{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T06:49:50Z","timestamp":1762325390567,"version":"3.37.3"},"reference-count":82,"publisher":"Springer Science and Business Media LLC","issue":"12","license":[{"start":{"date-parts":[[2022,7,26]],"date-time":"2022-07-26T00:00:00Z","timestamp":1658793600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,7,26]],"date-time":"2022-07-26T00:00:00Z","timestamp":1658793600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62103167"],"award-info":[{"award-number":["62103167"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20210451"],"award-info":[{"award-number":["BK20210451"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004028","name":"Jiangnan University","doi-asserted-by":"publisher","award":["JUSRP12028","JUSRP12040"],"award-info":[{"award-number":["JUSRP12028","JUSRP12040"]}],"id":[{"id":"10.13039\/501100004028","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12102146"],"award-info":[{"award-number":["12102146"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004608","name":"Natural Science Foundation of Jiangsu Province","doi-asserted-by":"publisher","award":["BK20200611"],"award-info":[{"award-number":["BK20200611"]}],"id":[{"id":"10.13039\/501100004608","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2022,12]]},"DOI":"10.1007\/s00034-022-02112-5","type":"journal-article","created":{"date-parts":[[2022,7,26]],"date-time":"2022-07-26T11:02:51Z","timestamp":1658833371000},"page":"6750-6773","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Auxiliary Model-Based Iterative Estimation Algorithms for Nonlinear Systems Using the Covariance Matrix Adaptation Strategy"],"prefix":"10.1007","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6297-9475","authenticated-orcid":false,"given":"Yawen","family":"Mao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chen","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jing","family":"Chen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Pu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qingyuan","family":"Hu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,7,26]]},"reference":[{"key":"2112_CR1","doi-asserted-by":"publisher","DOI":"10.1155\/2021\/6613425","author":"IA Aljamaan","year":"2021","unstructured":"I.A. Aljamaan, M.M. Al-Dhaifallah, D.T. Westwick, Hammerstein Box-Jenkins system identification of the cascaded tanks benchmark system. Math. Probl. Eng. (2021). https:\/\/doi.org\/10.1155\/2021\/6613425","journal-title":"Math. Probl. Eng."},{"issue":"5","key":"2112_CR2","doi-asserted-by":"publisher","first-page":"772","DOI":"10.3390\/electronics11050772","volume":"11","author":"Y An","year":"2022","unstructured":"Y. An, Y.J. Zhang, W.J. Cao et al., A lightweight and practical anonymous authentication protocol based on bit-self-test PUF. Electronics 11(5), 772 (2022)","journal-title":"Electronics"},{"key":"2112_CR3","doi-asserted-by":"crossref","unstructured":"D. V. Arnold, N.A. Hansen, (1+1)-CMA-ES for constrained optimisation. in Proceedings of the 14th annual conference on Genetic and evolutionary computation, July, 2012, 297\u2013304","DOI":"10.1145\/2330163.2330207"},{"issue":"4","key":"2112_CR4","doi-asserted-by":"publisher","first-page":"480","DOI":"10.1109\/TEVC.2006.882427","volume":"11","author":"DV Arnold","year":"2007","unstructured":"D.V. Arnold, R. Salomon, Evolutionary gradient search revisited. IEEE Trans. Evol. Comput. 11(4), 480\u2013495 (2007)","journal-title":"IEEE Trans. Evol. Comput."},{"key":"2112_CR5","doi-asserted-by":"crossref","unstructured":"A. Auger, M. Schoenauer, N. Vanhaecke, LS-CMA-ES: A second-order algorithm for covariance matrix adaptation. in International Conference on Parallel Problem Solving from Nature, September, 182\u2013191. (2004) Springer, Berlin","DOI":"10.1007\/978-3-540-30217-9_19"},{"issue":"7","key":"2112_CR6","doi-asserted-by":"publisher","first-page":"1610","DOI":"10.1109\/TSP.2002.1011202","volume":"50","author":"B Bai","year":"2002","unstructured":"B. Bai, M. Fu, A blind approach to Hammerstein model identification. IEEE Trans. Signal Process. 