{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T17:59:29Z","timestamp":1762624769567,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2022,1,21]],"date-time":"2022-01-21T00:00:00Z","timestamp":1642723200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62073114, 11971032"],"award-info":[{"award-number":["62073114, 11971032"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fractal Fract"],"abstract":"<jats:p>The accuracy of the state-of-charge (SOC) estimation of lithium batteries affects the battery life, driving performance, and the safety of electric vehicles. This paper presents a SOC estimation method based on the fractional-order square-root unscented Kalman filter (FSR-UKF). Firstly, a fractional second-order Resistor-Capacitance (RC) circuit model of the lithium battery is derived. The accuracy of the parameterized model is verified, revealing its superiority over integer-order standard descriptions. Then, the FSR-UKF algorithm is developed, combining the advantages of the square-root unscented Kalman filter and the fractional calculus. The effectiveness of the proposed algorithm is proven under a variety of operational conditions in the perspective of the root-mean-squared error, which is shown to be below 1.0%. In addition, several experiments illustrate the performance of the FSR-UKF.<\/jats:p>","DOI":"10.3390\/fractalfract6020052","type":"journal-article","created":{"date-parts":[[2022,1,21]],"date-time":"2022-01-21T08:37:18Z","timestamp":1642754238000},"page":"52","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["State-of-Charge Estimation of Lithium-Ion Batteries Based on Fractional-Order Square-Root Unscented Kalman Filter"],"prefix":"10.3390","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8110-5378","authenticated-orcid":false,"given":"Liping","family":"Chen","sequence":"first","affiliation":[{"name":"School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China"}]},{"given":"Xiaobo","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4274-4879","authenticated-orcid":false,"given":"Jos\u00e9","family":"Tenreiro Machado","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Rua Dr. Ant\u00f3nio Bernardino de Almeida 431, 4249-015 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7359-4370","authenticated-orcid":false,"given":"Ant\u00f3nio","family":"Lopes","sequence":"additional","affiliation":[{"name":"UISPA\u2013LAETA\/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"given":"Penghua","family":"Li","sequence":"additional","affiliation":[{"name":"Automotive Electronics Engineering Research Center, College of Automation, Chongqing University of Posts and Telecommunications, Chongqing 400065, China"}]},{"given":"Xueping","family":"Dong","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Automation, Hefei University of Technology, Hefei 230009, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,1,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1032","DOI":"10.1016\/j.jclepro.2015.11.011","article-title":"Integration issues of lithium-ion battery into electric vehicles battery pack","volume":"113","author":"Saw","year":"2016","journal-title":"J. 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