{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T05:05:12Z","timestamp":1770786312210,"version":"3.50.0"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2018,9,24]],"date-time":"2018-09-24T00:00:00Z","timestamp":1537747200000},"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":["61573332"],"award-info":[{"award-number":["61573332"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61601431"],"award-info":[{"award-number":["61601431"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2019,9]]},"DOI":"10.1007\/s11075-018-0600-5","type":"journal-article","created":{"date-parts":[[2018,9,24]],"date-time":"2018-09-24T06:46:52Z","timestamp":1537771612000},"page":"201-222","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A bias-compensated fractional order normalized least mean square algorithm with noisy inputs"],"prefix":"10.1007","volume":"82","author":[{"given":"Weidi","family":"Yin","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Songsong","family":"Cheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiheng","family":"Wei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3357-6407","authenticated-orcid":false,"given":"Jianmei","family":"Shuai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,9,24]]},"reference":[{"key":"600_CR1","volume-title":"Adaptive Filter Theory","author":"SS Haykin","year":"2008","unstructured":"Haykin, S.S.: Adaptive Filter Theory. Pearson Education, Upper Saddle River (2008)"},{"key":"600_CR2","doi-asserted-by":"crossref","unstructured":"Ljung, L.: System identification. In: Signal Analysis and Prediction, pp 163\u2013173. Springer, New York (1998)","DOI":"10.1007\/978-1-4612-1768-8_11"},{"key":"600_CR3","volume-title":"Adaptive Inverse Control, Reissue Edition: a Signal Processing Approach","author":"B Widrow","year":"2008","unstructured":"Widrow, B., Walach, E.: Adaptive Inverse Control, Reissue Edition: a Signal Processing Approach. Wiley, Hoboken (2008)"},{"issue":"1","key":"600_CR4","doi-asserted-by":"publisher","first-page":"122","DOI":"10.1007\/s10957-015-0851-4","volume":"174","author":"YH Wei","year":"2017","unstructured":"Wei, Y.H., Du, B., Cheng, S.S., Wang, Y.: Fractional order systems time-optimal control and its application. J. Optim. Theory Appl. 174(1), 122\u2013138 (2017)","journal-title":"J. Optim. Theory Appl."},{"issue":"9","key":"600_CR5","doi-asserted-by":"publisher","first-page":"1244","DOI":"10.1109\/LSP.2015.2394301","volume":"22","author":"Y Tan","year":"2015","unstructured":"Tan, Y., He, Z.Q., Tian, B.Y.: A novel generalization of modified LMS algorithm to fractional order. IEEE Signal Process. Lett. 22(9), 1244\u20131248 (2015)","journal-title":"IEEE Signal Process. Lett."},{"key":"600_CR6","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1016\/j.amc.2017.07.023","volume":"314","author":"YQ Chen","year":"2017","unstructured":"Chen, Y.Q., Gao, Q., Wei, Y.H., Wang, Y.: Study on fractional order gradient methods. Appl. Math. Comput. 314, 310\u2013321 (2017)","journal-title":"Appl. Math. Comput."},{"issue":"10","key":"600_CR7","doi-asserted-by":"publisher","first-page":"2554","DOI":"10.1016\/j.sigpro.2006.02.004","volume":"86","author":"CC Tseng","year":"2006","unstructured":"Tseng, C.C.: Design of variable and adaptive fractional order FIR differentiators. Signal Process. 86(10), 2554\u20132566 (2006)","journal-title":"Signal Process."},{"key":"600_CR8","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1016\/j.sigpro.2016.11.026","volume":"133","author":"SS Cheng","year":"2017","unstructured":"Cheng, S.S., Wei, Y.H., Chen, Y.Q., Li, Y., Wang, Y.: An innovative fractional order LMS based on variable initial value and gradient order. Signal Process. 133, 260\u2013269 (2017)","journal-title":"Signal Process."