{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T09:46:24Z","timestamp":1771235184680,"version":"3.50.1"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2015,9,8]],"date-time":"2015-09-08T00:00:00Z","timestamp":1441670400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61304138"],"award-info":[{"award-number":["61304138"]}],"id":[{"id":"10.13039\/501100001809","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":[[2016,7]]},"DOI":"10.1007\/s00034-015-0164-8","type":"journal-article","created":{"date-parts":[[2015,9,8]],"date-time":"2015-09-08T07:35:10Z","timestamp":1441697710000},"page":"2655-2667","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["A Recursive Least Squares Algorithm for Pseudo-Linear ARMA Systems Using the Auxiliary Model and the Filtering Technique"],"prefix":"10.1007","volume":"35","author":[{"given":"Lanjie","family":"Guo","sequence":"first","affiliation":[]},{"given":"Yanjiao","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Cheng","family":"Wang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,9,8]]},"reference":[{"issue":"2","key":"164_CR1","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1007\/s00034-011-9341-6","volume":"31","author":"MS Ahmad","year":"2012","unstructured":"M.S. Ahmad, O. Kukrer, A. Hocanin, Robust recursive inverse adaptive algorithm in impulsive noise. Circuits Syst. Signal Process. 31(2), 703\u2013710 (2012)","journal-title":"Circuits Syst. Signal Process."},{"issue":"4","key":"164_CR2","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1016\/j.dsp.2011.03.001","volume":"21","author":"MS Ahmad","year":"2011","unstructured":"M.S. Ahmad, O. Kukrer, A. Hocanin, Recursive inverse adaptive filtering algorithm. Digit. Signal Process. 21(4), 491\u2013496 (2011)","journal-title":"Digit. Signal Process."},{"issue":"4","key":"164_CR3","doi-asserted-by":"crossref","first-page":"1993","DOI":"10.1109\/TIE.2013.2266076","volume":"61","author":"KH Choi","year":"2014","unstructured":"K.H. Choi, W.S. Ra, S.Y. Park, J.B. Park, Robust least squares approach to passive target localization using ultrasonic receiver array. IEEE Trans. Ind. Electron. 61(4), 1993\u20132002 (2014)","journal-title":"IEEE Trans. Ind. Electron."},{"key":"164_CR4","volume-title":"System Identification\u2014New Theory and Methods","author":"F Ding","year":"2013","unstructured":"F. Ding, System Identification\u2014New Theory and Methods (Science Press, Beijing, 2013)"},{"key":"164_CR5","volume-title":"System Identification\u2014Performances Analysis for Identification Methods","author":"F Ding","year":"2014","unstructured":"F. Ding, System Identification\u2014Performances Analysis for Identification Methods (Science Press, Beijing, 2014)"},{"key":"164_CR6","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1016\/j.sigpro.2014.03.031","volume":"104","author":"F Ding","year":"2014","unstructured":"F. Ding, State filtering and parameter estimation for state space systems with scarce measurements. Signal Process. 104, 369\u2013380 (2014)","journal-title":"Signal Process."},{"key":"164_CR7","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1016\/j.ins.2014.02.103","volume":"277","author":"F Ding","year":"2014","unstructured":"F. Ding, Hierarchical parameter estimation algorithms for multivariable systems using measurement information. Inf. Sci. 277, 396\u2013405 (2014)","journal-title":"Inf. Sci."},{"issue":"9","key":"164_CR8","doi-asserted-by":"crossref","first-page":"2881","DOI":"10.1007\/s00034-014-9772-y","volume":"33","author":"F Ding","year":"2014","unstructured":"F. Ding, K.P. Deng, X.M. Liu, Decomposition based Newton iterative identification method for a Hammerstein nonlinear FIR system with ARMA noise. Circuits Syst. Signal Process. 