{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,25]],"date-time":"2025-10-25T21:55:28Z","timestamp":1761429328993,"version":"3.38.0"},"reference-count":38,"publisher":"SAGE Publications","issue":"9","license":[{"start":{"date-parts":[[2020,1,2]],"date-time":"2020-01-02T00:00:00Z","timestamp":1577923200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100002858","name":"china postdoctoral science foundation","doi-asserted-by":"publisher","award":["2019M651206"],"award-info":[{"award-number":["2019M651206"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005047","name":"natural science foundation of liaoning province","doi-asserted-by":"publisher","award":["20180520009"],"award-info":[{"award-number":["20180520009"]}],"id":[{"id":"10.13039\/501100005047","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Liaoning University Science Research Fund","award":["LDGY2019020"],"award-info":[{"award-number":["LDGY2019020"]}]},{"DOI":"10.13039\/501100018617","name":"Liaoning Revitalization Talents Program","doi-asserted-by":"crossref","award":["XLYC1807229"],"award-info":[{"award-number":["XLYC1807229"]}],"id":[{"id":"10.13039\/501100018617","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Transactions of the Institute of Measurement and Control"],"published-print":{"date-parts":[[2020,6]]},"abstract":"<jats:p> Hybrid extended-unscented Kalman filters (HEUKFs) for continuous-time nonlinear fractional-order systems with process and measurement noises are investigated in this paper. The Gr\u00fcnwald-Letnikov difference and the fractional-order average derivative (FOAD) method are adopted to discretize the investigated nonlinear fractional-order system, and the nonlinear functions in the system description are coped with the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). The first-order Taylor expansion used in the EKF method is performed for the nonlinear function at the current time. Meanwhile, the unscented transformation used in the UKF is also concerned for the nonlinear function at the previous time. By using the HEUKF designed in this paper, the third-order approximations for the nonlinear function can be achieved to enhance the accuracy of state estimation and estimation error matrix. Finally, numerical examples are provided to illustrate the effectiveness of the proposed HEUKF for nonlinear fractional-order systems. <\/jats:p>","DOI":"10.1177\/0142331219893788","type":"journal-article","created":{"date-parts":[[2020,1,3]],"date-time":"2020-01-03T06:43:47Z","timestamp":1578033827000},"page":"1618-1631","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":10,"title":["Hybrid extended-unscented Kalman filters for continuous-time nonlinear fractional-order systems involving process and measurement noises"],"prefix":"10.1177","volume":"42","author":[{"given":"Xiaojiao","family":"Chen","sequence":"first","affiliation":[{"name":"School of Mathematics, Liaoning University, PR China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7084-5426","authenticated-orcid":false,"given":"Zhe","family":"Gao","sequence":"additional","affiliation":[{"name":"College of Light Industry, Liaoning University, PR 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