affine projection algorithm for in-car echo cancellation and channel estimation","author":"Li","year":"2025","journal-title":"IEEE Trans. Veh. Technol."},{"issue":"13","key":"10.1016\/j.jfranklin.2026.108748_bib0021","doi-asserted-by":"crossref","first-page":"7025","DOI":"10.1016\/j.jfranklin.2022.07.012","article-title":"Variable step-size saturation affine projection algorithm against impulsive noise","volume":"359","year":"2022","journal-title":"J. Franklin Inst."},{"issue":"12","key":"10.1016\/j.jfranklin.2026.108748_bib0022","article-title":"A variable step size bias-compensated affine projection algorithm with noisy inputs","volume":"362","year":"2025","journal-title":"J. Franklin Inst."},{"issue":"3","key":"10.1016\/j.jfranklin.2026.108748_bib0023","doi-asserted-by":"crossref","first-page":"1274","DOI":"10.1016\/j.jfranklin.2021.12.018","article-title":"Bias-compensated affine-projection-like algorithm based on maximum correntropy criterion for robust filtering","volume":"359","year":"2022","journal-title":"J. Franklin Inst."},{"issue":"5","key":"10.1016\/j.jfranklin.2026.108748_bib0024","first-page":"1020","article-title":"Stochastic Analysis of the Normalized Subband Adaptive Filter Algorithm","volume":"58","author":"Yin","year":"2011","journal-title":"IEEE Trans. Circuits Syst. I: Regular Pap."},{"key":"10.1016\/j.jfranklin.2026.108748_bib0025","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/j.isatra.2024.12.016","article-title":"A generalized maximum correntropy based constraint adaptive filtering: Constraint-forcing and performance analyses","volume":"157","author":"Zhao","year":"2025","journal-title":"ISA Trans."},{"issue":"2","key":"10.1016\/j.jfranklin.2026.108748_bib0026","doi-asserted-by":"crossref","first-page":"754","DOI":"10.1109\/TCSI.2023.3339632","article-title":"Correntropy-Based Data Selective Adaptive Filtering","volume":"71","author":"Chien","year":"2024","journal-title":"IEEE Trans. Circuits Syst. I Regular Pap."},{"key":"10.1016\/j.jfranklin.2026.108748_bib0027","doi-asserted-by":"crossref","first-page":"2199","DOI":"10.1109\/TSP.2020.2983905","article-title":"Diffusion normalized least mean M-estimate algorithms: Design and performance analysis","volume":"68","author":"Yu","year":"2020","journal-title":"IEEE Trans. Signal Process."},{"issue":"1","key":"10.1016\/j.jfranklin.2026.108748_bib0028","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1109\/TSP.2003.820077","article-title":"Mean-square performance of a family of affine projection algorithms","volume":"52","author":"Shin","year":"2004","journal-title":"IEEE Trans. Signal Process."},{"issue":"4","key":"10.1016\/j.jfranklin.2026.108748_bib0029","first-page":"2444","article-title":"Robust proportionate subband adaptive filter algorithms with optimal variable step-size","volume":"71","author":"Yu","year":"2023","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"issue":"12","key":"10.1016\/j.jfranklin.2026.108748_bib0030","doi-asserted-by":"crossref","first-page":"8074","DOI":"10.1007\/s00034-024-02829-5","article-title":"Affine Projection Algorithms with Novel Schemes of Variable Projection Order","volume":"43","author":"Luo","year":"2024","journal-title":"Circuits, Syst. Signal Process."},{"key":"10.1016\/j.jfranklin.2026.108748_bib0031","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.sigpro.2019.04.014","article-title":"Combined regularization parameter for normalized LMS algorithm and its performance analysis","volume":"162","author":"Shi","year":"2019","journal-title":"Signal Process."},{"key":"10.1016\/j.jfranklin.2026.108748_bib0032","series-title":"Technical Report","article-title":"15, Digital network echo cancellers (recommendation)","author":"TSG","year":"2004"},{"issue":"6","key":"10.1016\/j.jfranklin.2026.108748_bib0033","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1109\/89.876299","article-title":"Double-talk robust fast converging algorithms for network echo cancellation","volume":"8","author":"Gansler","year":"2002","journal-title":"IEEE Trans. Speech Audio Process."},{"key":"10.1016\/j.jfranklin.2026.108748_bib0034","doi-asserted-by":"crossref","unstructured":"J. Benesty, T. G\u00e4nsler, D.R. Morgan, M.M. Sondhi, S.L. Gay, et al., Advances in network and acoustic echo cancellation(2001).","DOI":"10.1007\/978-3-662-04437-7"},{"issue":"8","key":"10.1016\/j.jfranklin.2026.108748_bib0035","doi-asserted-by":"crossref","first-page":"2273","DOI":"10.1109\/TASL.2011.2125955","article-title":"Proportionate affine projection sign algorithms for network echo cancellation","volume":"19","author":"Yang","year":"2011","journal-title":"IEEE Trans. Audio Speech Language Process."},{"key":"10.1016\/j.jfranklin.2026.108748_bib0036","article-title":"Optimal subband adaptive filter over functional link neural network: algorithms and applications","author":"Ye","year":"2024","journal-title":"IEEE Trans. Circuits Syst. I Regular Pap."}],"container-title":["Journal of the Franklin Institute"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0016003226003480?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0016003226003480?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T05:18:50Z","timestamp":1783055930000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0016003226003480"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":36,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["S0016003226003480"],"URL":"https:\/\/doi.org\/10.1016\/j.jfranklin.2026.108748","relation":{},"ISSN":["0016-0032"],"issn-type":[{"value":"0016-0032","type":"print"}],"subject":[],"published":{"date-parts":[[2026,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Low-complexity decorrelation affine projection algorithms: Formulations and applications","name":"articletitle","label":"Article Title"},{"value":"Journal of the Franklin Institute","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jfranklin.2026.108748","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Franklin Institute. Published by Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"108748"}}