{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,11]],"date-time":"2025-09-11T19:09:26Z","timestamp":1757617766144,"version":"3.44.0"},"reference-count":60,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2025,4,11]],"date-time":"2025-04-11T00:00:00Z","timestamp":1744329600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,4,11]],"date-time":"2025-04-11T00:00:00Z","timestamp":1744329600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2025,9]]},"DOI":"10.1007\/s00034-025-03076-y","type":"journal-article","created":{"date-parts":[[2025,4,11]],"date-time":"2025-04-11T16:28:31Z","timestamp":1744388911000},"page":"6352-6373","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Exponential Inverse Square Root Recursive Spline Adaptive Filter for Nonlinear System Identification"],"prefix":"10.1007","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4892-0768","authenticated-orcid":false,"given":"Neetu","family":"Chikyal","sequence":"first","affiliation":[]},{"family":"Vasundhara","sequence":"additional","affiliation":[]},{"given":"Chayan","family":"Bhar","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,4,11]]},"reference":[{"key":"3076_CR1","doi-asserted-by":"publisher","DOI":"10.1002\/0471691852","volume-title":"Nonlinear Signal Processing: A Statistical Approach","author":"GR Arce","year":"2004","unstructured":"G.R. Arce, Nonlinear Signal Processing: A Statistical Approach (Wiley, 2004). https:\/\/doi.org\/10.1002\/0471691852"},{"issue":"12","key":"3076_CR2","doi-asserted-by":"publisher","first-page":"3542","DOI":"10.1109\/TCSII.2020.2983128","volume":"67","author":"SS Bhattacharjee","year":"2020","unstructured":"S.S. Bhattacharjee, N.V. George, Nonlinear system identification using exact and approximate improved adaptive exponential functional link networks. IEEE Trans. Circuits Syst. II Express Briefs 67(12), 3542\u20133546 (2020). https:\/\/doi.org\/10.1109\/TCSII.2020.2983128","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"3076_CR3","doi-asserted-by":"publisher","unstructured":"E. Catmull, A Class of Local Interpolating Splines. Computer Aided Geometric Design\/Academic Press, 317-326 (1974). https:\/\/doi.org\/10.1016\/B978-0-12-079050-0.50020-5","DOI":"10.1016\/B978-0-12-079050-0.50020-5"},{"key":"3076_CR4","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2019.107348","volume":"168","author":"L Chang","year":"2020","unstructured":"L. Chang, J. Ming, Robust adaptive filter with lncosh cost. Signal Process. 168, 107348 (2020). https:\/\/doi.org\/10.1016\/j.sigpro.2019.107348","journal-title":"Signal Process."},{"issue":"8","key":"3076_CR5","doi-asserted-by":"publisher","first-page":"1212","DOI":"10.1109\/LSP.2019.2925692","volume":"26","author":"B Chen","year":"2019","unstructured":"B. Chen, X. Wang, Y. Li, J.C. Pr\u00edncipe, Maximum correntropy criterion with variable center. IEEE Signal Process. Lett. 26(8), 1212\u20131216 (2019). https:\/\/doi.org\/10.1109\/LSP.2019.2925692","journal-title":"IEEE Signal Process. Lett."},{"issue":"13","key":"3076_CR6","doi-asserted-by":"publisher","first-page":"3376","DOI":"10.1109\/TSP.2016.2539127","volume":"64","author":"B Chen","year":"2016","unstructured":"B. Chen, L. Xing, H. Zhao, N. Zheng, J.C. Pr\u0131ncipe, Generalized correntropy for robust adaptive filtering. IEEE Trans. Signal Process. 64(13), 3376\u20133387 (2016). https:\/\/doi.org\/10.1109\/TSP.2016.2539127","journal-title":"IEEE Trans. Signal Process."