{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T11:05:41Z","timestamp":1780657541024,"version":"3.54.1"},"reference-count":36,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"NSFC","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Digital Signal Processing"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.dsp.2026.106299","type":"journal-article","created":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T06:43:14Z","timestamp":1780382594000},"page":"106299","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Quaternion Euclidean direction search algorithm"],"prefix":"10.1016","volume":"182","author":[{"given":"Siyu","family":"He","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hai","family":"Yuan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6077-0977","authenticated-orcid":false,"given":"Lu","family":"Lu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenxing","family":"Yang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"2","key":"10.1016\/j.dsp.2026.106299_bib0001","first-page":"216","article-title":"New trinion and quaternion set-membership affine projection algorithms","volume":"64","author":"Yazdanpanah","year":"2017","journal-title":"IEEE Trans. Circuits Syst. II Express Br."},{"issue":"8","key":"10.1016\/j.dsp.2026.106299_bib0002","doi-asserted-by":"crossref","first-page":"4427","DOI":"10.1109\/TSP.2010.2048323","article-title":"A quaternion widely linear adaptive filter","volume":"58","author":"Took","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"issue":"2","key":"10.1016\/j.dsp.2026.106299_bib0003","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1007\/BF01075944","article-title":"Compact quaternion spaces","volume":"2","author":"Alekseevskii","year":"1968","journal-title":"Funct. Anal. Appl."},{"issue":"9","key":"10.1016\/j.dsp.2026.106299_bib0004","doi-asserted-by":"crossref","first-page":"2146","DOI":"10.3390\/s17092146","article-title":"A new quaternion-based Kalman filter for real-time attitude estimation using the two-step geometrically-intuitive correction algorithm","volume":"17","author":"Feng","year":"2017","journal-title":"Sensors"},{"issue":"4","key":"10.1016\/j.dsp.2026.106299_bib0005","doi-asserted-by":"crossref","first-page":"1316","DOI":"10.1109\/TSP.2008.2010600","article-title":"The quaternion LMS algorithm for adaptive filtering of hypercomplex processes","volume":"57","author":"Took","year":"2008","journal-title":"IEEE Trans. Signal Process."},{"key":"10.1016\/j.dsp.2026.106299_bib0006","series-title":"Asian Conference on Machine Learning","first-page":"236","article-title":"Quaternion graph neural networks","author":"Nguyen","year":"2021"},{"key":"10.1016\/j.dsp.2026.106299_bib0007","doi-asserted-by":"crossref","first-page":"5914","DOI":"10.1109\/TSP.2020.3029959","article-title":"Widely linear quaternion-valued least-mean kurtosis algorithm","volume":"68","author":"Meng\u00fc\u00e7","year":"2020","journal-title":"IEEE Trans. Signal Process."},{"issue":"6","key":"10.1016\/j.dsp.2026.106299_bib0008","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1109\/MSP.2023.3278071","article-title":"Quaternions in signal and image processing: a comprehensive and objective overview","volume":"40","author":"Miron","year":"2023","journal-title":"IEEE Signal Process. Mag."},{"key":"10.1016\/j.dsp.2026.106299_bib0009","first-page":"1","article-title":"Quaternion algebra and calculus","volume":"26","author":"Eberly","year":"2002","journal-title":"Magic Softw. Inc"},{"issue":"6","key":"10.1016\/j.dsp.2026.106299_bib0010","doi-asserted-by":"crossref","first-page":"1754","DOI":"10.1016\/j.renene.2010.12.013","article-title":"Quaternion-valued short-term joint forecasting of three-dimensional wind and atmospheric parameters","volume":"36","author":"Took","year":"2011","journal-title":"Renew. Energy"},{"issue":"7","key":"10.1016\/j.dsp.2026.106299_bib0011","doi-asserted-by":"crossref","first-page":"1712","DOI":"10.1016\/j.sigpro.2012.12.019","article-title":"A class of quaternion valued affine projection algorithms","volume":"93","author":"Jahanchahi","year":"2013","journal-title":"Signal Process."