{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T08:03:37Z","timestamp":1770019417700,"version":"3.49.0"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2022,6,17]],"date-time":"2022-06-17T00:00:00Z","timestamp":1655424000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,6,17]],"date-time":"2022-06-17T00:00:00Z","timestamp":1655424000000},"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":["62171303"],"award-info":[{"award-number":["62171303"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"China South Industries Group Corporation (Chengdu) Fire Control Technology Center Project","award":["HK20-03"],"award-info":[{"award-number":["HK20-03"]}]},{"name":"National Key Research and Development Program Foundation of China","award":["2018YFC0830300"],"award-info":[{"award-number":["2018YFC0830300"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2022,10]]},"DOI":"10.1007\/s00034-022-02053-z","type":"journal-article","created":{"date-parts":[[2022,6,17]],"date-time":"2022-06-17T11:26:24Z","timestamp":1655465184000},"page":"5785-5806","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Widely Linear Complex-Valued Least Mean M-Estimate Algorithms: Design and Performance Analysis"],"prefix":"10.1007","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1262-9733","authenticated-orcid":false,"given":"Lei","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yi-Fei","family":"Pu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,6,17]]},"reference":[{"issue":"5","key":"2053_CR1","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1109\/MSP.2013.2287951","volume":"31","author":"T Adal\u0131","year":"2014","unstructured":"T. Adal\u0131, P.J. Schreier, Optimization and estimation of complex-valued signals: theory and applications in filtering and blind source separation. IEEE Signal Process. Mag. 31(5), 112\u2013128 (2014)","journal-title":"IEEE Signal Process. Mag."},{"issue":"11","key":"2053_CR2","doi-asserted-by":"publisher","first-page":"5101","DOI":"10.1109\/TSP.2011.2162954","volume":"59","author":"T Adali","year":"2011","unstructured":"T. Adali, P.J. Schreier, L.L. Scharf, Complex-valued signal processing: the proper way to deal with impropriety. IEEE Trans. Signal Process. 59(11), 5101\u20135125 (2011)","journal-title":"IEEE Trans. Signal Process."},{"issue":"13","key":"2053_CR3","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. Principe, Generalized correntropy for robust adaptive filtering. IEEE Trans. Signal Process. 64(13), 3376\u20133387 (2016)","journal-title":"IEEE Trans. Signal Process."},{"issue":"11","key":"2053_CR4","doi-asserted-by":"publisher","first-page":"5323","DOI":"10.1109\/TSP.2007.899394","volume":"55","author":"P Chevalier","year":"2007","unstructured":"P. Chevalier, A. Blin, Widely linear mvdr beamformers for the reception of an unknown signal corrupted by noncircular interferences. IEEE Trans. Signal Process. 55(11), 5323\u20135336 (2007)","journal-title":"IEEE Trans. Signal Process."},{"issue":"5","key":"2053_CR5","doi-asserted-by":"publisher","first-page":"725","DOI":"10.1587\/transfun.E102.A.725","volume":"102","author":"Y-R Chien","year":"2019","unstructured":"Y.-R. Chien, Variable regularization affine projection sign algorithm in impulsive noisy environment. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 102(5), 725\u2013728 (2019)","journal-title":"IEICE Trans. Fundam. Electron. Commun. Comput. Sci."},{"key":"2053_CR6","doi-asserted-by":"crossref","unstructured":"S.C. Douglas, D.P. Mandic, Performance analysis of the conventional complex LMS and augmented complex LMS algorithms, in: 2010 IEEE International Conference on Acoustics, Speech and Signal Processing, IEEE, 2010, pp. 3794\u20133797.","DOI":"10.1109\/ICASSP.2010.5495851"},{"key":"2053_CR7","doi-asserted-by":"crossref","unstructured":"S.C. Douglas, Widely-linear recursive least-squares algorithm for adaptive beamforming, in: 2009 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2009: 2041\u20132044.","DOI":"10.1109\/ICASSP.2009.4960015"},{"key":"2053_CR8","doi-asserted-by":"publisher","first-page":"1061","DOI":"10.1016\/j.neunet.2007.09.015","volume":"20","author":"SL Goh","year":"2007","unstructured":"S.L. Goh, D.P. Mandic, An augmented CRTRL for complex-valued recurrent neural networks. Neural Netw. 20, 1061\u20131066 (2007)","journal-title":"Neural Netw."