},{"issue":"7","key":"3076_CR7","doi-asserted-by":"publisher","first-page":"880","DOI":"10.1109\/LSP.2014.2319308","volume":"21","author":"B Chen","year":"2014","unstructured":"B. Chen, L. Xing, H. Zhao, N. Zheng, J.C. Pr\u0131ncipe, Steady state mean square error analysis for adaptive filtering under maximum correntropy criterion. IEEE Signal Process. Lett. 21(7), 880\u2013884 (2014). https:\/\/doi.org\/10.1109\/LSP.2014.2319308","journal-title":"IEEE Signal Process. Lett."},{"issue":"19","key":"3076_CR8","doi-asserted-by":"publisher","first-page":"17087","DOI":"10.1007\/s11071-024-09950-9","volume":"112","author":"N Chikyal","year":"2024","unstructured":"N. Chikyal, C. Vasundhara, A. Bhar, M. Kar, Christensen, Hermite polynomial based affine projection Blake Zisserman algorithm for identification of robust sparse nonlinear system. Nonlinear Dyn. 112(19), 17087\u201317105 (2024). https:\/\/doi.org\/10.1007\/s11071-024-09950-9","journal-title":"Nonlinear Dyn."},{"key":"3076_CR9","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00034-024-02839-3","volume":"3","author":"N Chikyal","year":"2024","unstructured":"N. Chikyal, C. Vasundhara, A. Bhar, M.C. Kar, Individually weighted modified logarithmic hyperbolic sine curvelet based recursive FLN for nonlinear system identification. Circuits Syst Signal Process 3, 1\u201332 (2024). https:\/\/doi.org\/10.1007\/s00034-024-02839-3","journal-title":"Circuits Syst Signal Process"},{"key":"3076_CR10","doi-asserted-by":"publisher","unstructured":"N. Chikyal, C. Bhar. Vasundhara, Chebyshev individual adaptive exponential functional link filter for nonlinear system identification. In IEEE 20th India Council International Conference (INDICON). Hyderabad, India 718\u2013722(2023). https:\/\/doi.org\/10.1109\/INDICON59947.2023.10440942","DOI":"10.1109\/INDICON59947.2023.10440942"},{"key":"3076_CR11","doi-asserted-by":"publisher","unstructured":"D. Comminiello, M. Scarpiniti, S. Scardapane, A. Uncini, Sparse functional link adaptive filter using an $$l_1$$-norm regularization. In 2018 IEEE International Symposium on Circuits and Systems (ISCAS), Florence, Italy 1-5 (2018) https:\/\/doi.org\/10.1109\/ISCAS.2018.8351345","DOI":"10.1109\/ISCAS.2018.8351345"},{"issue":"7","key":"3076_CR12","doi-asserted-by":"publisher","first-page":"1502","DOI":"10.1109\/TASL.2013.2255276","volume":"21","author":"C Danilo","year":"2013","unstructured":"C. Danilo, S. Michele, A. Luis, A.G. Jeronimo, U. Aurelio, Functional link adaptive filters for nonlinear acoustic echo cancellation. IEEE Trans. Audio Speech Language Processing. 21(7), 1502\u20131512 (2013). https:\/\/doi.org\/10.1109\/TASL.2013.2255276","journal-title":"IEEE Trans. Audio Speech Language Processing."},{"key":"3076_CR13","doi-asserted-by":"publisher","unstructured":"A. Das, Vasundhara, Recursive Chebyshev functional link adaptive filter for sparse nonlinear system identification with impulsive noise interference. In 2022 3rd International Conference for Emerging Technology (INCET), Belgaum, India, 1\u20135 (2022) https:\/\/doi.org\/10.1109\/INCET54531.2022.9824312.","DOI":"10.1109\/INCET54531.2022.9824312."},{"issue":"4","key":"3076_CR14","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1007\/s10010-011-0144-5","volume":"75","author":"V Filipovic","year":"2011","unstructured":"V. Filipovic, N. Nedic, V. Stojanovic, Robuste identifikation von pneumatischen servo-aktuatoren in der realen situationen. Forsch. Ingenieurwes. 