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This paper develops a gradient-based and a least-squares-based iterative estimation algorithms to estimate the parameters for a multi-input multi-output (MIMO) system with coloured auto-regressive moving average (ARMA) noise from input\u2013output data, based on the gradient search and least-squares principles, respectively. The key is to replace the unknown noise terms and residuals contained in the information vector with their corresponding estimates at the previous iteration. The simulation test results indicate that the proposed algorithms are effective. <\/jats:p>","DOI":"10.1177\/0959651811409491","type":"journal-article","created":{"date-parts":[[2011,9,17]],"date-time":"2011-09-17T01:54:45Z","timestamp":1316224485000},"page":"43-55","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":123,"title":["Gradient-based and least-squares-based iterative estimation algorithms for multi-input multi-output systems"],"prefix":"10.1177","volume":"226","author":[{"given":"F","family":"Ding","sequence":"first","affiliation":[{"name":"Key Laboratory of Advanced Process Control for Light Industry, Jiangnan University, Wuxi, People\u2019s Republic of China"},{"name":"Control Science and Engineering Research Center, Jiangnan University, Wuxi, People\u2019s Republic of China"}]},{"given":"Y","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Process Control for Light Industry, Jiangnan University, Wuxi, People\u2019s Republic of China"}]},{"given":"B","family":"Bao","sequence":"additional","affiliation":[{"name":"Control Science and Engineering Research Center, Jiangnan University, Wuxi, People\u2019s Republic of China"}]}],"member":"179","published-online":{"date-parts":[[2011,9,16]]},"reference":[{"key":"bibr1-0959651811409491","doi-asserted-by":"publisher","DOI":"10.1243\/09596518JSCE686"},{"key":"bibr2-0959651811409491","doi-asserted-by":"publisher","DOI":"10.1080\/00207170903273987"},{"key":"bibr3-0959651811409491","doi-asserted-by":"publisher","DOI":"10.1243\/09596518JSCE888"},{"issue":"7","key":"bibr4-0959651811409491","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1002\/acs.1141","volume":"24","author":"Ding F.","year":"2010","journal-title":"Int. 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