},{"key":"2053_CR9","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1016\/j.eswa.2018.04.020","volume":"107","author":"JP Guimar\u00e3es","year":"2018","unstructured":"J.P. Guimar\u00e3es, A.I. Fontes, J.B. Rego, A.D.M. Martins, J.C. Principe, Complex correntropy function: properties, and application to a channel equalization problem. Expert Syst. Appl. 107, 173\u2013181 (2018)","journal-title":"Expert Syst. Appl."},{"key":"2053_CR10","doi-asserted-by":"publisher","first-page":"1530","DOI":"10.1109\/LSP.2020.3018652","volume":"27","author":"JJ Jeong","year":"2020","unstructured":"J.J. Jeong, A robust affine projection algorithm against impulsive noise. IEEE Signal Process. Lett. 27, 1530\u20131534 (2020)","journal-title":"IEEE Signal Process. Lett."},{"issue":"4","key":"2053_CR11","doi-asserted-by":"publisher","first-page":"800","DOI":"10.1109\/TCSII.2019.2925626","volume":"67","author":"L Li","year":"2020","unstructured":"L. Li, H. Zhao, A robust total least mean m-estimate adaptive algorithm for impulsive noise suppression. IEEE Trans Circuits Syst. II Express Briefs. 67(4), 800\u2013804 (2020)","journal-title":"IEEE Trans Circuits Syst. II Express Briefs."},{"issue":"11","key":"2053_CR12","doi-asserted-by":"publisher","first-page":"5286","DOI":"10.1109\/TSP.2007.896065","volume":"55","author":"W Liu","year":"2007","unstructured":"W. Liu, P.P. Pokharel, J.C. Principe, Correntropy: properties and applications in non-Gaussian signal processing. IEEE Trans. Signal Process 55(11), 5286\u20135298 (2007)","journal-title":"IEEE Trans. Signal Process"},{"key":"2053_CR13","doi-asserted-by":"publisher","DOI":"10.1002\/9780470742624","volume-title":"Complex valued nonlinear adaptive filters: noncircularity","author":"DP Mandic","year":"2009","unstructured":"D.P. Mandic, V.S.L. Goh, Complex valued nonlinear adaptive filters: noncircularity (Widely Linear and Neural Models. Wiley, New York, 2009)"},{"key":"2053_CR14","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1016\/j.renene.2008.03.022","volume":"34","author":"DP Mandic","year":"2009","unstructured":"D.P. Mandic, S. Javidi, S.L. Goh, A. Kuh, K. Aihara, Complex-valued prediction of wind profile using augmented complex statistics. Renew. Energy. 34, 196\u2013201 (2009)","journal-title":"Renew. Energy."},{"issue":"12","key":"2053_CR15","doi-asserted-by":"publisher","first-page":"6123","DOI":"10.1109\/TNNLS.2018.2826442","volume":"29","author":"EC Menguc","year":"2018","unstructured":"E.C. Menguc, N. Acir, Kurtosis-based CRTRL algorithms for fully connected recurrent neural networks. IEEE Trans. Neural Networks Learn. Syst. 29(12), 6123\u20136131 (2018)","journal-title":"IEEE Trans. Neural Networks Learn. Syst."},{"issue":"2","key":"2053_CR16","doi-asserted-by":"publisher","first-page":"438","DOI":"10.1109\/TSP.2017.2768024","volume":"66","author":"EC Meng\u00fc\u00e7","year":"2018","unstructured":"E.C. Meng\u00fc\u00e7, N. Ac\u0131r, An augmented complex-valued least-mean kurtosis algorithm for the filtering of noncircular signals. IEEE Trans. Signal Process. 66(2), 438\u2013448 (2018)","journal-title":"IEEE Trans. Signal Process."},{"key":"2053_CR17","first-page":"256","volume":"69","author":"E Ollila","year":"2021","unstructured":"E. Ollila, D.P. Palomar, F. Pascal, Shrinking the eigenvalues of m-estimators of covariance matrix. IEEE Trans. Signal Process. 69, 256\u2013269 (2021)","journal-title":"IEEE Trans. Signal Process."},{"issue":"8","key":"2053_CR18","doi-asserted-by":"publisher","first-page":"2030","DOI":"10.1109\/78.403373","volume":"43","author":"B Picinbono","year":"1995","unstructured":"B. Picinbono, P. Chevalier, Widely linear estimation with complex data. IEEE Trans. Signal Process. 43(8), 2030\u20132033 (1995)","journal-title":"IEEE Trans. Signal Process."},{"key":"2053_CR19","doi-asserted-by":"publisher","first-page":"19113","DOI":"10.1109\/ACCESS.2018.2821141","volume":"6","author":"G Qian","year":"2018","unstructured":"G. Qian, S. Wang, Generalized complex correntropy: application to adaptive filtering of complex data. IEEE Access. 