75(4), 183\u2013196 (2011). https:\/\/doi.org\/10.1007\/s10010-011-0144-5","journal-title":"Forsch. Ingenieurwes."},{"issue":"11","key":"3076_CR15","doi-asserted-by":"publisher","first-page":"6636","DOI":"10.1007\/s00034-023-02411-5","volume":"42","author":"Y Gao","year":"2023","unstructured":"Y. Gao, H. Zhao, Y. Zhu, Spline adaptive filtering algorithm-based generalized maximum correntropy and its application to nonlinear active noise control. Circuits Syst. Signal Process. 42(11), 6636\u20136659 (2023). https:\/\/doi.org\/10.1007\/s00034-023-02411-5","journal-title":"Circuits Syst. Signal Process."},{"issue":"3","key":"3076_CR16","doi-asserted-by":"publisher","first-page":"222","DOI":"10.1504\/IJMIC.2022.127513","volume":"41","author":"T Gargi","year":"2022","unstructured":"T. Gargi, T.K. Rawat, Volterra series based nonlinear system identification methods and modelling capabilities. Int. J. Model. Ident. Control 41(3), 222\u2013230 (2022). https:\/\/doi.org\/10.1504\/IJMIC.2022.127513","journal-title":"Int. J. Model. Ident. Control"},{"issue":"5","key":"3076_CR17","doi-asserted-by":"publisher","first-page":"1333","DOI":"10.1007\/s11760-021-02085-z","volume":"16","author":"S Guan","year":"2022","unstructured":"S. Guan, Q. Cheng, Y. Zhao, B. Biswal, Spline adaptive filtering algorithm based on Heaviside step function. SIViP 16(5), 1333\u20131343 (2022). https:\/\/doi.org\/10.1007\/s11760-021-02085-z","journal-title":"SIViP"},{"key":"3076_CR18","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1007\/s11063-017-9606-6","volume":"46","author":"S Guan","year":"2017","unstructured":"S. Guan, Z. Li, Normalised spline adaptive filtering algorithm for nonlinear system identification. Neural Process. Lett. 46, 595\u2013607 (2017). https:\/\/doi.org\/10.1007\/s11063-017-9606-6","journal-title":"Neural Process. Lett."},{"issue":"1","key":"3076_CR19","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1007\/s00034-021-01798-3","volume":"41","author":"W Guo","year":"2022","unstructured":"W. Guo, Z. Yongfeng, Nonlinear spline adaptive filtering against non-gaussian noise. Circuits Syst. Signal Process. 41(1), 579\u2013596 (2022). https:\/\/doi.org\/10.1007\/s00034-021-01798-3","journal-title":"Circuits Syst. Signal Process."},{"issue":"4","key":"3076_CR20","doi-asserted-by":"publisher","first-page":"651","DOI":"10.1016\/0005-1098(90)90044-I","volume":"26","author":"R Haber","year":"1990","unstructured":"R. Haber, H. Unbehauen, Structure identification of nonlinear dynamic systems-a survey on input\/output approaches. Automatica 26(4), 651\u2013677 (1990). https:\/\/doi.org\/10.1016\/0005-1098(90)90044-I","journal-title":"Automatica"},{"key":"3076_CR21","volume-title":"Adaptive Filter Theory","author":"SS Haykin","year":"2002","unstructured":"S.S. Haykin, Adaptive Filter Theory (Pearson Education India, 2002)"},{"issue":"1","key":"3076_CR22","doi-asserted-by":"publisher","first-page":"334","DOI":"10.1016\/j.engappai.2012.02.004","volume":"26","author":"J Herrera","year":"2013","unstructured":"J. Herrera, I. Asier, S. Manuel, Identification and control of integrative MIMO systems using pattern search algorithms: an application to irrigation channels. Eng. Appl. Artif. Intell. 26(1), 334\u2013346 (2013). https:\/\/doi.org\/10.1016\/j.engappai.2012.02.004","journal-title":"Eng. Appl. Artif. Intell."},{"key":"3076_CR23","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/j.sigpro.2018.03.013","volume":"149","author":"F Huang","year":"2018","unstructured":"F. Huang, J. Zhang, S. Zhang, A family of robust adaptive filtering algorithms based on sigmoid cost. Signal Process. 