50(7), 1610\u20131619 (2002)","journal-title":"IEEE Trans. Signal Process."},{"issue":"5","key":"2112_CR7","doi-asserted-by":"publisher","first-page":"746","DOI":"10.1109\/TEVC.2017.2680320","volume":"21","author":"HG Beyer","year":"2017","unstructured":"H.G. Beyer, B. Sendhoff, Simplify your covariance matrix adaptation evolution strategy. IEEE Trans. Evol. Comput. 21(5), 746\u2013759 (2017)","journal-title":"IEEE Trans. Evol. Comput."},{"issue":"1","key":"2112_CR8","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/s40846-022-00681-z","volume":"42","author":"YF Chen","year":"2022","unstructured":"Y.F. Chen, C. Zhang, C.Y. Liu, Atrial fibrillation detection using feedforward neural network. J. Med. Biolog. Eng. 42(1), 63\u201373 (2022)","journal-title":"J. Med. Biolog. Eng."},{"key":"2112_CR9","volume-title":"System Identification - Auxiliary Model Identification Idea and Methods","author":"F Ding","year":"2017","unstructured":"F. Ding, System Identification - Auxiliary Model Identification Idea and Methods (Science Press, Beijing, 2017)"},{"issue":"4","key":"2112_CR10","doi-asserted-by":"publisher","first-page":"1694","DOI":"10.1016\/j.apm.2012.04.039","volume":"37","author":"F Ding","year":"2013","unstructured":"F. Ding, Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling. Appl. Math. Modell. 37(4), 1694\u20131704 (2013)","journal-title":"Appl. Math. Modell."},{"issue":"1","key":"2112_CR11","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1049\/iet-cta.2012.0171","volume":"7","author":"F Ding","year":"2013","unstructured":"F. Ding, Coupled-least-squares identification for multivariable systems. IET Control Theory Appl. 7(1), 68\u201379 (2013)","journal-title":"IET Control Theory Appl."},{"issue":"1","key":"2112_CR12","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1016\/j.apm.2013.06.007","volume":"38","author":"F Ding","year":"2014","unstructured":"F. Ding, Combined state and least squares parameter estimation algorithms for dynamic systems. Appl. Math. Modell. 38(1), 403\u2013412 (2014)","journal-title":"Appl. Math. Modell."},{"issue":"10","key":"2112_CR13","doi-asserted-by":"publisher","first-page":"1739","DOI":"10.1016\/j.automatica.2004.05.001","volume":"40","author":"F Ding","year":"2004","unstructured":"F. Ding, T. Chen, Combined parameter and output estimation of dual-rate systems using an auxiliary model. Automatica 40(10), 1739\u20131748 (2004)","journal-title":"Automatica"},{"issue":"9","key":"2112_CR14","doi-asserted-by":"publisher","first-page":"1436","DOI":"10.1109\/TAC.2005.854654","volume":"50","author":"F Ding","year":"2005","unstructured":"F. Ding, T. Chen, Parameter estimation of dual-rate stochastic systems by using an output error method. IEEE Trans. Autom. Control 50(9), 1436\u20131441 (2005)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"8","key":"2112_CR15","doi-asserted-by":"publisher","first-page":"1976","DOI":"10.1109\/TAC.2010.2050713","volume":"55","author":"F Ding","year":"2010","unstructured":"F. Ding, G. Liu, X.P. Liu, Partially coupled stochastic gradient identification methods for non-uniformly sampled systems. IEEE Trans. Automat Control 55(8), 1976\u20131981 (2010)","journal-title":"IEEE Trans. Automat Control"},{"issue":"1","key":"2112_CR16","first-page":"43","volume":"226","author":"F Ding","year":"2012","unstructured":"F. Ding, Y.J. Liu, B. Bao, Gradient based and least squares based iterative estimation algorithms for multi-input multi-output systems. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng. 226(1), 43\u201355 (2012)","journal-title":"Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng."},{"issue":"9","key":"2112_CR17","doi-asserted-by":"publisher","first-page":"1754","DOI":"10.1002\/acs.3287","volume":"35","author":"JL Ding","year":"2021","unstructured":"J.L. Ding, W.H. Zhang, Finite-time adaptive control for nonlinear systems with uncertain parameters based on the command filters. Int. J. Adapt. Control Signal Process. 35(9), 1754\u20131767 (2021)","journal-title":"Int. J. Adapt. Control Signal Process."