6, 19113\u201319120 (2018)","journal-title":"IEEE Access."},{"key":"2053_CR20","doi-asserted-by":"publisher","first-page":"978","DOI":"10.1109\/TSP.2020.2969042","volume":"68","author":"G Qian","year":"2020","unstructured":"G. Qian, S. Wang, H.H.C. Iu, Maximum total complex correntropy for adaptive filter. IEEE Trans. Signal Process. 68, 978\u2013989 (2020)","journal-title":"IEEE Trans. Signal Process."},{"key":"2053_CR21","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1016\/j.sigpro.2019.05.014","volume":"163","author":"C Safarian","year":"2019","unstructured":"C. Safarian, T. Ogunfunmi, The quaternion minimum error entropy algorithm with fiducial point for nonlinear adaptive systems. Signal Process. 163, 188\u2013200 (2019)","journal-title":"Signal Process."},{"key":"2053_CR22","doi-asserted-by":"crossref","unstructured":"P. J. Schreier and L. L. Scharf, Statistical Signal Processing of Complex-Valued Data: The Theory of Improper and Noncircular Signals. Cambridge University Press, 2010.","DOI":"10.1017\/CBO9780511815911"},{"key":"2053_CR23","doi-asserted-by":"publisher","first-page":"5940","DOI":"10.1109\/TSP.2020.3029884","volume":"68","author":"L Shi","year":"2020","unstructured":"L. Shi, H. Zhao, Y. Zakharov, B. Chen, Y. Yang, Variable step-size widely linear complex-valued affine projection algorithm and performance analysis. IEEE Trans. Signal Process. 68, 5940\u20135953 (2020)","journal-title":"IEEE Trans. Signal Process."},{"key":"2053_CR24","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.sigpro.2019.06.029","volume":"165","author":"L Shi","year":"2019","unstructured":"L. Shi, H. Zhao, X. Zeng, Y. Yu, Variable step-size widely linear complex-valued NLMS algorithm and its performance analysis. Signal Process. 165, 1\u20136 (2019)","journal-title":"Signal Process."},{"issue":"9","key":"2053_CR25","doi-asserted-by":"publisher","first-page":"2811","DOI":"10.1109\/78.236504","volume":"41","author":"D Slock","year":"1993","unstructured":"D. Slock, 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":"1","key":"2053_CR26","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1109\/TSP.2014.2367452","volume":"63","author":"Y-M Shi","year":"2015","unstructured":"Y.-M. Shi, L. Huang, C. Qian, H.-C. So, Shrinkage linear and widely linear complex-valued least mean squares algorithms for adaptive beamforming. IEEE Trans. Signal Process. 63(1), 119\u2013131 (2015)","journal-title":"IEEE Trans. Signal Process."},{"key":"2053_CR27","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1016\/j.sigpro.2017.05.029","volume":"141","author":"F Wang","year":"2017","unstructured":"F. Wang, Y. He, S. Wang, B. Chen, Maximum total correntropy adaptive filtering against heavy-tailed noises. Signal Process. 141, 84\u201395 (2017)","journal-title":"Signal Process."},{"issue":"5","key":"2053_CR28","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1109\/MSP.2012.2183689","volume":"29","author":"Y Xia","year":"2012","unstructured":"Y. Xia, S.C. Douglas, D.P. Mandic, Adaptive frequency estimation in smart grid applications: Exploiting noncircularity and widely linear adaptive estimators. IEEE Signal Process. Mag. 29(5), 44\u201354 (2012)","journal-title":"IEEE Signal Process. Mag."},{"issue":"9","key":"2053_CR29","first-page":"1413","volume":"24","author":"Y Xia","year":"2017","unstructured":"Y. Xia, D.P. Mandic, Complementary mean square analysis of augmented CLMS for second-order noncircular Gaussian signals. IEEE Signal Process. Lett. 24(9), 1413\u20131417 (2017)","journal-title":"IEEE Signal Process. Lett."},{"issue":"1","key":"2053_CR30","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1109\/TIM.2011.2159409","volume":"61","author":"Y Xia","year":"2011","unstructured":"Y. Xia, D.P. Mandic, Widely linear adaptive frequency estimation of unbalanced three-phase power systems. IEEE Trans. Instrum. Meas. 61(1), 74\u201383 (2011)","journal-title":"IEEE Trans. Instrum. Meas."