149, 179\u2013192 (2018). https:\/\/doi.org\/10.1016\/j.sigpro.2018.03.013","journal-title":"Signal Process."},{"key":"3076_CR24","doi-asserted-by":"publisher","first-page":"1410","DOI":"10.1109\/LSP.2021.3093862","volume":"28","author":"K Kumar","year":"2021","unstructured":"K. Kumar, P. Rajlaxmi Pandey, S.S. Bhattacharjee, N.V. George, Exponential hyperbolic cosine robust adaptive filters for audio signal processing. IEEE Signal Process. Lett. 28, 1410\u20131414 (2021). https:\/\/doi.org\/10.1109\/LSP.2021.3093862","journal-title":"IEEE Signal Process. Lett."},{"issue":"1","key":"3076_CR25","doi-asserted-by":"publisher","first-page":"647","DOI":"10.1109\/TSMC.2022.3184073","volume":"53","author":"K Kumar","year":"2022","unstructured":"K. Kumar, M.L. Karthik, N.V. George, Generalized modified Blake-Zisserman robust sparse adaptive filters. IEEE Trans. Syst. Man Cybern. Syst. 53(1), 647\u201352 (2022). https:\/\/doi.org\/10.1109\/TSMC.2022.3184073","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"issue":"3","key":"3076_CR26","doi-asserted-by":"publisher","first-page":"1967","DOI":"10.1109\/TCSII.2021.3129536","volume":"69","author":"K Kumar","year":"2021","unstructured":"K. Kumar, R. Pandey, S.S. Bora, N.V. George, A robust family of algorithms for adaptive filtering based on the arctangent framework. IEEE Trans. Circuits Syst. II Express Briefs 69(3), 1967\u20131971 (2021). https:\/\/doi.org\/10.1109\/TCSII.2021.3129536","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"issue":"11","key":"3076_CR27","doi-asserted-by":"publisher","first-page":"2541","DOI":"10.1016\/j.sigpro.2011.05.007","volume":"91","author":"JM Le Caillec","year":"2011","unstructured":"J.M. Le Caillec, Spectral inversion of second order Volterra models based on the blind identification of Wiener models. Signal Process. 91(11), 2541\u20132555 (2011). https:\/\/doi.org\/10.1016\/j.sigpro.2011.05.007","journal-title":"Signal Process."},{"key":"3076_CR28","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2024.120888","volume":"677","author":"W Li","year":"2024","unstructured":"W. Li, Z. Zhou, H. Li, M. Xu, J. Tang, Sigmoid distance metric-based spline adaptive filters for nonlinear adaptive noise cancellation. Inf. Sci. 677, 120888 (2024). https:\/\/doi.org\/10.1016\/j.ins.2024.120888","journal-title":"Inf. Sci."},{"key":"3076_CR29","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1016\/j.sigpro.2018.02.022","volume":"148","author":"C Liu","year":"2018","unstructured":"C. Liu, Z. Zhang, X. Tang, Sign normalized spline adaptive filtering algorithms against impulsive noise. Signal Process. 148, 234\u2013240 (2018). https:\/\/doi.org\/10.1016\/j.sigpro.2018.02.022","journal-title":"Signal Process."},{"issue":"6","key":"3076_CR30","doi-asserted-by":"publisher","first-page":"393","DOI":"10.1049\/el.2017.4434","volume":"54","author":"C Liu","year":"2018","unstructured":"C. Liu, Z. Zhang, Set membership normalized least M-estimate spline adaptive filtering algorithm in impulsive noise. Electron. Lett. 54(6), 393\u2013395 (2018). https:\/\/doi.org\/10.1049\/el.2017.4434","journal-title":"Electron. Lett."