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Universities","award":["36261402"],"award-info":[{"award-number":["36261402"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["XLYC2007188"],"award-info":[{"award-number":["XLYC2007188"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["2018RJ08"],"award-info":[{"award-number":["2018RJ08"]}]},{"name":"Fundamental Research Funds for the Central Universities","award":["LJKQZ2021007"],"award-info":[{"award-number":["LJKQZ2021007"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>As a power source for autonomous underwater vehicles (AUVs), lithium-ion batteries play an important role in ensuring AUVs\u2019 electric power propulsion performance. An accurate state of charge (SOC) estimation method is the key to achieving energy optimization for lithium-ion batteries. Due to the complicated ocean environments, traditional filtering methods cannot effectively estimate the SOC of lithium-ion batteries in an AUV. Based on the standard extended Kalman filter (EKF), an adaptive iterative extended Kalman filter (AIEKF) method for the SOC in an AUV is proposed to address the traditional filter\u2019s problems, such as low accuracy and large errors. In this method, the adaptive update is introduced to deal with the uncertain noise from the lithium-ion battery. The iteration is used to improve the convergence speed and to reduce the computational burden. Compared with the EKF, iterative extended Kalman filter (IEKF) and adaptive extended Kalman filter (AEKF), the proposed AIEKF has a higher estimation accuracy and anti-interference capability, which is suitable for the AUV\u2019s SOC estimation. In addition, based on the second-order equivalent circuit model of the lithium-ion battery, a forgetting factor recursive least squares (FFRLS) method is proposed to deal with the multi-variability problem. In the end, four different methods, including EKF, IEKF, AEKF, and the proposed AIEKF, are compared in computational time. The experiment results show that the proposed method has high accuracy and fast estimation speed, meaning that it has good application potential in AUVs.<\/jats:p>","DOI":"10.3390\/s22239277","type":"journal-article","created":{"date-parts":[[2022,11,29]],"date-time":"2022-11-29T02:09:58Z","timestamp":1669687798000},"page":"9277","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 an Adaptive Iterative Extended Kalman Filter for AUVs"],"prefix":"10.3390","volume":"22","author":[{"given":"You","family":"Fu","sequence":"first","affiliation":[{"name":"School of Marine Electrical Engineering, Dalian Maritime University, Dalian 116024, China"}]},{"given":"Binhao","family":"Zhai","sequence":"additional","affiliation":[{"name":"School of Marine Electrical Engineering, Dalian Maritime University, Dalian 116024, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7543-8133","authenticated-orcid":false,"given":"Zhuoqun","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Marine Electrical Engineering, Dalian Maritime University, Dalian 116024, China"}]},{"given":"Jun","family":"Liang","sequence":"additional","affiliation":[{"name":"School of Marine Electrical Engineering, Dalian Maritime University, Dalian 116024, China"}]},{"given":"Zhouhua","family":"Peng","sequence":"additional","affiliation":[{"name":"School of Marine Electrical Engineering, Dalian Maritime University, Dalian 116024, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3287","DOI":"10.1039\/c1ee01388b","article-title":"Lithium-ion batteries. A look into the future","volume":"4","author":"Scrosati","year":"2011","journal-title":"Energy Environ. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.est.2016.05.007","article-title":"Validation and benchmark methods for battery management system functionalities: State of charge estimation algorithms","volume":"7","author":"Campestrini","year":"2016","journal-title":"J. Energy Storage"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1425","DOI":"10.1109\/TVT.2007.912176","article-title":"Battery management system based on battery nonlinear dynamics modeling","volume":"57","author":"Szumanowski","year":"2008","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.jpowsour.2017.03.001","article-title":"On state-of-charge determination for lithium-ion batteries","volume":"348","author":"Li","year":"2017","journal-title":"J. Power Sources"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/j.apenergy.2016.09.010","article-title":"Influence of different open circuit voltage tests on state of charge online estimation for lithium-ion batteries","volume":"183","author":"Zheng","year":"2016","journal-title":"Appl. Energy"},{"key":"ref_6","first-page":"1","article-title":"A degradation empirical-model-free battery end-of-life prediction framework based on gaussian process regression and Kalman filter","volume":"8","author":"Meng","year":"2022","journal-title":"IEEE Trans. Transp. Electrif."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3004","DOI":"10.3390\/en7053004","article-title":"A combined state of charge estimation method for lithium-ion batteries used in a wide ambient temperature range","volume":"7","author":"Feng","year":"2014","journal-title":"Energies"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.apenergy.2013.07.008","article-title":"State of charge estimation of lithium-ion batteries using the open-circuit voltage at various ambient temperatures","volume":"113","author":"Xing","year":"2014","journal-title":"Appl. Energy"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"10069","DOI":"10.1109\/ACCESS.2018.2797976","article-title":"Neural network approach for estimating state of charge of lithium-ion battery using backtracking search algorithm","volume":"6","author":"Hannan","year":"2018","journal-title":"IEEE Access"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"682","DOI":"10.1016\/j.jpowsour.2014.07.016","article-title":"State-of-charge estimation for battery management system using optimized support vector machine for regression","volume":"269","author":"Hu","year":"2014","journal-title":"J. Power Sources"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"5217","DOI":"10.3390\/en8065217","article-title":"Extended Kalman filter with a fuzzy method for accurate battery pack state of charge estimation","volume":"8","author":"Sepasi","year":"2015","journal-title":"Energies"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1109\/TVT.2017.2751613","article-title":"The co-estimation of state of charge, state of health, and state of function for lithium-ion batteries in electric vehicles","volume":"67","author":"Shen","year":"2017","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/j.jpowsour.2011.10.013","article-title":"A comparative study of equivalent circuit models for Li-ion batteries","volume":"198","author":"Hu","year":"2012","journal-title":"J. Power Sources"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"566","DOI":"10.1016\/j.electacta.2017.10.153","article-title":"A