},{"issue":"6","key":"2053_CR31","doi-asserted-by":"publisher","first-page":"1788","DOI":"10.1016\/j.sigpro.2009.11.026","volume":"90","author":"Y Xia","year":"2010","unstructured":"Y. Xia, C.C. Took, D.P. Mandic, An augmented affine projection algorithm for the filtering of noncircular complex signals. Signal Process. 90(6), 1788\u20131799 (2010)","journal-title":"Signal Process."},{"key":"2053_CR32","doi-asserted-by":"publisher","first-page":"3824","DOI":"10.1109\/TSP.2020.3001404","volume":"68","author":"Y Xie","year":"2020","unstructured":"Y. Xie, Y. Li, Y. Gu, J. Cao, B. Chen, Fixed-point minimum error entropy with fiducial points. IEEE Trans. Signal Process. 68, 3824\u20133833 (2020)","journal-title":"IEEE Trans. Signal Process."},{"key":"2053_CR33","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1016\/j.neunet.2015.05.003","volume":"69","author":"D Xu","year":"2015","unstructured":"D. Xu, H. Zhang, D.P. Mandic, Convergence analysis of an augmented algorithm for fully complex-valued neural networks. Neural Netw. 69, 44\u201350 (2015)","journal-title":"Neural Netw."},{"key":"2053_CR34","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1109\/TASLP.2019.2950597","volume":"28","author":"Y Yu","year":"2020","unstructured":"Y. Yu, H. He, B. Chen, J. Li, Y. Zhang, L. Lu, M-Estimate based normalized subband adaptive filter algorithm: performance analysis and improvements. IEEE\/ACM Trans. Audio Speech Lang. Process. 28, 225\u2013239 (2020)","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"2053_CR35","doi-asserted-by":"publisher","first-page":"2199","DOI":"10.1109\/TSP.2020.2983905","volume":"68","author":"Y Yu","year":"2020","unstructured":"Y. Yu, H. He, T. Yang, X. Wang, R.C. de Lamare, Diffusion normalized least mean M-Estimate algorithms: design and performance analysis. IEEE Trans. Signal Process. 68, 2199\u20132214 (2020)","journal-title":"IEEE Trans. Signal Process."},{"issue":"13","key":"2053_CR36","doi-asserted-by":"publisher","first-page":"3592","DOI":"10.1109\/TSP.2019.2919412","volume":"67","author":"S Zhang","year":"2019","unstructured":"S. Zhang, J. Zhang, W.X. Zheng, H.C. So, Widely linear complex-valued estimated-input LMS algorithm for bias-compensated adaptive filtering with noisy measurements. IEEE Trans. Signal Process. 67(13), 3592\u20133605 (2019)","journal-title":"IEEE Trans. Signal Process."},{"issue":"12","key":"2053_CR37","doi-asserted-by":"publisher","first-page":"1564","DOI":"10.1109\/82.899657","volume":"47","author":"Y Zou","year":"2000","unstructured":"Y. Zou, S.C. Chan, T.S. Ng, Least mean M-Estimate algorithms for robust adaptive filtering in impulse noise. IEEE Trans Circuits Syst II: Analog and Digital Signal Process. 47(12), 1564\u20131569 (2000)","journal-title":"IEEE Trans Circuits Syst II: Analog and Digital Signal Process."},{"issue":"9","key":"2053_CR38","doi-asserted-by":"publisher","first-page":"4455","DOI":"10.1109\/TIE.2010.2098359","volume":"58","author":"Y Zhou","year":"2011","unstructured":"Y. Zhou, S.C. Chan, K.L. Ho, New sequential partial-update least mean M-Estimate algorithms for robust adaptive system identification in impulsive noise. IEEE Trans. Ind. Electron. 58(9), 4455\u20134470 (2011)","journal-title":"IEEE Trans. Ind. Electron."}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-022-02053-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00034-022-02053-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-022-02053-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,9]],"date-time":"2022-08-09T08:11:22Z","timestamp":1660032682000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00034-022-02053-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,17]]},"references-count":38,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["2053"],"URL":"https:\/\/doi.org\/10.1007\/s00034-022-02053-z","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"value":"0278-081X","type":"print"},{"value":"1531-5878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,17]]},"assertion":[{"value":"25 October 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 May 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 May 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 June 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}