},{"issue":"14","key":"2112_CR18","doi-asserted-by":"publisher","first-page":"5492","DOI":"10.1002\/rnc.5084","volume":"30","author":"YM Fan","year":"2020","unstructured":"Y.M. Fan, X.M. Liu, Two-stage auxiliary model gradient-based iterative algorithm for the input nonlinear controlled autoregressive system with variable-gain nonlinearity. Int. J. Robust Nonlinear Control 30(14), 5492\u20135509 (2020)","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"2112_CR19","doi-asserted-by":"publisher","DOI":"10.1016\/j.aml.2021.107525","volume":"122","author":"FZ Geng","year":"2021","unstructured":"F.Z. Geng, X.Y. Wu, Reproducing kernel functions based univariate spline interpolation. Appl. Math. Lett. 122, 107525 (2021)","journal-title":"Appl. Math. Lett."},{"issue":"4","key":"2112_CR20","doi-asserted-by":"publisher","first-page":"2613","DOI":"10.1007\/s11071-019-04946-2","volume":"96","author":"K Hammar","year":"2019","unstructured":"K. Hammar, T. Djamah, M. Bettayeb, Identification of fractional Hammerstein system with application to a heating process. Nonlinear Dyn. 96(4), 2613\u20132626 (2019)","journal-title":"Nonlinear Dyn."},{"key":"2112_CR21","doi-asserted-by":"crossref","unstructured":"N. Hansen, The CMA evolution strategy: a comparing review. Towards a new evolutionary computation, 75\u2013102 (2006)","DOI":"10.1007\/3-540-32494-1_4"},{"key":"2112_CR22","unstructured":"N. Hansen, The CMA evolution strategy: A tutorial. (2016). arXiv preprint arXiv:1604.00772"},{"issue":"10","key":"2112_CR23","doi-asserted-by":"publisher","first-page":"9941","DOI":"10.1109\/TIE.2020.3026286","volume":"68","author":"J Hou","year":"2021","unstructured":"J. Hou, F.W. Chen, P.H. Li, Z.Q. Zhu, Gray-box parsimonious subspace identification of Hammerstein-type systems. IEEE Trans. Ind. Electron. 68(10), 9941\u20139951 (2021)","journal-title":"IEEE Trans. Ind. Electron."},{"issue":"1","key":"2112_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1162\/evco.2007.15.1.1","volume":"15","author":"C Igel","year":"2007","unstructured":"C. Igel, N. Hansen, S. Roth, Covariance matrix adaptation for multi-objective optimization. Evol. Comput. 15(1), 1\u201328 (2007)","journal-title":"Evol. Comput."},{"issue":"8","key":"2112_CR25","doi-asserted-by":"publisher","first-page":"5019","DOI":"10.1016\/j.jfranklin.2020.03.027","volume":"357","author":"Y Ji","year":"2020","unstructured":"Y. Ji, X.K. Jiang, L.J. Wan, Hierarchical least squares parameter estimation algorithm for two-input Hammerstein finite impulse response systems. J. Frankl. Inst. 357(8), 5019\u20135032 (2020)","journal-title":"J. Frankl. Inst."},{"issue":"5","key":"2112_CR26","doi-asserted-by":"publisher","first-page":"2317","DOI":"10.1016\/j.jfranklin.2022.01.032","volume":"359","author":"Y Ji","year":"2022","unstructured":"Y. Ji, Z. Kang, X. Zhang, Model recovery for multi-input signal-output nonlinear systems based on the compressed sensing recovery theory. J. Frankl. Inst. 359(5), 2317\u20132339 (2022)","journal-title":"J. Frankl. Inst."},{"issue":"3","key":"2112_CR27","doi-asserted-by":"publisher","first-page":"971","DOI":"10.1002\/rnc.5323","volume":"31","author":"Y Ji","year":"2021","unstructured":"Y. Ji, Z. Kang, Three-stage forgetting factor stochastic gradient parameter estimation methods for a class of nonlinear systems. Int. J. Robust Nonlinear Control 31(3), 971\u2013987 (2021)","journal-title":"Int. J. Robust Nonlinear Control"},{"issue":"15","key":"2112_CR28","doi-asserted-by":"publisher","first-page":"7007","DOI":"10.1002\/rnc.5675","volume":"31","author":"Y Ji","year":"2021","unstructured":"Y. Ji, Z. Kang, X.M. Liu, The data filtering based multiple-stage Levenberg-Marquardt algorithm for Hammerstein nonlinear systems. Int. J. Robust Nonlinear Control 31(15), 7007\u20137025 (2021)","journal-title":"Int. J. Robust Nonlinear Control"},{"issue":"8","key":"2112_CR29","doi-asserted-by":"publisher","first-page":"2706","DOI":"10.1007\/s12555-019-1060-y","volume":"19","author":"Y Ji","year":"2021","unstructured":"Y. Ji, Z. Kang, C. Zhang, Two-stage gradient-based recursive estimation for nonlinear models by using the data filtering. Int. J. Control Autom. Syst. 19(8), 2706\u20132715 (2021)","journal-title":"Int. J. Control Autom. Syst."