},{"issue":"6","key":"3076_CR31","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfranklin.2024.106713","volume":"361","author":"MM Morato","year":"2024","unstructured":"M.M. Morato, V.M. Cunha, T.L. Santos, J.E. Normey-Rico, O. Sename, A robust nonlinear tracking MPC using qLPV embedding and zonotopic uncertainty propagation. J. Franklin Inst. 361(6), 106713 (2024). https:\/\/doi.org\/10.1016\/j.jfranklin.2024.106713","journal-title":"J. Franklin Inst."},{"key":"3076_CR32","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-68630-1","volume-title":"Adaptive Nonlinear System Identification: the Volterra and Wiener Model Approaches","author":"T Ogunfunmi","year":"2007","unstructured":"T. Ogunfunmi, Adaptive Nonlinear System Identification: the Volterra and Wiener Model Approaches (Springer, 2007)"},{"issue":"9","key":"3076_CR33","doi-asserted-by":"publisher","first-page":"1434","DOI":"10.1109\/TCSI.2016.2572091","volume":"63","author":"V Patel","year":"2016","unstructured":"V. Patel, Design of adaptive exponential functional link network-based nonlinear filters. IEEE Trans. Circuits Syst. I Regul. Pap. 63(9), 1434\u20131442 (2016). https:\/\/doi.org\/10.1109\/TCSI.2016.2572091","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"issue":"4","key":"3076_CR34","doi-asserted-by":"publisher","first-page":"505","DOI":"10.1109\/TSMCB.2002.1018769","volume":"32","author":"JC Patra","year":"2002","unstructured":"J.C. Patra, A.C. Kot, Nonlinear dynamic system identification using Chebyshev functional link artificial neural networks. IEEE Trans. Syst. Man Cybern. Part B (Cybernetics) 32(4), 505\u2013511 (2002). https:\/\/doi.org\/10.1109\/TSMCB.2002.1018769","journal-title":"IEEE Trans. Syst. Man Cybern. Part B (Cybernetics)"},{"key":"3076_CR35","doi-asserted-by":"publisher","unstructured":"S. Peng, Z. Wu, X. Zhang, B. Chen, Nonlinear spline adaptive filtering under maximum correntropy criterion, TENCON 2015-2015 IEEE Region 10 Conference,1\u20135 (2015) https:\/\/doi.org\/10.1007\/s00034-021-01798-3","DOI":"10.1007\/s00034-021-01798-3"},{"key":"3076_CR36","doi-asserted-by":"publisher","first-page":"22571","DOI":"10.1109\/ACCESS.2020.2969219","volume":"8","author":"L Qianqian","year":"2020","unstructured":"L. Qianqian, H. Yigang, Robust Geman-McClure based nonlinear spline adaptive filter against impulsive noise. IEEE Explor. 8, 22571\u201322580 (2020). https:\/\/doi.org\/10.1109\/ACCESS.2020.2969219","journal-title":"IEEE Explor."},{"issue":"12","key":"3076_CR37","doi-asserted-by":"publisher","first-page":"5149","DOI":"10.1109\/TCSII.2022.3200523","volume":"69","author":"S Radhika","year":"2022","unstructured":"S. Radhika, F. Albu, A. Chandrasekar, Robust exponential hyperbolic sine adaptive filter for impulsive noise environments. IEEE Trans. Circuits Syst. II Express Briefs 69(12), 5149\u20135153 (2022). https:\/\/doi.org\/10.1109\/TCSII.2022.3200523","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"3076_CR38","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1016\/j.eswa.2017.04.043","volume":"83","author":"M Rathod","year":"2017","unstructured":"M. Rathod, V. Patel, N. George, Generalized spline nonlinear adaptive filters. Expert Syst. Appl. 83, 122\u2013130 (2017). https:\/\/doi.org\/10.1016\/j.eswa.2017.04.043","journal-title":"Expert Syst. Appl."},{"issue":"3","key":"3076_CR39","doi-asserted-by":"publisher","first-page":"672","DOI":"10.1109\/72.761726","volume":"10","author":"G Samantha","year":"1999","unstructured":"G. Samantha, P. Francesco, U. Aurelio, Multilayer feedforward networks with adaptive spline activation function. IEEE Trans. Neural Netw. IEEE Neural Netw. Council Public. 