33(9), 2881\u20132893 (2014)","journal-title":"Circuits Syst. Signal Process."},{"issue":"3","key":"164_CR9","doi-asserted-by":"crossref","first-page":"1801","DOI":"10.1016\/j.jfranklin.2013.10.018","volume":"351","author":"S Ding","year":"2014","unstructured":"S. Ding, R. Ding, E.F. Yang, A filtering based recursive least squares estimation algorithm for pseudo-linear auto-regressive systems. J. Frankl. Inst. 351(3), 1801\u20131809 (2014)","journal-title":"J. Frankl. Inst."},{"issue":"6","key":"164_CR10","doi-asserted-by":"crossref","first-page":"4051","DOI":"10.1016\/j.apm.2012.09.016","volume":"37","author":"J Ding","year":"2013","unstructured":"J. Ding, C.X. Fan, J.X. Lin, Auxiliary model based parameter estimation for dual-rate output error systems with colored noise. Appl. Math. Model. 37(6), 4051\u20134058 (2013)","journal-title":"Appl. Math. Model."},{"issue":"5","key":"164_CR11","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1007\/s00034-013-9704-2","volume":"33","author":"J Ding","year":"2014","unstructured":"J. Ding, J.X. Lin, Modified subspace identification for periodically non-uniformly sampled systems by using the lifting technique. Circuits Syst. Signal Process. 33(5), 1439\u20131449 (2014)","journal-title":"Circuits Syst. Signal Process."},{"key":"164_CR12","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.sigpro.2013.10.018","volume":"97","author":"F Ding","year":"2014","unstructured":"F. Ding, X.M. Liu, H.B. Chen, G.Y. Yao, Hierarchical gradient based and hierarchical least squares based iterative parameter identification for CARARMA systems. Signal Process. 97, 31\u201339 (2014)","journal-title":"Signal Process."},{"key":"164_CR13","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.dsp.2014.10.005","volume":"37","author":"F Ding","year":"2015","unstructured":"F. Ding, Y.J. Wang, J. Ding, Recursive least squares parameter identification for systems with colored noise using the filtering technique and the auxiliary model. Digit. Signal Process. 37, 100\u2013108 (2015)","journal-title":"Digit. Signal Process."},{"issue":"5","key":"164_CR14","doi-asserted-by":"crossref","first-page":"1145","DOI":"10.1109\/TCST.2008.2002041","volume":"17","author":"P Santos dos","year":"2009","unstructured":"P. dos Santos, J. Ramos, J. de Carvalho, Identification of bilinear systems with white noise inputs: an iterative deterministic-stochastic subspace approach. IEEE Trans. Control Syst. Technol. 17(5), 1145\u20131153 (2009)","journal-title":"IEEE Trans. Control Syst. Technol."},{"issue":"6","key":"164_CR15","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1007\/s00034-011-9289-6","volume":"30","author":"JX Feng","year":"2011","unstructured":"J.X. Feng, Z.D. Wang, M. Zeng, Recursive robust filtering with finite-step correlated process noises and missing measurements. Circuits Syst. Signal Process. 30(6), 1355\u20131368 (2011)","journal-title":"Circuits Syst. Signal Process."},{"issue":"2","key":"164_CR16","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/s12530-013-9076-7","volume":"4","author":"A Ghazikhani","year":"2013","unstructured":"A. Ghazikhani, R. Monsefi, H.S. Yazdi, Recursive least square perceptron model for non-stationary and imbalanced data stream classification. Evol. Syst. 4(2), 119\u2013131 (2013)","journal-title":"Evol. Syst."},{"key":"164_CR17","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1016\/j.sigpro.2014.08.011","volume":"106","author":"Y Gu","year":"2015","unstructured":"Y. Gu, F. Ding, J.H. Li, States based iterative parameter estimation for a state space model with multi-state delays using decomposition. Signal Process. 106, 294\u2013300 (2015)","journal-title":"Signal Process."