},{"issue":"9","key":"2112_CR30","doi-asserted-by":"publisher","first-page":"3727","DOI":"10.1002\/rnc.4961","volume":"30","author":"Y Ji","year":"2020","unstructured":"Y. Ji, C. Zhang, Z. Kang, Parameter estimation for block-oriented nonlinear systems using the key term separation. Int. J. Robust Nonlinear Control 30(9), 3727\u20133752 (2020)","journal-title":"Int. J. Robust Nonlinear Control"},{"issue":"7","key":"2112_CR31","doi-asserted-by":"publisher","first-page":"3470","DOI":"10.1007\/s00034-019-01329-1","volume":"39","author":"J Li","year":"2020","unstructured":"J. Li, T. Zong, J. Gu, L. Hua, Parameter estimation of Wiener systems based on the particle swarm iteration and gradient search principle. Circuits Syst. Signal Process. 39(7), 3470\u20133495 (2020)","journal-title":"Circuits Syst. Signal Process."},{"key":"2112_CR32","doi-asserted-by":"publisher","first-page":"1302","DOI":"10.1109\/LSP.2022.3177352","volume":"29","author":"JM Li","year":"2022","unstructured":"J.M. Li, F. Ding, Fitting nonlinear signal models using the increasing-data criterion. IEEE Signal Process. Lett. 29, 1302\u20131306 (2022)","journal-title":"IEEE Signal Process. Lett."},{"key":"2112_CR33","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.matcom.2021.10.003","volume":"193","author":"M Li","year":"2022","unstructured":"M. Li, G. Xu, Q. Lai, J. Chen, A chaotic strategy-based quadratic opposition-based learning adaptive variable-speed whale optimization algorithm. Math. Comput. Simul. 193, 71\u201399 (2022)","journal-title":"Math. Comput. Simul."},{"issue":"6","key":"2112_CR34","doi-asserted-by":"publisher","first-page":"1581","DOI":"10.1007\/s12555-019-0191-5","volume":"18","author":"MH Li","year":"2020","unstructured":"M.H. Li, X.M. Liu, Maximum likelihood least squares based iterative estimation for a class of bilinear systems using the data filtering technique. Int. J. Control Autom. Syst. 18(6), 1581\u20131592 (2020)","journal-title":"Int. J. Control Autom. Syst."},{"issue":"2","key":"2112_CR35","doi-asserted-by":"publisher","first-page":"240","DOI":"10.1002\/acs.3203","volume":"35","author":"MH Li","year":"2021","unstructured":"M.H. Li, X.M. Liu, Maximum likelihood hierarchical least squares-based iterative identification for dual-rate stochastic systems. Int. J. Adapt. Control Signal Process. 35(2), 240\u2013261 (2021)","journal-title":"Int. J. Adapt. Control Signal Process."},{"issue":"10","key":"2112_CR36","doi-asserted-by":"publisher","first-page":"2056","DOI":"10.1002\/acs.3308","volume":"35","author":"MH Li","year":"2021","unstructured":"M.H. Li, X.M. Liu, Iterative identification methods for a class of bilinear systems by using the particle filtering technique. Int. J. Adapt. Control Signal Process. 35(10), 2056\u20132074 (2021)","journal-title":"Int. J. Adapt. Control Signal Process."},{"key":"2112_CR37","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1016\/j.apnum.2021.10.008","volume":"172","author":"XY Li","year":"2022","unstructured":"X.Y. Li, H.L. Wang, B.Y. Wu, A stable and efficient technique for linear boundary value problems by applying kernel functions. Appl. Numer. Math. 172, 206\u2013214 (2022)","journal-title":"Appl. Numer. Math."},{"key":"2112_CR38","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1016\/j.apnum.2021.05.004","volume":"167","author":"XY Li","year":"2021","unstructured":"X.Y. Li, B.Y. Wu, Superconvergent kernel functions approaches for the second kind Fredholm integral equations. Appl. Numer. Math. 167, 202\u2013210 (2021)","journal-title":"Appl. Numer. Math."