10(3), 672\u2013683 (1999). https:\/\/doi.org\/10.1109\/72.761726","journal-title":"IEEE Trans. Neural Netw. IEEE Neural Netw. Council Public."},{"issue":"3","key":"3076_CR40","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1080\/02564602.2020.1732233","volume":"38","author":"G Saurav","year":"2021","unstructured":"G. Saurav, S.A. Kumar, S.U. Kumar, Volterra and Wiener model based temporally and spatio temporally coupled nonlinear system identification: a synthesized review. IETE Tech. Rev. 38(3), 303\u2013327 (2021). https:\/\/doi.org\/10.1080\/02564602.2020.1732233","journal-title":"IETE Tech. Rev."},{"key":"3076_CR41","doi-asserted-by":"publisher","first-page":"30","DOI":"10.1016\/j.sigpro.2014.08.045","volume":"108","author":"M Scarpiniti","year":"2015","unstructured":"M. Scarpiniti, D. Comminiello, R. Parisi, A. Uncini, Nonlinear system identification using IIR spline adaptive filters. Signal Process. 108, 30\u201335 (2015). https:\/\/doi.org\/10.1016\/j.sigpro.2014.08.045","journal-title":"Signal Process."},{"issue":"4","key":"3076_CR42","doi-asserted-by":"publisher","first-page":"772","DOI":"10.1016\/j.sigpro.2012.09.021","volume":"93","author":"M Scarpiniti","year":"2013","unstructured":"M. Scarpiniti, D. Comminiello, R. Parisi, A. Uncini, Nonlinear spline adaptive filtering. Signal Process. 93(4), 772\u2013783 (2013). https:\/\/doi.org\/10.1016\/j.sigpro.2012.09.021","journal-title":"Signal Process."},{"issue":"7","key":"3076_CR43","doi-asserted-by":"publisher","first-page":"1825","DOI":"10.1109\/TCSI.2015.2423791","volume":"62","author":"M Scarpiniti","year":"2015","unstructured":"M. Scarpiniti, D. Comminiello, R. Parisi, A. Uncini, Novel cascade spline architectures for the identification of nonlinear systems. IEEE Trans. Circuits Syst. I Regul. Pap. 62(7), 1825\u20131835 (2015). https:\/\/doi.org\/10.1109\/TCSI.2015.2423791","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"3076_CR44","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1016\/j.sigpro.2014.01.019","volume":"100","author":"M Scarpiniti","year":"2014","unstructured":"M. Scarpiniti, D. Comminiello, R. Parisi, A. Uncini, Hammerstein uniform cubic spline adaptive filters: Learning and convergence properties. Signal Process. 100, 112\u2013123 (2014). https:\/\/doi.org\/10.1016\/j.sigpro.2014.01.019","journal-title":"Signal Process."},{"issue":"18","key":"3076_CR45","doi-asserted-by":"publisher","first-page":"3974","DOI":"10.1002\/rnc.3544","volume":"26","author":"V Stojanovic","year":"2016","unstructured":"V. Stojanovic, N. Nedic, Identification of time-varying OE models in the presence of non-Gaussian noise: application to pneumatic servo drives. Int. J. Robust Nonlinear Control 26(18), 3974\u20133995 (2016). https:\/\/doi.org\/10.1002\/rnc.3544","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"3076_CR46","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). https:\/\/doi.org\/10.1007\/s00034-013-9633-0","journal-title":"Circuits Syst Signal Process"},{"key":"3076_CR47","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1109\/LCSYS.2022.3202827","volume":"7","author":"SP Talebi","year":"2023","unstructured":"S.P. Talebi, S.J. Godsill, D.P. Mandic, Filtering structures for $$\\alpha $$-stable systems. IEEE Control Syst. Lett. 7, 553\u2013558 (2023). https:\/\/doi.org\/10.1109\/LCSYS.2022.3202827","journal-title":"IEEE Control Syst. Lett."