},{"key":"164_CR18","doi-asserted-by":"crossref","unstructured":"L.J. Guo, F. Ding, Least squares based iterative algorithm for pseudo-linear autoregressive moving average systems using the data filtering technique. J. Frankl. Inst. Eng. Appl. Math. 352(10), 4339\u20134353 (2015)","DOI":"10.1016\/j.jfranklin.2015.06.010"},{"key":"164_CR19","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/j.simpat.2012.12.009","volume":"34","author":"YB Hu","year":"2013","unstructured":"Y.B. Hu, Iterative and recursive least squares estimation algorithms for moving average systems. Simul. Model. Pract. Theory 34, 12\u201319 (2013)","journal-title":"Simul. Model. Pract. Theory"},{"issue":"2","key":"164_CR20","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1007\/s00034-013-9652-x","volume":"33","author":"YB Hu","year":"2014","unstructured":"Y.B. Hu, B.L. Liu, Q. Zhou, C. Yang, Recursive extended least squares parameter estimation for Wiener nonlinear systems with moving average noises. Circuits Syst. Signal Process. 33(2), 655\u2013664 (2014)","journal-title":"Circuits Syst. Signal Process."},{"issue":"5","key":"164_CR21","doi-asserted-by":"crossref","first-page":"1499","DOI":"10.1007\/s00034-014-9916-0","volume":"34","author":"Y Ji","year":"2015","unstructured":"Y. Ji, X.M. Liu, Unified synchronization criteria for hybrid switching-impulsive dynamical networks. Circuits Syst. Signal Process. 34(5), 1499\u20131517 (2015)","journal-title":"Circuits Syst. Signal Process."},{"issue":"1","key":"164_CR22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11071-014-1640-6","volume":"79","author":"Y Ji","year":"2015","unstructured":"Y. Ji, X.M. Liu et al., New criteria for the robust impulsive synchronization of uncertain chaotic delayed nonlinear systems. Nonlinear Dyn. 79(1), 1\u20139 (2015)","journal-title":"Nonlinear Dyn."},{"issue":"1","key":"164_CR23","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/s00034-012-9445-7","volume":"32","author":"AK Kohli","year":"2013","unstructured":"A.K. Kohli, A. Rai, Numeric variable forgetting factor RLS algorithm for second-order volterra filtering. Circuits Syst. Signal Process. 32(1), 223\u2013232 (2013)","journal-title":"Circuits Syst. Signal Process."},{"issue":"8","key":"164_CR24","doi-asserted-by":"crossref","first-page":"4717","DOI":"10.1109\/TGRS.2013.2284110","volume":"52","author":"D Lange","year":"2014","unstructured":"D. Lange, J.T. Alsina, U. Saeed, S. Tom\u00e1s, F. Rocadenbosch, Atmospheric boundary layer height monitoring using a Kalman filter and backscatter lidar returns. IEEE Trans. Geosci. Remote Sens. 52(8), 4717\u20134728 (2014)","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"issue":"1","key":"164_CR25","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.aml.2012.03.038","volume":"26","author":"JH Li","year":"2013","unstructured":"J.H. Li, Parameter estimation for Hammerstein CARARMA systems based on the Newton iteration. Appl. Math. Lett. 26(1), 91\u201396 (2013)","journal-title":"Appl. Math. Lett."},{"issue":"1","key":"164_CR26","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/j.automatica.2011.09.045","volume":"48","author":"H Li","year":"2012","unstructured":"H. Li, Y. Shi, Robust H-infty filtering for nonlinear stochastic systems with uncertainties and random delays modeled by Markov chains. Automatica 48(1), 159\u2013166 (2012)","journal-title":"Automatica"},{"issue":"3","key":"164_CR27","doi-asserted-by":"crossref","first-page":"962","DOI":"10.1016\/j.automatica.2013.12.025","volume":"50","author":"YJ Liu","year":"2014","unstructured":"Y.J. Liu, F. Ding, Y. Shi, An efficient hierarchical identification method for general dual-rate sampled-data systems. Automatica 