},{"key":"600_CR9","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/j.isatra.2016.11.019","volume":"67","author":"SS Cheng","year":"2017","unstructured":"Cheng, S.S., Wei, Y.H., Chen, Y.Q., Liang, S., Wang, Y.: A universal modified LMS algorithm with iteration order hybrid switching. ISA Trans. 67, 67\u201375 (2017)","journal-title":"ISA Trans."},{"issue":"3","key":"600_CR10","doi-asserted-by":"publisher","first-page":"1150","DOI":"10.1109\/TAC.2016.2575830","volume":"62","author":"X Wei","year":"2017","unstructured":"Wei, X., Liu, D.Y., Boutat, D.: Nonasymptotic pseudo-state estimation for a class of fractional order linear systems. IEEE Trans. Autom. Control 62(3), 1150\u20131164 (2017)","journal-title":"IEEE Trans. Autom. Control"},{"key":"600_CR11","doi-asserted-by":"publisher","first-page":"113","DOI":"10.5890\/JAND.2012.05.001","volume":"1","author":"MD Ortigueira","year":"2012","unstructured":"Ortigueira, M.D., Coito, F.: On the usefulness of Riemann-Liouville and Caputo derivatives in describing fractional shift-invariant linear systems. J. Appl. Nonlinear Dyn. 1, 113\u2013124 (2012)","journal-title":"J. Appl. Nonlinear Dyn."},{"key":"600_CR12","doi-asserted-by":"publisher","first-page":"94","DOI":"10.1016\/j.isatra.2016.01.010","volume":"62","author":"YH Wei","year":"2016","unstructured":"Wei, Y.H., Tse, P.W., Du, B., Wang, Y.: An innovative fixed-pole numerical approximation for fractional order systems. ISA Trans. 62, 94\u2013102 (2016)","journal-title":"ISA Trans."},{"issue":"6","key":"600_CR13","doi-asserted-by":"publisher","first-page":"883","DOI":"10.1137\/0717073","volume":"17","author":"GH Golub","year":"1980","unstructured":"Golub, G.H., Van Loan, C.F.: An analysis of the total least squares problem. SIAM J. Numer. Anal. 17(6), 883\u2013893 (1980)","journal-title":"SIAM J. Numer. Anal."},{"issue":"10","key":"600_CR14","doi-asserted-by":"publisher","first-page":"2729","DOI":"10.1109\/TSP.2004.834260","volume":"52","author":"DZ Feng","year":"2004","unstructured":"Feng, D.Z., Zhang, X.D., Chang, D.X., Zheng, W.X.: A fast recursive total least squares algorithm for adaptive FIR filtering. IEEE Trans. Signal Process. 52(10), 2729\u20132737 (2004)","journal-title":"IEEE Trans. Signal Process."},{"issue":"2","key":"600_CR15","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1109\/78.275601","volume":"42","author":"CE Davila","year":"1994","unstructured":"Davila, C.E.: An efficient recursive total least squares algorithm for FIR adaptive filtering. IEEE Trans. Signal Process. 42(2), 268\u2013280 (1994)","journal-title":"IEEE Trans. Signal Process."},{"issue":"8","key":"600_CR16","doi-asserted-by":"publisher","first-page":"2122","DOI":"10.1109\/78.705421","volume":"46","author":"DZ Feng","year":"1998","unstructured":"Feng, D.Z., Bao, Z., Jiao, L.C.: Total least mean squares algorithm. IEEE Trans. Signal Process. 46(8), 2122\u20132130 (1998)","journal-title":"IEEE Trans. Signal Process."},{"key":"600_CR17","doi-asserted-by":"crossref","unstructured":"Ma, W., Zheng, D., Tong, X., Zhang, Z., Chen, B.: Proportionate nlms with unbiasedness criterion for sparse system identification in the presence of input and output noises. IEEE Transactions on Circuits and Systems II: Express Briefs (2017)","DOI":"10.1109\/TCSII.2017.2785306"},{"key":"600_CR18","doi-asserted-by":"crossref","unstructured":"Ma, W., Zheng, D., Li, Y., Zhang, Z., Chen, B.: Bias-compensated normalized maximum correntropy criterion algorithm for system identification with noisy input. Signal Processing (2018)","DOI":"10.1016\/j.sigpro.2018.05.029"},{"key":"600_CR19","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1109\/LSP.2008.919813","volume":"15","author":"R Diversi","year":"2008","unstructured":"Diversi, R.: A bias-compensated identification approach for noisy fir models. IEEE Signal Process. Lett. 15, 325\u2013328 (2008)","journal-title":"IEEE Signal Process. Lett."