},{"key":"3076_CR48","doi-asserted-by":"publisher","unstructured":"Y. Tao, L. Wenqi, C. Rodrigo, Y. Yi. Lamare, M-estimate affine projection spline adaptive filtering algorithm: analysis and implementation. Digital Signal Process. 123, 103452 (2022). https:\/\/doi.org\/10.1016\/j.dsp.2022.103452","DOI":"10.1016\/j.dsp.2022.103452"},{"key":"3076_CR49","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-02807-1","volume-title":"Fundamentals of Adaptive Signal Processing","author":"A Uncini","year":"2015","unstructured":"A. Uncini, Fundamentals of Adaptive Signal Processing (Springer, 2015). https:\/\/doi.org\/10.1007\/978-3-319-02807-1"},{"issue":"6","key":"3076_CR50","doi-asserted-by":"publisher","first-page":"1154","DOI":"10.1109\/TCSII.2019.2929536","volume":"67","author":"W Wang","year":"2019","unstructured":"W. Wang, H. Zhao, X. Zeng, K. Do\u01e7an\u00e7ay, Steady-state performance analysis of nonlinear spline adaptive filter under maximum correntropy criterion. IEEE Trans. Circuits Syst. II Express Briefs 67(6), 1154\u20131158 (2019). https:\/\/doi.org\/10.1109\/TCSII.2019.2929536","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"issue":"1","key":"3076_CR51","doi-asserted-by":"publisher","first-page":"832","DOI":"10.1016\/j.egyr.2021.11.068","volume":"8","author":"W Xingyu","year":"2022","unstructured":"W. Xingyu, W. Anna, W. Dazhi, W. Wenhui, An improved spline adaptive filter for nonlinear system identification under impulsive noise environment. Energy Rep. 8(1), 832\u2013840 (2022). https:\/\/doi.org\/10.1016\/j.egyr.2021.11.068","journal-title":"Energy Rep."},{"issue":"8","key":"3076_CR52","doi-asserted-by":"publisher","first-page":"1895","DOI":"10.1007\/s00034-021-01874-8","volume":"41","author":"T Xu","year":"2022","unstructured":"T. Xu, J. Chen, Y. Pu, Fractional-based stochastic gradient algorithms for time-delayed ARX models. Circuits Syst. Signal Process. 41(8), 1895\u20131912 (2022). https:\/\/doi.org\/10.1007\/s00034-021-01874-8","journal-title":"Circuits Syst. Signal Process."},{"key":"3076_CR53","doi-asserted-by":"publisher","first-page":"657","DOI":"10.1007\/s11071-020-05899-7","volume":"103","author":"L Yang","year":"2021","unstructured":"L. Yang, J. Liu, R. Sun, Spline adaptive filters based on real-time over-sampling strategy for nonlinear system identification. Nonlinear Dyn. 103, 657\u2013675 (2021). https:\/\/doi.org\/10.1007\/s11071-020-05899-7","journal-title":"Nonlinear Dyn."},{"issue":"3","key":"3076_CR54","doi-asserted-by":"publisher","first-page":"1629","DOI":"10.1007\/s11071-019-05243-8","volume":"98","author":"L Yang","year":"2019","unstructured":"L. Yang, J. Liu, Z. Zhao, R. Yan, X. Chen, Interval variable step-size spline adaptive filter for the identification of nonlinear block-oriented system. Nonlinear Dyn. 98(3), 1629\u20131643 (2019). https:\/\/doi.org\/10.1007\/s11071-019-05243-8","journal-title":"Nonlinear Dyn."},{"key":"3076_CR55","doi-asserted-by":"publisher","first-page":"1647","DOI":"10.1007\/s11071-017-3754-0","volume":"90","author":"Y Yang","year":"2017","unstructured":"Y. Yang, B. Yang, M. Niu, Spline adaptive filter with fractional-order adaptive strategy for nonlinear model identification of magnetostrictive actuator. Nonlinear Dyn. 90, 1647\u20131659 (2017). https:\/\/doi.org\/10.1007\/s11071-017-3754-0","journal-title":"Nonlinear Dyn."