},{"issue":"6","key":"10.1016\/j.dsp.2026.106299_bib0012","first-page":"598","article-title":"The quarternion maximum correntropy algorithm","volume":"62","author":"Ogunfunmi","year":"2015","journal-title":"IEEE Trans. Circuits Syst. II Express Br."},{"issue":"2","key":"10.1016\/j.dsp.2026.106299_bib0013","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1109\/TNNLS.2015.2440473","article-title":"Optimization in quaternion dynamic systems: gradient, hessian, and learning algorithms","volume":"27","author":"Xu","year":"2015","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"issue":"2","key":"10.1016\/j.dsp.2026.106299_bib0014","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/j.sigpro.2010.06.024","article-title":"Augmented second-order statistics of quaternion random signals","volume":"91","author":"Took","year":"2011","journal-title":"Signal Process."},{"issue":"6","key":"10.1016\/j.dsp.2026.106299_bib0015","doi-asserted-by":"crossref","first-page":"1543","DOI":"10.1109\/TSP.2015.2399865","article-title":"The theory of quaternion matrix derivatives","volume":"63","author":"Xu","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"issue":"7","key":"10.1016\/j.dsp.2026.106299_bib0016","first-page":"3578","article-title":"Robust widely nonlinear quaternion Volterra adaptive filter based on recursive general barron algorithm and its performance analysis","volume":"71","author":"Liu","year":"2024","journal-title":"IEEE Trans. Circuits Syst. II: Express Br."},{"issue":"4","key":"10.1016\/j.dsp.2026.106299_bib0017","doi-asserted-by":"crossref","first-page":"3951","DOI":"10.1007\/s11071-022-07425-3","article-title":"A family of quaternion-valued pipelined second-order Volterra adaptive filters for nonlinear system identification","volume":"108","author":"Liu","year":"2022","journal-title":"Nonlinear Dyn."},{"issue":"7","key":"10.1016\/j.dsp.2026.106299_bib0018","first-page":"2715","article-title":"A novel quaternion kernel LMS algorithm with variable kernel width","volume":"68","author":"Huang","year":"2021","journal-title":"IEEE Trans. Circuits Syst. II Express Br."},{"key":"10.1016\/j.dsp.2026.106299_bib0019","doi-asserted-by":"crossref","DOI":"10.1016\/j.sigpro.2020.107810","article-title":"Quaternion kernel recursive least-squares algorithm","volume":"178","author":"Wang","year":"2021","journal-title":"Signal Process."},{"key":"10.1016\/j.dsp.2026.106299_bib0020","series-title":"IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","first-page":"4149","article-title":"A quaternion kernel minimum error entropy adaptive filter","author":"Ogunfunmi","year":"2018"},{"issue":"8","key":"10.1016\/j.dsp.2026.106299_bib0021","doi-asserted-by":"crossref","first-page":"1193","DOI":"10.1109\/TNN.2011.2157358","article-title":"Quaternion-valued nonlinear adaptive filtering","volume":"22","author":"Ujang","year":"2011","journal-title":"IEEE Trans. Neural Netw."},{"key":"10.1016\/j.dsp.2026.106299_bib0022","series-title":"IEEE International Conference on Acoustics, Speech, and Signal Processing","first-page":"V","article-title":"A Euclidean direction based algorithm for blind source separation using a natural gradient","volume":"Vol. 5","author":"Mabey","year":"2004"},{"key":"10.1016\/j.dsp.2026.106299_bib0023","doi-asserted-by":"crossref","first-page":"4967","DOI":"10.1109\/TSP.2022.3215291","article-title":"Maximum total quaternion correntropy for adaptive filtering","volume":"70","author":"Lin","year":"2022","journal-title":"IEEE Trans. Signal Process."},{"issue":"1","key":"10.1016\/j.dsp.2026.106299_bib0024","first-page":"480","article-title":"Maximum total quaternion generalized correntropy adaptive filtering","volume":"71","author":"Lin","year":"2023","journal-title":"IEEE Trans. Circuits Syst. II Express Br."},{"key":"10.1016\/j.dsp.2026.106299_bib0025","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1109\/LSP.2024.3515813","article-title":"Minimum total quaternion error entropy filtering with fiducial points against asymmetric noise","volume":"32","author":"Lin","year":"2025","journal-title":"IEEE Signal Process. Lett."