},{"issue":"11","key":"600_CR20","doi-asserted-by":"publisher","first-page":"5212","DOI":"10.1109\/TSP.2011.2163631","volume":"59","author":"A Bertrand","year":"2011","unstructured":"Bertrand, A., Moonen, M., Sayed, A.H.: Diffusion bias-compensated RLS estimation over adaptive networks. IEEE Trans. Signal Process. 59(11), 5212\u20135224 (2011)","journal-title":"IEEE Trans. Signal Process."},{"issue":"20","key":"600_CR21","doi-asserted-by":"publisher","first-page":"1270","DOI":"10.1049\/el.2013.2482","volume":"49","author":"SM Jung","year":"2013","unstructured":"Jung, S.M., Park, P.G.: Normalised least-mean-square algorithm for adaptive filtering of impulsive measurement noises and noisy inputs. Electron. Lett. 49(20), 1270\u20131272 (2013)","journal-title":"Electron. Lett."},{"issue":"8","key":"600_CR22","doi-asserted-by":"publisher","first-page":"1941","DOI":"10.1109\/TSP.2015.2405492","volume":"63","author":"R Arablouei","year":"2015","unstructured":"Arablouei, R., Do\u011fan\u00e7ay, K., Werner, S.: Recursive total least-squares algorithm based on inverse power method and dichotomous coordinate-descent iterations. IEEE Trans. Signal Process. 63(8), 1941\u20131949 (2015)","journal-title":"IEEE Trans. Signal Process."},{"issue":"11","key":"600_CR23","doi-asserted-by":"publisher","first-page":"2973","DOI":"10.1109\/TSP.2014.2316162","volume":"62","author":"R Arablouei","year":"2014","unstructured":"Arablouei, R., Do\u011fan\u00e7ay, K., Adali, T.: Unbiased recursive least-squares estimation utilizing dichotomous coordinate-descent iterations. IEEE Trans. Signal Process. 62(11), 2973\u20132983 (2014)","journal-title":"IEEE Trans. Signal Process."},{"issue":"11","key":"600_CR24","doi-asserted-by":"publisher","first-page":"2949","DOI":"10.1109\/TSP.2017.2675865","volume":"65","author":"SM Jung","year":"2017","unstructured":"Jung, S.M., Park, P.G.: Stabilization of a bias-compensated normalized least-mean-square algorithm for noisy inputs. IEEE Trans. Signal Process. 65(11), 2949\u20132961 (2017)","journal-title":"IEEE Trans. Signal Process."},{"issue":"6","key":"600_CR25","doi-asserted-by":"publisher","first-page":"809","DOI":"10.1109\/LSP.2016.2532340","volume":"23","author":"ZS Zheng","year":"2016","unstructured":"Zheng, Z.S., Zhao, H.Q.: Bias-compensated normalized subband adaptive filter algorithm. IEEE Signal Process. Lett. 23(6), 809\u2013813 (2016)","journal-title":"IEEE Signal Process. Lett."},{"issue":"6","key":"600_CR26","doi-asserted-by":"publisher","first-page":"2112","DOI":"10.1109\/TSP.2005.847845","volume":"53","author":"SE Jo","year":"2005","unstructured":"Jo, S.E., Kim, S.W.: Consistent normalized least mean square filtering with noisy data matrix. IEEE Trans. Signal Process. 53(6), 2112\u20132123 (2005)","journal-title":"IEEE Trans. Signal Process."},{"key":"600_CR27","volume-title":"Fractional Differential Equations: an Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications","author":"I Podlubny","year":"1999","unstructured":"Podlubny, I.: Fractional Differential Equations: an Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications. Academic Press, New York (1999)"},{"key":"600_CR28","doi-asserted-by":"crossref","unstructured":"Widrow, B., Hoff, M.E.: Adaptive Switching Circuits, tech. rep. Stanford University Stanford Electronics Laboratories, Stanford (1960)","DOI":"10.21236\/AD0241531"},{"issue":"9","key":"600_CR29","doi-asserted-by":"publisher","first-page":"1073","DOI":"10.1002\/acs.2518","volume":"29","author":"B Jelfs","year":"2015","unstructured":"Jelfs, B., Mandic, D.P.: A unifying framework for the analysis of proportionate nlms algorithms. Int. J. Adapt. Control Signal Process. 29(9), 1073\u20131085 (2015)","journal-title":"Int. J. Adapt. Control Signal Process."},{"issue":"6","key":"600_CR30","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1109\/MSP.2015.2461733","volume":"32","author":"DP Mandic","year":"2015","unstructured":"Mandic, D.P., Kanna, S., Constantinides, A.G.: On the intrinsic relationship between the least mean square and kalman filters [lecture notes]. IEEE Signal Process. Mag. 32(6), 117\u2013122 (2015)","journal-title":"IEEE Signal Process. Mag."