{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T06:20:35Z","timestamp":1773469235491,"version":"3.50.1"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,9,4]],"date-time":"2025-09-04T00:00:00Z","timestamp":1756944000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,9,4]],"date-time":"2025-09-04T00:00:00Z","timestamp":1756944000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62201480"],"award-info":[{"award-number":["62201480"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Sichuan Science and Technology Program","award":["2025YFHZ0283"],"award-info":[{"award-number":["2025YFHZ0283"]}]},{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62471412"],"award-info":[{"award-number":["62471412"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2026,2]]},"DOI":"10.1007\/s00034-025-03313-4","type":"journal-article","created":{"date-parts":[[2025,9,4]],"date-time":"2025-09-04T14:31:12Z","timestamp":1756996272000},"page":"1529-1543","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Collaborative Tensor Decomposable Volterra Filter and Its Convergence Analysis"],"prefix":"10.1007","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8008-0287","authenticated-orcid":false,"given":"Tao","family":"Yu","sequence":"first","affiliation":[]},{"given":"Jianfan","family":"Lai","sequence":"additional","affiliation":[]},{"given":"Binyu","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Xiang","family":"Li","sequence":"additional","affiliation":[]},{"given":"Yi","family":"Yu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,9,4]]},"reference":[{"issue":"1","key":"3313_CR1","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1109\/MSP.2015.2481746","volume":"33","author":"J Arenas-Garc\u00eda","year":"2016","unstructured":"J. Arenas-Garc\u00eda, L.A. Azpicueta-Ruiz, M.T.M. Silva, V.H. Nascimento, A.H. Sayed, Combinations of adaptive filters: Performance and convergence properties. IEEE Signal Process. Mag. 33(1), 120\u2013140 (2016)","journal-title":"IEEE Signal Process. Mag."},{"issue":"3","key":"3313_CR2","doi-asserted-by":"publisher","first-page":"1078","DOI":"10.1109\/TSP.2005.863126","volume":"54","author":"J Arenas-Garc\u00eda","year":"2006","unstructured":"J. Arenas-Garc\u00eda, A.R. Figueiras-Vidal, A.H. Sayed, Mean-square performance of a convex combination of two adaptive filters. IEEE Trans. Signal Process. 54(3), 1078\u20131090 (2006)","journal-title":"IEEE Trans. Signal Process."},{"issue":"1","key":"3313_CR3","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1109\/TASL.2010.2045185","volume":"19","author":"LA Azpicueta-Ruiz","year":"2011","unstructured":"L.A. Azpicueta-Ruiz, M. Zeller, A.R. Figueiras-Vidal, J. Arenas-Garc\u00eda, W. Kellermann, Adaptive combination of Volterra kernels and its application to nonlinear acoustic echo cancellation. IEEE Trans. Audio Speech Lang. Process. 19(1), 97\u2013110 (2011)","journal-title":"IEEE Trans. Audio Speech Lang. Process."},{"key":"3313_CR4","doi-asserted-by":"publisher","first-page":"2111","DOI":"10.1109\/TASLP.2021.3084755","volume":"29","author":"SS Bhattacharjee","year":"2021","unstructured":"S.S. Bhattacharjee, N.V. George, Nearest Kronecker product decomposition based linear-in-the-parameters nonlinear filters. IEEE\/ACM Trans. Audio, Speech, Lang. Process. 29, 2111\u20132122 (2021)","journal-title":"IEEE\/ACM Trans. Audio, Speech, Lang. Process."},{"issue":"3","key":"3313_CR5","doi-asserted-by":"publisher","first-page":"1384","DOI":"10.1109\/TSMC.2022.3202656","volume":"53","author":"D Comminiello","year":"2023","unstructured":"D. Comminiello, A. Nezamdoust, S. Scardapane, M. Scarpiniti, A. Hussain, A. Uncini, A new class of efficient adaptive filters for online nonlinear modeling. IEEE Trans. Syst. Man, Cybern.: Syst. 53(3), 1384\u20131396 (2023)","journal-title":"IEEE Trans. Syst. Man, Cybern.: Syst."},{"issue":"7","key":"3313_CR6","doi-asserted-by":"publisher","first-page":"1502","DOI":"10.1109\/TASL.2013.2255276","volume":"21","author":"D Comminiello","year":"2013","unstructured":"D. Comminiello, M. Scarpiniti, L.A. Azpicueta-Ruiz, J. Arenas-Garc\u00eda, A. Uncini, Functional link adaptive filters for nonlinear acoustic echo cancellation. IEEE Trans. Audio Speech Lang. Process. 21(7), 1502\u20131512 (2013)","journal-title":"IEEE Trans. Audio Speech Lang. Process."},{"key":"3313_CR7","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1016\/j.sigpro.2017.01.009","volume":"135","author":"D Comminiello","year":"2017","unstructured":"D. Comminiello, M. Scarpiniti, L.A. Azpicueta-Ruiz, J. Arenas-Garc\u00eda, A. Uncini, Combined nonlinear filtering architectures involving sparse functional link adaptive filters. Signal Process. 