},{"key":"2112_CR39","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2022.110365","volume":"142","author":"SY Liu","year":"2022","unstructured":"S.Y. Liu, X. Zhang, L. Xu et al., Expectation-maximization algorithm for bilinear systems by using the Rauch-Tung-Striebel smoother. Automatica 142, 110365 (2022)","journal-title":"Automatica"},{"issue":"9","key":"2112_CR40","doi-asserted-by":"publisher","first-page":"4017","DOI":"10.1002\/rnc.5450","volume":"31","author":"XM Liu","year":"2021","unstructured":"X.M. Liu, Y.M. Fan, Maximum likelihood extended gradient-based estimation algorithms for the input nonlinear controlled autoregressive moving average system with variable-gain nonlinearity. Int. J. Robust Nonlinear Control 31(9), 4017\u20134036 (2021)","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"2112_CR41","volume-title":"System Identification: Theory for the User","author":"L Ljung","year":"1999","unstructured":"L. Ljung, System Identification: Theory for the User, 2nd edn. (Prentice Hall, Englewood Cliffs, New Jersey, 1999)","edition":"2"},{"issue":"9","key":"2112_CR42","doi-asserted-by":"publisher","first-page":"1898","DOI":"10.1002\/acs.3302","volume":"35","author":"P Ma","year":"2021","unstructured":"P. Ma, L. Wang, Filtering-based recursive least squares estimation approaches for multivariate equation-error systems by using the multiinnovation theory. Int. J. Adapt. Control Signal Process. 35(9), 1898\u20131915 (2021)","journal-title":"Int. J. Adapt. Control Signal Process."},{"issue":"18","key":"2112_CR43","doi-asserted-by":"publisher","first-page":"3040","DOI":"10.1049\/iet-cta.2019.0112","volume":"13","author":"H Ma","year":"2019","unstructured":"H. Ma, J. Pan, W. Ding, Partially-coupled least squares based iterative parameter estimation for multi-variable output-error-like autoregressive moving average systems. IET Control Theory Appl. 13(18), 3040\u20133051 (2019)","journal-title":"IET Control Theory Appl."},{"issue":"17","key":"2112_CR44","doi-asserted-by":"publisher","first-page":"2613","DOI":"10.1049\/iet-cta.2019.1027","volume":"14","author":"H Ma","year":"2020","unstructured":"H. Ma, X. Zhang, Q.Y. Liu, Partially-coupled gradient-based iterative algorithms for multivariable output-error-like systems with autoregressive moving average noises. IET Control Theory Appl. 14(17), 2613\u20132627 (2020)","journal-title":"IET Control Theory Appl."},{"issue":"2","key":"2112_CR45","doi-asserted-by":"publisher","first-page":"651","DOI":"10.1007\/s00034-015-0064-y","volume":"35","author":"Y Mao","year":"2016","unstructured":"Y. Mao, Data filtering-based multi-innovation stochastic gradient algorithm for nonlinear output error autoregressive systems. Circuits Syst. Signal Process. 35(2), 651\u2013667 (2016)","journal-title":"Circuits Syst. Signal Process."},{"key":"2112_CR46","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.aml.2016.03.016","volume":"60","author":"Y Mao","year":"2016","unstructured":"Y. Mao, A novel parameter separation based identification algorithm for Hammerstein systems. Appl. Math. Lett. 60, 21\u201327 (2016)","journal-title":"Appl. Math. Lett."},{"key":"2112_CR47","doi-asserted-by":"publisher","DOI":"10.1007\/s42835-022-01130-2","author":"J Pan","year":"2022","unstructured":"J. Pan, Q. Chen, J. Xiong, G. Chen, A novel quadruple boost nine level switched capacitor inverter. J. Electr. Eng. Technol. (2022). https:\/\/doi.org\/10.1007\/s42835-022-01130-2","journal-title":"J. Electr. Eng. Technol."},{"issue":"3","key":"2112_CR48","doi-asserted-by":"publisher","first-page":"1189","DOI":"10.1007\/s12555-016-0081-z","volume":"15","author":"J Pan","year":"2017","unstructured":"J. Pan, X. Jiang, X.K. Wan, A filtering based multi-innovation extended stochastic gradient algorithm for multivariable control systems. Int. J. Control Autom. Syst. 15(3), 1189\u20131197 (2017)","journal-title":"Int. J. Control Autom. Syst."},{"issue":"7","key":"2112_CR49","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1049\/iet-spr.2019.0481","volume":"14","author":"J Pan","year":"2020","unstructured":"J. Pan, H. Ma, X. Zhang, Recursive coupled projection algorithms for multivariable output-error-like systems with coloured noises. IET Signal Process. 14(7), 455\u2013466 (2020)","journal-title":"IET Signal Process."},{"key":"2112_CR50","unstructured":"M. Schoukens, P. Mattson, T. Wigren, Cascaded tanks benchmark combining soft and hard nonlinearities. Workshop on Nonlinear System Identification Benchmarks, April, 20\u201323 (2016)"},{"key":"2112_CR51","doi-asserted-by":"crossref","unstructured":"J. Shu, J. He, L. Li, MSIS: Multispectral instance segmentation method for power equipment. Comput. Intell. Neurosci. 