50(3), 962\u2013970 (2014)","journal-title":"Automatica"},{"issue":"3","key":"164_CR28","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1016\/j.automatica.2010.01.007","volume":"46","author":"XG Liu","year":"2010","unstructured":"X.G. Liu, J. Lu, Least squares based iterative identification for a class of multirate systems. Automatica 46(3), 549\u2013554 (2010)","journal-title":"Automatica"},{"issue":"8","key":"164_CR29","doi-asserted-by":"crossref","first-page":"4744","DOI":"10.1109\/TGRS.2013.2284293","volume":"52","author":"R Lopez","year":"2014","unstructured":"R. Lopez, J.P. Malard\u00e9, F. Royer, P. Gaspar, Improving argos doppler location using multiple-model Kalman filtering. IEEE Trans. Geosci. Remote Sens. 52(8), 4744\u20134755 (2014)","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"164_CR30","doi-asserted-by":"crossref","unstructured":"Y.W. Mao, F. Ding, Data filtering-based multi-innovation stochastic gradient algorithm for nonlinear output error autoregressive systems. Circuits Syst. Signal Process. (2015). doi: 10.1007\/s00034-015-0064-y","DOI":"10.1007\/s00034-015-0064-y"},{"issue":"3","key":"164_CR31","doi-asserted-by":"crossref","first-page":"1745","DOI":"10.1007\/s11071-014-1771-9","volume":"79","author":"YW Mao","year":"2015","unstructured":"Y.W. Mao, F. Ding, Multi-innovation stochastic gradient identification for Hammerstein controlled autoregressive autoregressive systems based on the filtering technique. Nonlinear Dyn. 79(3), 1745\u20131755 (2015)","journal-title":"Nonlinear Dyn."},{"key":"164_CR32","doi-asserted-by":"crossref","unstructured":"Y.W. Mao, F. Ding, A novel data filtering based multi-innovation stochastic gradient algorithm for Hammerstein nonlinear systems. Digit. Signal Process. (2015). doi: 10.1016\/j.dsp.2015.07.002","DOI":"10.1016\/j.dsp.2015.07.002"},{"key":"164_CR33","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.mechmachtheory.2014.01.010","volume":"75","author":"R P\u00e0mies-Vil\u00e0","year":"2004","unstructured":"R. P\u00e0mies-Vil\u00e0, J.M. Font-Llagunes, U. Lugr\u00eds, J. Cuadrado, Parameter identification method for a three-dimensional foot-ground contact model. Mech. Mach. Theory 75, 107\u2013116 (2004)","journal-title":"Mech. Mach. Theory"},{"issue":"1","key":"164_CR34","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.automatica.2010.10.013","volume":"47","author":"T Schon","year":"2011","unstructured":"T. Schon, A. Wills, B. Ninness, System identification of nonlinear state-space models. Automatica 47(1), 39\u201349 (2011)","journal-title":"Automatica"},{"issue":"3","key":"164_CR35","doi-asserted-by":"crossref","first-page":"538","DOI":"10.1080\/00207170903273987","volume":"83","author":"Y Shi","year":"2010","unstructured":"Y. Shi, H. Fang, Kalman filter based identification for systems with randomly missing measurements in a network environment. Int. J. Control. 83(3), 538\u2013551 (2010)","journal-title":"Int. J. Control."},{"issue":"4","key":"164_CR36","doi-asserted-by":"crossref","first-page":"754","DOI":"10.1016\/j.automatica.2011.01.022","volume":"47","author":"Y Shi","year":"2011","unstructured":"Y. Shi, B. Yu, Robust mixed H-2\/H-infinity control of networked control systems with random time delays in both forward and backward communication links. Automatica 47(4), 754\u2013760 (2011)","journal-title":"Automatica"},{"issue":"12","key":"164_CR37","doi-asserted-by":"crossref","first-page":"3374","DOI":"10.1109\/TIM.2013.2272868","volume":"62","author":"L Vanbeylen","year":"2013","unstructured":"L. Vanbeylen, Nonlinear LFR block-oriented model: potential benefits and improved, user-friendly identification method. IEEE Trans. Inst. Meas. 62(12), 3374\u20133383 (2013)","journal-title":"IEEE Trans. Inst. Meas."