comparative study of different equivalent circuit models for estimating state-of-charge of lithium-ion batteries","volume":"259","author":"Lai","year":"2018","journal-title":"Electrochim. Acta"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Meng, J., Boukhnifer, M., and Diallo, D. (2020, January 15\u201318). Lithium-ion battery monitoring and observability analysis with extended equivalent circuit model. Proceedings of the 2020 28th Mediterranean Conference on Control and Automation (MED), Saint-Rapha\u00ebl, France.","DOI":"10.1109\/MED48518.2020.9183112"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"4178","DOI":"10.1109\/TIE.2010.2043035","article-title":"State-of-charge estimation for lithium-ion batteries using neural networks and EKF","volume":"57","author":"Charkhgard","year":"2010","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1603","DOI":"10.1002\/er.3954","article-title":"Model-based unscented Kalman filter observer design for lithium-ion battery state of charge estimation","volume":"42","author":"Wang","year":"2018","journal-title":"Int. J. Energy Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"113520","DOI":"10.1016\/j.apenergy.2019.113520","article-title":"An improved state of charge estimation method based on cubature Kalman filter for lithium-ion batteries","volume":"253","author":"Peng","year":"2019","journal-title":"Appl. Energy"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1825","DOI":"10.1049\/iet-pel.2014.0523","article-title":"Design of adaptive H\u221e filter for implementing on state-of-charge estimation based on battery state-of-charge-varying modelling","volume":"8","author":"Charkhgard","year":"2015","journal-title":"IET Power Electron."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1028","DOI":"10.1016\/j.energy.2018.06.113","article-title":"Differential voltage analysis based state of charge estimation methods for lithium-ion batteries using extended Kalman filter and particle filter","volume":"158","author":"Zheng","year":"2018","journal-title":"Energy"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1109\/TEC.2018.2861994","article-title":"State-of-charge estimation for li-ion batteries: A more accurate hybrid approach","volume":"34","author":"Misyris","year":"2018","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"228450","DOI":"10.1016\/j.jpowsour.2020.228450","article-title":"A novel charged state prediction method of the lithium ion battery packs based on the composite equivalent modeling and improved splice Kalman filtering algorithm","volume":"471","author":"Wang","year":"2020","journal-title":"J. Power Sources"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Lao, Z., Xia, B., Wang, W., Lai, Y., and Wang, M. (2018). A novel method for lithium-ion battery online parameter identification based on variable forgetting factor recursive least squares. Energies, 11.","DOI":"10.3390\/en11061358"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"227984","DOI":"10.1016\/j.jpowsour.2020.227984","article-title":"Enhanced online model identification and state of charge estimation for lithium-ion battery under noise corrupted measurements by bias compensation recursive least squares","volume":"456","author":"Li","year":"2020","journal-title":"J. Power Sources"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"737","DOI":"10.1109\/TEC.2011.2155657","article-title":"Reliable state estimation of multicell lithium-ion battery systems","volume":"26","author":"Roscher","year":"2011","journal-title":"IEEE Trans. Energy Convers."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"115880","DOI":"10.1016\/j.energy.2019.115880","article-title":"A state of charge estimation method for lithium-ion batteries based on fractional order adaptive extended Kalman filter","volume":"187","author":"Zhu","year":"2019","journal-title":"Energy"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"113615","DOI":"10.1016\/j.apenergy.2019.113615","article-title":"An improved Thevenin model of lithium-ion battery with high accuracy for electric vehicles","volume":"254","author":"Ding","year":"2019","journal-title":"Appl. Energy"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1016\/j.electacta.2018.11.134","article-title":"A comparative study of global optimization methods for parameter identification of different equivalent circuit models for li-ion batteries","volume":"295","author":"Lai","year":"2019","journal-title":"Electrochim. Acta"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.enconman.2012.04.014","article-title":"Comparison study on the battery models used for the energy management of batteries in electric vehicles","volume":"64","author":"He","year":"2012","journal-title":"Energy Convers. Manag."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"114932","DOI":"10.1016\/j.apenergy.2020.114932","article-title":"A noise-tolerant model parameterization method for lithium-ion battery management system","volume":"268","author":"Wei","year":"2020","journal-title":"Appl. Energy"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"312","DOI":"10.1109\/TIE.2019.2962429","article-title":"Noise-immune model identification and state-of-charge estimation for lithium-ion battery using bilinear parameterization","volume":"68","author":"Wei","year":"2020","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1016\/j.jpowsour.2013.03.131","article-title":"Battery state of the charge estimation using Kalman filtering","volume":"239","author":"Mastali","year":"2013","journal-title":"J. Power Sources"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1461","DOI":"10.1109\/TVT.2011.2132812","article-title":"State-of-charge estimation of the lithium-ion battery using an adaptive extended Kalman filter based on an improved Thevenin model","volume":"60","author":"He","year":"2011","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1109\/TTE.2018.2802043","article-title":"Improved battery SOC estimation accuracy using a modified UKF with an adaptive cell model under real EV operating conditions","volume":"4","author":"Hussein","year":"2018","journal-title":"IEEE Trans. Transp. Electrif."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"13202","DOI":"10.1109\/ACCESS.2017.2725301","article-title":"State of charge estimation of battery energy storage systems based on adaptive unscented Kalman filter with a noise statistics estimator","volume":"5","author":"Peng","year":"2017","journal-title":"IEEE Access"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/23\/9277\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:28:55Z","timestamp":1760146135000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/23\/9277"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,29]]},"references-count":35,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["s22239277"],"URL":"https:\/\/doi.org\/10.3390\/s22239277","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,29]]}}}