2022, Article ID 2864717 (2022)","DOI":"10.1155\/2022\/2864717"},{"issue":"2","key":"2112_CR52","first-page":"469","volume":"68","author":"P Suominen","year":"2012","unstructured":"P. Suominen, A. Brink, T. Salmi, Parameter estimation of complex chemical kinetics with covariance matrix adaptation evolution strategy. Match-Commun. Math. Comput. Chem. 68(2), 469 (2012)","journal-title":"Match-Commun. Math. Comput. Chem."},{"issue":"2","key":"2112_CR53","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/s10994-009-5102-1","volume":"75","author":"T Suttorp","year":"2009","unstructured":"T. Suttorp, N. Hansen, C. Igel, Efficient covariance matrix update for variable metric evolution strategies. Mach. Learn. 75(2), 167\u2013197 (2009)","journal-title":"Mach. Learn."},{"key":"2112_CR54","doi-asserted-by":"crossref","unstructured":"D. Vermetten, S. van Rijn, T. B\u00e4ck, Online selection of CMA-ES variants. in Proceedings of the Genetic and Evolutionary Computation Conference, July, 951\u2013959 (2019)","DOI":"10.1145\/3321707.3321803"},{"key":"2112_CR55","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1016\/j.aml.2015.12.018","volume":"57","author":"D Wang","year":"2016","unstructured":"D. Wang, Hierarchical parameter estimation for a class of MIMO Hammerstein systems based on the reframed models. Appl. Math. Lett. 57, 13\u201319 (2016)","journal-title":"Appl. Math. Lett."},{"issue":"4","key":"2112_CR56","doi-asserted-by":"publisher","first-page":"2500","DOI":"10.1109\/TII.2019.2931792","volume":"16","author":"D Wang","year":"2019","unstructured":"D. Wang, S. Zhang, M. Gan, A novel EM identification method for Hammerstein systems with missing output data. IEEE Trans. Ind. Inf. 16(4), 2500\u20132508 (2019)","journal-title":"IEEE Trans. Ind. Inf."},{"issue":"8","key":"2112_CR57","doi-asserted-by":"publisher","first-page":"1562","DOI":"10.1002\/acs.3257","volume":"35","author":"JW Wang","year":"2021","unstructured":"J.W. Wang, Y. Ji, C. Zhang, Iterative parameter and order identification for fractional-order nonlinear finite impulse response systems using the key term separation. Int. J. Adapt. Control Signal Process. 35(8), 1562\u20131577 (2021)","journal-title":"Int. J. Adapt. Control Signal Process."},{"issue":"3","key":"2112_CR58","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1140\/epjs\/s11734-021-00423-3","volume":"231","author":"H Wang","year":"2022","unstructured":"H. Wang, G. Ke, J. Pan, Multitudinous potential hidden Lorenz-like attractors coined. Eur. Phys. J. Spec. Top. 231(3), 359\u2013368 (2022)","journal-title":"Eur. Phys. J. Spec. Top."},{"issue":"5","key":"2112_CR59","doi-asserted-by":"publisher","first-page":"2891","DOI":"10.3934\/dcdsb.2021165","volume":"27","author":"H Wang","year":"2022","unstructured":"H. Wang, H. Fan, J. Pan, A true three-scroll chaotic attractor coined. Discrete Continuous Dyn. Syst. Ser. B 27(5), 2891\u20132915 (2022)","journal-title":"Discrete Continuous Dyn. Syst. Ser. B"},{"issue":"14","key":"2112_CR60","doi-asserted-by":"publisher","first-page":"2150208","DOI":"10.1142\/S0218127421502084","volume":"31","author":"HJ Wang","year":"2021","unstructured":"H.J. Wang, H.D. Fan, J. Pan, Complex dynamics of a four-dimensional circuit system. Int. J. Bifur. Chaos 31(14), 2150208 (2021)","journal-title":"Int. J. Bifur. Chaos"},{"issue":"10","key":"2112_CR61","doi-asserted-by":"publisher","first-page":"10489","DOI":"10.1109\/TIE.2021.3137600","volume":"69","author":"JX Xiong","year":"2022","unstructured":"J.X. Xiong, J. Pan, G.Y. Chen, Sliding mode dual-channel disturbance rejection attitude control for a quadrotor. IEEE Trans. Ind. Electron. 69(10), 10489\u201310499 (2022)","journal-title":"IEEE Trans. Ind. Electron."},{"issue":"1","key":"2112_CR62","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1007\/s11071-014-1871-6","volume":"80","author":"W Xiong","year":"2015","unstructured":"W. Xiong, X. Yang, L. Ke, EM algorithm-based identification of a class of nonlinear Wiener systems with missing output data. Nonlinear Dyn. 80(1), 329\u2013339 (2015)","journal-title":"Nonlinear Dyn."