},{"key":"10.1016\/j.dsp.2026.106299_bib0026","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1016\/j.dsp.2018.09.005","article-title":"Efficient recursive least-squares algorithms for the identification of bilinear forms","volume":"83","author":"Elisei-Iliescu","year":"2018","journal-title":"Digit. Signal Process."},{"issue":"7","key":"10.1016\/j.dsp.2026.106299_bib0027","first-page":"1359","article-title":"DCD-based recursive adaptive algorithms robust against impulsive noise","volume":"67","author":"Yu","year":"2020","journal-title":"IEEE Trans. Circuits Syst. II Express Br."},{"key":"10.1016\/j.dsp.2026.106299_bib0028","doi-asserted-by":"crossref","first-page":"1032","DOI":"10.1109\/LSP.2023.3301808","article-title":"Euclidean direction search algorithm based on maximum correntropy criterion","volume":"30","author":"Wang","year":"2023","journal-title":"IEEE Signal Process. Lett."},{"issue":"3","key":"10.1016\/j.dsp.2026.106299_bib0029","first-page":"532","article-title":"The Euclidean direction search algorithm in adaptive filtering","volume":"85","author":"Bose","year":"2002","journal-title":"IEICE Trans. Fundam. Electron. Commun. Comput. Sci."},{"key":"10.1016\/j.dsp.2026.106299_bib0030","article-title":"Unbiased Euclidean direction search algorithm for partial discharge location in cable systems","volume":"74","author":"Wang","year":"2025","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"10.1016\/j.dsp.2026.106299_bib0031","doi-asserted-by":"crossref","DOI":"10.1016\/j.sigpro.2024.109759","article-title":"Euclidean direction search algorithm with maximum correntropy criterion for active noise control system","volume":"229","author":"Wang","year":"2025","journal-title":"Signal Process."},{"issue":"2","key":"10.1016\/j.dsp.2026.106299_bib0032","doi-asserted-by":"crossref","first-page":"1469","DOI":"10.1109\/TII.2024.3478273","article-title":"Partial discharge location with gradient-descent total least-squares Euclidean direction search algorithm for cable systems","volume":"21","author":"Wang","year":"2024","journal-title":"IEEE Trans. Ind. Inform."},{"issue":"12","key":"10.1016\/j.dsp.2026.106299_bib0033","doi-asserted-by":"crossref","first-page":"1815","DOI":"10.1109\/TASLP.2014.2352456","article-title":"Sliding-window RLS low-cost implementation of proportionate affine projection algorithms","volume":"22","author":"Zakharov","year":"2014","journal-title":"IEEE\/ACM Trans. Audio Speech Lang. Process."},{"key":"10.1016\/j.dsp.2026.106299_bib0034","doi-asserted-by":"crossref","first-page":"2773","DOI":"10.1109\/LSP.2025.3586987","article-title":"Widely linear complex-valued affine projection algorithm with a sliding-window step-size","volume":"32","author":"Luo","year":"2025","journal-title":"IEEE Signal Process. Lett."},{"key":"10.1016\/j.dsp.2026.106299_bib0035","article-title":"Finite sliding window maximum correntropy criterion conjugate gradient adaptive filtering algorithm","volume":"169","author":"Yang","year":"2025","journal-title":"Digit. Signal Process."},{"key":"10.1016\/j.dsp.2026.106299_bib0036","series-title":"2013 IEEE International Conference of IEEE Region 10 (TENCON 2013)","first-page":"1","article-title":"Frequency-domain quaternion-valued adaptive filtering and its application to wind profile prediction","author":"Jiang","year":"2013"}],"container-title":["Digital Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1051200426004173?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1051200426004173?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T10:16:18Z","timestamp":1780654578000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1051200426004173"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":36,"alternative-id":["S1051200426004173"],"URL":"https:\/\/doi.org\/10.1016\/j.dsp.2026.106299","relation":{},"ISSN":["1051-2004"],"issn-type":[{"value":"1051-2004","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Quaternion Euclidean direction search algorithm","name":"articletitle","label":"Article Title"},{"value":"Digital Signal Processing","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.dsp.2026.106299","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"106299"}}