135, 168\u2013178 (2017)","journal-title":"Signal Process."},{"key":"3313_CR8","volume":"470","author":"J Fang","year":"2024","unstructured":"J. Fang, C. Ren, H. Wang, V. Stojanovic, S. He, Finite-region asynchronous $$H_\\infty$$ filtering for 2-D Markov jump systems in Roesser model. Appl. Math. Comput. 470, 128573 (2024)","journal-title":"Appl. Math. Comput."},{"issue":"6","key":"3313_CR9","doi-asserted-by":"publisher","first-page":"672","DOI":"10.1109\/TSA.2003.818077","volume":"11","author":"A Gu\u00e9rin","year":"2003","unstructured":"A. Gu\u00e9rin, G. Faucon, R.L. Bouquin-Jeann\u00e8s, Nonlinear acoustic echo cancellation based on Volterra filters. IEEE Trans. Speech Audio Process. 11(6), 672\u2013683 (2003)","journal-title":"IEEE Trans. Speech Audio Process."},{"issue":"3","key":"3313_CR10","doi-asserted-by":"publisher","first-page":"482","DOI":"10.1109\/TIM.2017.2781992","volume":"67","author":"X Guo","year":"2018","unstructured":"X. Guo, Y. Li, J. Jiang, C. Dong, S. Du, L. Tan, Sparse modeling of nonlinear secondary path for nonlinear active noise control. IEEE Trans. Instrum. Meas. 67(3), 482\u2013496 (2018)","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"3313_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-74386-4","volume-title":"Tensor Computation for Data Analysis","author":"Y Liu","year":"2022","unstructured":"Y. Liu, J. Liu, Z. Long, C. Zhu, Tensor Computation for Data Analysis (Springer, Cham, 2022)"},{"issue":"17","key":"3313_CR12","doi-asserted-by":"publisher","first-page":"4500","DOI":"10.1016\/j.jfranklin.2016.08.025","volume":"353","author":"L Lu","year":"2016","unstructured":"L. Lu, H. Zhao, B. Chen, Collaborative adaptive Volterra filters for nonlinear system identification in $$\\alpha$$-stable noise environments. J. Franklin Inst. 353(17), 4500\u20134525 (2016)","journal-title":"J. Franklin Inst."},{"key":"3313_CR13","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1016\/j.apacoust.2019.06.024","volume":"156","author":"W Lu","year":"2019","unstructured":"W. Lu, L. Zhang, Collaborative block-delay Volterra filters for nonlinear acoustic echo cancellation. Appl. Acoust. 156, 83\u201391 (2019)","journal-title":"Appl. Acoust."},{"issue":"10","key":"3313_CR14","doi-asserted-by":"publisher","first-page":"1793","DOI":"10.1109\/TASLP.2018.2842146","volume":"26","author":"C Paleologu","year":"2018","unstructured":"C. Paleologu, J. Benesty, S. Ciochin\u0103, Linear system identification based on a Kronecker product decomposition. IEEE\/ACM Trans. Audio Speech Lang. Process. 26(10), 1793\u20131808 (2018)","journal-title":"IEEE\/ACM Trans. Audio, Speech, Lang. Process."},{"issue":"21","key":"3313_CR15","doi-asserted-by":"publisher","first-page":"5463","DOI":"10.1109\/TSP.2019.2932880","volume":"67","author":"FC Pinheiro","year":"2019","unstructured":"F.C. Pinheiro, C.G. Lopes, A low-complexity nonlinear least mean squares filter based on a decomposable Volterra model. IEEE Trans. Signal Process. 67(21), 5463\u20135478 (2019)","journal-title":"IEEE Trans. Signal Process."},{"issue":"11","key":"3313_CR16","doi-asserted-by":"publisher","first-page":"853","DOI":"10.1109\/LSP.2004.836944","volume":"11","author":"GL Sicuranza","year":"2004","unstructured":"G.L. Sicuranza, A. Carini, Filtered-x affine projection algorithm for multichannel active noise control using second-order Volterra filters. IEEE Signal Process. Lett. 11(11), 853\u2013857 (2004)","journal-title":"IEEE Signal Process. Lett."},{"issue":"13","key":"3313_CR17","doi-asserted-by":"publisher","first-page":"3551","DOI":"10.1109\/TSP.2017.2690524","volume":"65","author":"ND Sidiropoulos","year":"2017","unstructured":"N.D. Sidiropoulos, L. De Lathauwer, X. Fu, K. Huang, E.E. Papalexakis, C. Faloutsos, tensor decomposition for signal processing and machine learning. IEEE Trans. Signal Process. 65(13), 3551\u20133582 (2017)","journal-title":"IEEE Trans. Signal Process."},{"key":"3313_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2024.107945","volume":"132","author":"X Song","year":"2024","unstructured":"X. Song, Z. Peng, S. Song, V. Stojanovic, Anti-disturbance state estimation for PDT-switched RDNNs utilizing time-sampling and space-splitting measurements. Commun. Nonlinear Sci. Numer. Simul. 132, 107945 (2024)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"3313_CR19","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1007\/s00034-013-9633-0","volume":"33","author":"V Stojanovic","year":"2014","unstructured":"V. Stojanovic, V. Filipovic, Adaptive input design for identification of output error model with constrained output. Circuits Syst. Signal Process. 