},{"issue":"9","key":"2112_CR63","doi-asserted-by":"publisher","first-page":"5120","DOI":"10.1002\/rnc.6086","volume":"32","author":"CJ Xu","year":"2022","unstructured":"C.J. Xu, H.C. Xu, Adaptive biparite consensus of competitive linear multi-agent systems with asynchronous intermittent communication. Int. J. Robust Nonlinear Control 32(9), 5120\u20135140 (2022)","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"2112_CR64","doi-asserted-by":"publisher","first-page":"947","DOI":"10.1109\/LSP.2022.3152108","volume":"29","author":"H Xu","year":"2022","unstructured":"H. Xu, B. Champagne, Joint parameter and time-delay estimation for a class of nonlinear time-series models. IEEE Signal Process. Lett. 29, 947\u2013951 (2022)","journal-title":"IEEE Signal Process. Lett."},{"issue":"2","key":"2112_CR65","doi-asserted-by":"publisher","first-page":"805","DOI":"10.1007\/s00034-021-01801-x","volume":"41","author":"L Xu","year":"2022","unstructured":"L. Xu, Separable multi-innovation Newton iterative modeling algorithm for multi-frequency signals based on the sliding measurement window. Circuits Syst. Signal Process. 41(2), 805\u2013830 (2022)","journal-title":"Circuits Syst. Signal Process."},{"issue":"2","key":"2112_CR66","doi-asserted-by":"publisher","first-page":"432","DOI":"10.1007\/s12555-020-0619-y","volume":"20","author":"L Xu","year":"2022","unstructured":"L. Xu, Separable Newton recursive estimation method through system responses based on dynamically discrete measurements with increasing data length. Int. J. Control Autom. Syst. 20(2), 432\u2013443 (2022)","journal-title":"Int. J. Control Autom. Syst."},{"issue":"5","key":"2112_CR67","doi-asserted-by":"publisher","first-page":"676","DOI":"10.1002\/acs.3221","volume":"35","author":"L Xu","year":"2021","unstructured":"L. Xu, F.Y. Chen, T. Hayat, Hierarchical recursive signal modeling for multi-frequency signals based on discrete measured data. Int. J. Adapt. Control Signal Process. 35(5), 676\u2013693 (2021)","journal-title":"Int. J. Adapt. Control Signal Process."},{"issue":"1","key":"2112_CR68","doi-asserted-by":"publisher","first-page":"148","DOI":"10.1002\/rnc.5266","volume":"31","author":"L Xu","year":"2021","unstructured":"L. Xu, E.F. Yang, Auxiliary model multiinnovation stochastic gradient parameter estimation methods for nonlinear sandwich systems. Int. J. Robust Nonlinear Control 31(1), 148\u2013165 (2021)","journal-title":"Int. J. Robust Nonlinear Control"},{"key":"2112_CR69","first-page":"6501313","volume":"71","author":"L Xu","year":"2022","unstructured":"L. Xu, Q.M. Zhu, Separable synchronous multi-innovation gradient-based iterative signal modeling from on-line measurements. IEEE Trans. Instrum. Meas. 71, 6501313 (2022)","journal-title":"IEEE Trans. Instrum. Meas."},{"issue":"9","key":"2112_CR70","doi-asserted-by":"publisher","first-page":"1806","DOI":"10.1080\/00207721.2020.1871107","volume":"52","author":"L Xu","year":"2021","unstructured":"L. Xu, Q.M. Zhu, Decomposition strategy-based hierarchical least mean square algorithm for control systems from the impulse responses. Int. J. Syst. Sci. 52(9), 1806\u20131821 (2021)","journal-title":"Int. J. Syst. Sci."},{"issue":"3","key":"2112_CR71","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(3), 1647\u20131659 (2017)","journal-title":"Nonlinear Dyn."},{"issue":"3","key":"2112_CR72","doi-asserted-by":"publisher","first-page":"1001","DOI":"10.1007\/s11071-018-4105-5","volume":"92","author":"J Zhang","year":"2018","unstructured":"J. Zhang, K.S. Chin, M. \u0141awry\u0144czuk, Nonlinear model predictive control based on piecewise linear Hammerstein models. Nonlinear Dyn. 92(3), 1001\u20131021 (2018)","journal-title":"Nonlinear Dyn."