},{"key":"600_CR31","volume-title":"Fundamentals of Adaptive Filtering","author":"AH Sayed","year":"2003","unstructured":"Sayed, A.H.: Fundamentals of Adaptive Filtering. Wiley, Hoboken (2003)"},{"key":"600_CR32","doi-asserted-by":"publisher","DOI":"10.1002\/047084535X","volume-title":"Recurrent Neural Networks for Prediction: Learning Algorithms, Architectures and Stability","author":"DP Mandic","year":"2001","unstructured":"Mandic, D.P., Chambers, J.: Recurrent Neural Networks for Prediction: Learning Algorithms, Architectures and Stability. Wiley, Hoboken (2001)"},{"issue":"8","key":"600_CR33","doi-asserted-by":"publisher","first-page":"538","DOI":"10.1049\/el.2013.0246","volume":"49","author":"B Kang","year":"2013","unstructured":"Kang, B., Yoo, J., Park, P.G.: Bias-compensated normalised LMS algorithm with noisy input. Electron. Lett. 49(8), 538\u2013539 (2013)","journal-title":"Electron. Lett."},{"key":"600_CR34","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1016\/j.sigpro.2015.06.016","volume":"118","author":"S Ciochina\u0307","year":"2016","unstructured":"Ciochina\u0307, S., Paleologu, C., Benesty, J.: An optimized NLMS algorithm for system identification. Signal Process. 118, 115\u2013121 (2016)","journal-title":"Signal Process."},{"issue":"2","key":"600_CR35","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1109\/LSP.2003.821649","volume":"11","author":"DP Mandic","year":"2004","unstructured":"Mandic, D.P.: A generalized normalized gradient descent algorithm. IEEE Signal Process. Lett. 11(2), 115\u2013118 (2004)","journal-title":"IEEE Signal Process. Lett."},{"issue":"4","key":"600_CR36","doi-asserted-by":"publisher","first-page":"680","DOI":"10.1109\/18.9768","volume":"34","author":"M Tarrab","year":"1988","unstructured":"Tarrab, M., Feuer, A.: Convergence and performance analysis of the normalized LMS algorithm with uncorrelated Gaussian data. IEEE Trans. Inf. Theory 34(4), 680\u2013691 (1988)","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"9","key":"600_CR37","doi-asserted-by":"publisher","first-page":"2811","DOI":"10.1109\/78.236504","volume":"41","author":"DTM Slock","year":"1993","unstructured":"Slock, D.T.M.: On the convergence behavior of the LMS and the normalized LMS algorithms. IEEE Trans. Signal Process. 41(9), 2811\u20132825 (1993)","journal-title":"IEEE Trans. Signal Process."},{"issue":"6","key":"600_CR38","doi-asserted-by":"publisher","first-page":"646","DOI":"10.1109\/TAC.1968.1099025","volume":"13","author":"T Kailath","year":"1968","unstructured":"Kailath, T.: An innovations approach to least-squares estimation\u2013part I: linear filtering in additive white noise. IEEE Trans. Autom. Control 13(6), 646\u2013655 (1968)","journal-title":"IEEE Trans. Autom. Control"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-018-0600-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-018-0600-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-018-0600-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,2]],"date-time":"2022-09-02T13:45:08Z","timestamp":1662126308000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-018-0600-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,24]]},"references-count":38,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["600"],"URL":"https:\/\/doi.org\/10.1007\/s11075-018-0600-5","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,9,24]]},"assertion":[{"value":"19 March 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 September 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 September 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Compliance with Ethical Standards"}},{"value":"The authors declare that there is no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Conflict of interest"}}]}}