},{"issue":"9","key":"3076_CR56","doi-asserted-by":"publisher","first-page":"4314","DOI":"10.1109\/TNNLS.2017.2761259","volume":"29","author":"S Zhang","year":"2018","unstructured":"S. Zhang, W.X. Zheng, Recursive adaptive sparse exponential functional link neural network for nonlinear AEC in impulsive noise environment. IEEE Trans. Neural Netw. Learn. Syst. 29(9), 4314\u20134323 (2018). https:\/\/doi.org\/10.1109\/TNNLS.2017.2761259","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"3","key":"3076_CR57","doi-asserted-by":"publisher","first-page":"1907","DOI":"10.1109\/TCSII.2021.3111919","volume":"69","author":"Z Zhang","year":"2022","unstructured":"Z. Zhang, J. Zhang, Chebyshev functional link spline neural filter for nonlinear dynamic system identification. IEEE Trans. Circuits Syst. II Express Briefs 69(3), 1907\u20131911 (2022). https:\/\/doi.org\/10.1109\/TCSII.2021.3111919","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"issue":"5","key":"3076_CR58","doi-asserted-by":"publisher","first-page":"6275","DOI":"10.1109\/TAES.2024.3403073","volume":"60","author":"H Zhao","year":"2024","unstructured":"H. Zhao, Y. Gao, R. Zhu, Least mean p-power Hammerstein spline adaptive filtering algorithm: formulation and analysis. IEEE Trans. Aerosp. Electron. Syst. 60(5), 6275\u20136283 (2024). https:\/\/doi.org\/10.1109\/TAES.2024.3403073","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"3076_CR59","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2023.109000","volume":"208","author":"Z Zhao","year":"2023","unstructured":"Z. Zhao, L. Defang, Z. Jiashu, Nonlinear autoregressive spline neural filter and its application. Signal Process. 208, 109000 (2023). https:\/\/doi.org\/10.1016\/j.sigpro.2023.109000","journal-title":"Signal Process."},{"key":"3076_CR60","doi-asserted-by":"publisher","first-page":"1282","DOI":"10.1109\/TASLP.2020.2982030","volume":"28","author":"Y Zhu","year":"2020","unstructured":"Y. Zhu, H. Zhao, X. Zeng, B. Chen, Robust generalized maximum Correntropy criterion algorithms for active noise control. IEEE\/ACM Trans. Audio Speech Language Process. 28, 1282\u20131292 (2020). https:\/\/doi.org\/10.1109\/TASLP.2020.2982030","journal-title":"IEEE\/ACM Trans. Audio Speech Language Process."}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-025-03076-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00034-025-03076-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-025-03076-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,6]],"date-time":"2025-09-06T11:10:56Z","timestamp":1757157056000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00034-025-03076-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,11]]},"references-count":60,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["3076"],"URL":"https:\/\/doi.org\/10.1007\/s00034-025-03076-y","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"type":"print","value":"0278-081X"},{"type":"electronic","value":"1531-5878"}],"subject":[],"published":{"date-parts":[[2025,4,11]]},"assertion":[{"value":"1 October 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 February 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 February 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 April 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 whose names are listed certify that they have NO affiliations with or involvement in any organization or entity with any financial interest (such as honorarium; educational grants; participation in speakers\u2019 bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge, or beliefs) in the subject matter or materials discussed in this manuscript.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}