},{"issue":"4","key":"2112_CR73","doi-asserted-by":"publisher","first-page":"1351","DOI":"10.1002\/rnc.4819","volume":"30","author":"X Zhang","year":"2020","unstructured":"X. Zhang, Adaptive parameter estimation for a general dynamical system with unknown states. Int. J. Robust Nonlinear Control 30(4), 1351\u20131372 (2020)","journal-title":"Int. J. Robust Nonlinear Control"},{"issue":"4","key":"2112_CR74","doi-asserted-by":"publisher","first-page":"1373","DOI":"10.1002\/rnc.4824","volume":"30","author":"X Zhang","year":"2020","unstructured":"X. Zhang, L. Xu, Recursive parameter estimation methods and convergence analysis for a special class of nonlinear systems. Int. J. Robust Nonlinear Control 30(4), 1373\u20131393 (2020)","journal-title":"Int. J. Robust Nonlinear Control"},{"issue":"6","key":"2112_CR75","doi-asserted-by":"publisher","first-page":"875","DOI":"10.1002\/acs.2995","volume":"33","author":"X Zhang","year":"2019","unstructured":"X. Zhang, E.F. Yang, Highly computationally efficient state filter based on the delta operator. Int. J. Adapt. Control Signal Process. 33(6), 875\u2013889 (2019)","journal-title":"Int. J. Adapt. Control Signal Process."},{"issue":"7","key":"2112_CR76","doi-asserted-by":"publisher","first-page":"1157","DOI":"10.1002\/acs.3027","volume":"33","author":"X Zhang","year":"2019","unstructured":"X. Zhang, E.F. Yang, State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors. Int. J. Adapt. Control Signal Process. 33(7), 1157\u20131173 (2019)","journal-title":"Int. J. Adapt. Control Signal Process."},{"key":"2112_CR77","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1109\/LSP.2021.3136504","volume":"29","author":"X Zhang","year":"2022","unstructured":"X. Zhang, Optimal adaptive filtering algorithm by using the fractional-order derivative. IEEE Signal Process. Lett. 29, 399\u2013403 (2022)","journal-title":"IEEE Signal Process. Lett."},{"issue":"3","key":"2112_CR78","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1109\/LCOMM.2021.3138075","volume":"26","author":"N Zhao","year":"2022","unstructured":"N. Zhao, A. Wu, Y. Pei, Spatial-temporal aggregation graph convolution network for efficient mobile cellular traffic prediction. IEEE Commun. Lett. 26(3), 587\u2013591 (2022)","journal-title":"IEEE Commun. Lett."},{"issue":"12","key":"2112_CR79","first-page":"3597","volume":"68","author":"YH Zhou","year":"2021","unstructured":"Y.H. Zhou, Hierarchical estimation approach for RBF-AR models with regression weights based on the increasing data length. IEEE Trans. Circuits Syst. II Express Briefs 68(12), 3597\u20133601 (2021)","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"2112_CR80","volume":"414","author":"YH Zhou","year":"2022","unstructured":"Y.H. Zhou, Partially-coupled nonlinear parameter optimization algorithm for a class of multivariate hybrid models. Appl. Math. Comput. 414, 126663 (2022)","journal-title":"Appl. Math. Comput."},{"key":"2112_CR81","doi-asserted-by":"publisher","first-page":"1600","DOI":"10.1109\/LSP.2020.3021925","volume":"27","author":"YH Zhou","year":"2020","unstructured":"Y.H. Zhou, Modeling nonlinear processes using the radial basis function-based state-dependent autoregressive models. IEEE Signal Process. Lett. 27, 1600\u20131604 (2020)","journal-title":"IEEE Signal Process. Lett."},{"key":"2112_CR82","doi-asserted-by":"crossref","unstructured":"Y. Zhu, Multivariable System Identification for Process Control. Elsevier. 2001","DOI":"10.1016\/B978-008043985-3\/50012-0"}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-022-02112-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00034-022-02112-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-022-02112-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,16]],"date-time":"2022-11-16T06:04:35Z","timestamp":1668578675000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00034-022-02112-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,26]]},"references-count":82,"journal-issue":{"issue":"12","published-print":{"date-parts":[[2022,12]]}},"alternative-id":["2112"],"URL":"https:\/\/doi.org\/10.1007\/s00034-022-02112-5","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"type":"print","value":"0278-081X"},{"type":"electronic","value":"1531-5878"}],"subject":[],"published":{"date-parts":[[2022,7,26]]},"assertion":[{"value":"7 December 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 July 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 July 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 July 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}