},{"issue":"12","key":"164_CR38","doi-asserted-by":"crossref","first-page":"2203","DOI":"10.1109\/TAC.2003.820146","volume":"48","author":"J V\u00f6r\u00f6s","year":"2003","unstructured":"J. V\u00f6r\u00f6s, Recursive identification of Hammerstein systems with discontinuous nonlinearities containing dead-zones. Trans. Autom. Control 48(12), 2203\u20132206 (2003)","journal-title":"Trans. Autom. Control"},{"issue":"14","key":"164_CR39","doi-asserted-by":"crossref","first-page":"1648","DOI":"10.1049\/iet-cta.2010.0416","volume":"5","author":"DQ Wang","year":"2011","unstructured":"D.Q. Wang, Least squares-based recursive and iterative estimation for output error moving average systems using data filtering. IET Control Theory Appl. 5(14), 1648\u20131657 (2011)","journal-title":"IET Control Theory Appl."},{"key":"164_CR40","doi-asserted-by":"crossref","unstructured":"X.H. Wang, F. Ding, Convergence of the auxiliary model based multi-innovation generalized extended stochastic gradient algorithm for Box\u2013Jenkins systems. Nonlinear Dyn. (2015). doi: 10.1007\/s11071-015-2155-5","DOI":"10.1007\/s11071-015-2155-5"},{"key":"164_CR41","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1016\/j.sigpro.2015.05.010","volume":"117","author":"XH Wang","year":"2015","unstructured":"X.H. Wang, F. Ding, Recursive parameter and state estimation for an input nonlinear state space system using the hierarchical identification principle. Signal Process. 117, 208\u2013218 (2015)","journal-title":"Signal Process."},{"key":"164_CR42","doi-asserted-by":"crossref","unstructured":"D.Q. Wang, H.B. Liu et al., Highly efficient identification methods for dual-rate Hammerstein systems. IEEE Trans. Control Syst. Technol. 23(5), 1952\u20131960 (2015)","DOI":"10.1109\/TCST.2014.2387216"},{"issue":"3","key":"164_CR43","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1007\/s11071-014-1338-9","volume":"77","author":"C Wang","year":"2014","unstructured":"C. Wang, T. Tang, Several gradient-based iterative estimation algorithms for a class of nonlinear systems using the filtering technique. Nonlinear Dyn. 77(3), 769\u2013780 (2014)","journal-title":"Nonlinear Dyn."},{"key":"164_CR44","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.aml.2013.10.011","volume":"29","author":"C Wang","year":"2014","unstructured":"C. Wang, T. Tang, Recursive least squares estimation algorithm applied to a class of linear-in-parameters output error moving average systems. Appl. Math. Lett. 29, 36\u201341 (2014)","journal-title":"Appl. Math. Lett."},{"issue":"4","key":"164_CR45","doi-asserted-by":"crossref","first-page":"1709","DOI":"10.1016\/j.apm.2010.10.003","volume":"35","author":"Y Zhang","year":"2011","unstructured":"Y. Zhang, G.M. Cui, Bias compensation methods for stochastic systems with colored noise. Appl. Math. Model. 35(4), 1709\u20131716 (2011)","journal-title":"Appl. Math. Model."}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-015-0164-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00034-015-0164-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-015-0164-8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,22]],"date-time":"2019-05-22T11:01:52Z","timestamp":1558522912000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00034-015-0164-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9,8]]},"references-count":45,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2016,7]]}},"alternative-id":["164"],"URL":"https:\/\/doi.org\/10.1007\/s00034-015-0164-8","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"value":"0278-081X","type":"print"},{"value":"1531-5878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,9,8]]}}}