33, 97\u2013113 (2014)","journal-title":"Circuits, Syst., Signal Process."},{"issue":"2","key":"3313_CR20","doi-asserted-by":"publisher","first-page":"576","DOI":"10.1016\/j.jfranklin.2015.12.007","volume":"353","author":"V Stojanovic","year":"2016","unstructured":"V. Stojanovic, N. Nedic, Robust identification of OE model with constrained output using optimal input design. J. Franklin Inst. 353(2), 576\u2013593 (2016)","journal-title":"J. Franklin Inst."},{"issue":"13\u201314","key":"3313_CR21","doi-asserted-by":"publisher","first-page":"6676","DOI":"10.1016\/j.apm.2016.02.014","volume":"40","author":"V Stojanovic","year":"2016","unstructured":"V. Stojanovic, N. Nedic, D. Prsic, L. Dubonjic, Optimal experiment design for identification of ARX models with constrained output in non-Gaussian noise. Appl. Math. Modell. 40(13\u201314), 6676\u20136689 (2016)","journal-title":"Appl. Math. Modell."},{"issue":"8","key":"3313_CR22","doi-asserted-by":"publisher","first-page":"1667","DOI":"10.1109\/78.934136","volume":"49","author":"L Tan","year":"2001","unstructured":"L. Tan, J. Jiang, Adaptive Volterra filters for active control of nonlinear noise processes. IEEE Trans. Signal Process. 49(8), 1667\u20131676 (2001)","journal-title":"IEEE Trans. Signal Process."},{"key":"3313_CR23","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1016\/j.ins.2023.03.070","volume":"634","author":"H Wan","year":"2023","unstructured":"H. Wan, X. Luan, V. Stojanovic, F. Liu, Self-triggered finite-time control for discrete-time Markov jump systems. Inf. Sci. 634, 101\u2013121 (2023)","journal-title":"Inf. Sci."},{"issue":"3","key":"3313_CR24","first-page":"1043","volume":"68","author":"N Zhang","year":"2021","unstructured":"N. Zhang, J. Ni, J. Chen, Z. Li, Steady-state mean-square error performance analysis of the tensor LMS algorithm. IEEE Trans. Circuits Syst. II: Exp. Briefs 68(3), 1043\u20131047 (2021)","journal-title":"IEEE Trans. Circuits Syst. II: Exp. Briefs"},{"issue":"4","key":"3313_CR25","doi-asserted-by":"publisher","first-page":"1394","DOI":"10.1109\/TASL.2011.2175383","volume":"20","author":"H Zhao","year":"2012","unstructured":"H. Zhao, X. Zeng, X. Zhang, Z. He, T. Li, W. Jin, Adaptive extended pipelined second-order Volterra filter for nonlinear active noise controller. IEEE Trans. Audio Speech Lang. Process. 20(4), 1394\u20131399 (2012)","journal-title":"IEEE Trans. Audio Speech Lang. Process."},{"issue":"1","key":"3313_CR26","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1109\/TSP.2008.2007105","volume":"57","author":"H Zhao","year":"2009","unstructured":"H. Zhao, J. Zhang, A novel adaptive nonlinear filter-based pipelined feedforward second-order Volterra architecture. IEEE Trans. Signal Process. 57(1), 237\u2013246 (2009)","journal-title":"IEEE Trans. Signal Process."},{"key":"3313_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.apacoust.2020.107799","volume":"175","author":"S Zhao","year":"2021","unstructured":"S. Zhao, L. Zhang, W. Lu, A generalized collaborative functional link adaptive filter for nonlinear active noise control. Appl. Acoust. 175, 107799 (2021)","journal-title":"Appl. Acoust."},{"key":"3313_CR28","doi-asserted-by":"publisher","first-page":"1699","DOI":"10.1007\/s00034-020-01544-1","volume":"40","author":"YB Zhao","year":"2021","unstructured":"Y.B. Zhao, T. Yan, W.Y. Chen, H.Z. Lu, A collaborative spline adaptive filter for nonlinear echo cancellation. Circuits Syst. Signal Process. 40, 1699\u20131719 (2021)","journal-title":"Circuits, Syst., Signal Process."}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-025-03313-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00034-025-03313-4","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-025-03313-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T05:40:19Z","timestamp":1773466819000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00034-025-03313-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,4]]},"references-count":28,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["3313"],"URL":"https:\/\/doi.org\/10.1007\/s00034-025-03313-4","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"value":"0278-081X","type":"print"},{"value":"1531-5878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,4]]},"assertion":[{"value":"18 June 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 August 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 August 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 September 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}