Parameter identification and state of charge estimation for lithium-ion batteries based on trust region least squares

Jun Wang , Dexing Wang , Hui Li , Chao Ma , Changhai Liu , Bin Wang

AIMS Energy ›› 2026, Vol. 14 ›› Issue (1) : 23 -46.

PDF (1758KB)
AIMS Energy ›› 2026, Vol. 14 ›› Issue (1) :23 -46. DOI: 10.3934/energy.2026002
Research article
research-article
Parameter identification and state of charge estimation for lithium-ion batteries based on trust region least squares
Author information +
History +
PDF (1758KB)

Abstract

To address issues of inaccurate parameter identification and large state of charge (SOC) estimation error for lithium-ion batteries in electric vehicle (EV) applications, we proposed a parameter identification and corresponding SOC estimation method based on a trust region least squares (TRLS) algorithm. First, a second-order resistor-capacitor (RC) equivalent circuit model for the lithium-ion battery was established. To effectively describe the dynamic characteristics of the lithium-ion battery, discharge experiments were designed and conducted to collect the data of terminal voltage, current, and time. The initial parameters of this model were then obtained through a segmented identification based on the Levenberg-Marquardt (LM) algorithm. Subsequently, an improved parameter identification algorithm based on the TRLS was constructed. This algorithm conducted the iterative optimization of model parameters by searching for the best solution within the trust region, thereby achieving precise identification of model parameters. Finally, the SOC estimation was achieved using the TRLS-based optimization solution of model parameters in conjunction with the dual extended Kalman filter (DEKF) algorithm. With the proposed TRLS-based method, the Mean Absolute Error (MAE) values of the estimated SOC were 0.0031, 0.0066, 0.0052, and 0.0044 under the static open-circuit voltage (OCV), the dynamic Urban Dynamometer Driving Schedule (UDDS), Hybrid Pulse Power Characterization (HPPC), and Dynamic Stress Test (DST) conditions, respectively. The comparative results successfully verified the reliability and effectiveness of the proposed TRLS-based method, which demonstrated significant potential and advantages for battery management applications.

Keywords

lithium-ion battery / parameter identification / state of charge estimation / trust region least squares / dual extended kalman filter

Cite this article

Download citation ▾
Jun Wang, Dexing Wang, Hui Li, Chao Ma, Changhai Liu, Bin Wang. Parameter identification and state of charge estimation for lithium-ion batteries based on trust region least squares. AIMS Energy, 2026, 14 (1) : 23-46 DOI:10.3934/energy.2026002

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

He M, Hector LJ, Dai F, et al. (2024) Industry needs for practical lithium-metal battery designs in electric vehicles. Nat Energy 9: 1199-1205. https://doi.org/10.1038/s41560-024-01624-5

[2]

Miao K, Ma C, Zhou J (2025) Advances and prospects of low temperature Li-S batteries. Appl Energy 388: 125720. https://doi.org/10.1016/j.apenergy.2025.125720

[3]

Andersson M, Streb M, Prathimala V, et al. (2024) Electrochemical model-based aging-adaptive fast charging of automotive lithium-ion cells. Appl Energy 372: 123644. https://doi.org/10.1016/j.apenergy.2024.123644

[4]

Geslin A, Xu L, Ganapathi D, et al. (2025) Dynamic cycling enhances battery lifetime. Nat Energy 10: 172-180. https://doi.org/10.1038/s41560-024-01675-8

[5]

Kurucan M, Özbaltan M, Yetgin Z, et al. (2024) Applications of artificial neural network based battery management systems: A literature review. Renewable Sustainable Energy Rev 192: 114262. https://doi.org/10.1016/j.rser.2023.114262

[6]

Wu L, Lyu Z, Huang Z, et al. (2024) Physics-based battery SOC estimation methods: Recent advances and future perspectives. J Energy Chem 89: 27-40. https://doi.org/10.1016/j.jechem.2023.09.045

[7]

Degen F, Winter M, Bendig D, et al. (2023) Energy consumption of current and future production of lithium-ion and post lithium-ion battery cells. Nat Energy 8: 1284-1295. https://doi.org/10.1038/s41560-023-01355-z

[8]

Kong C, Zhu G, Wang J, et al. (2025) A simplified electrochemical lithium-ion batteries model based on-informed LSTM_Res network. Int J Heat Mass Transfer, 246. https://doi.org/10.1016/j.ijheatmasstransfer.2025.127024

[9]

Fornaro P, Puleston P, Battaiotto P (2023) State-of-Charge and State-of-Health variable-gain estimation based on tracking sliding mode differentiators for an electric vehicle Lithium-ion battery. J Energy Storage, 65. https://doi.org/10.1016/j.est.2023.107299

[10]

Li J, Bai G, Yan J, et al. (2024) On-line parameter identification and SOC estimation of nonlinear model of lithium-ion battery based on Wiener structure. J Energy Storage, 92. https://doi.org/10.1016/j.est.2024.112094

[11]

Miranda D, Gonçalves R, Wuttke S, et al. (2023) Overview on theoretical simulations of lithium-ion batteries and their application to battery separators. Adv Energy Mater, 13: 2203874. https://doi.org/10.1002/aenm.202203874

[12]

Tang A, Huang Y, Xu Y, et al. (2024) Data-physics-driven estimation of battery state of charge and capacity. Energy, 294. https://doi.org/10.1016/j.energy.2024.130776

[13]

Chen M, Xie X, He C, et al. (2025) An integrated framework for ARX model identification and its application to lithium-ion battery. IEEE Trans Instrum Meas 74: 1-14. https://doi.org/10.1109/TIM.2025.3545698

[14]

Wang J, Du J, Tan B, et al. (2023) Establishment of a lithium-ion battery model considering environmental temperature for battery state of charge estimation. J Electrochem Soc 170: 120507. https://doi.org/10.1149/1945-7111/ad11af

[15]

Li H, Fu L, Long X, et al. (2024) A hybrid deep learning model for lithium-ion batteries state of charge estimation based on quantile regression and attention. Energy, 294. https://doi.org/10.1016/j.energy.2024.130834

[16]

Wang S, Wu Y, Zhou H, et al. (2025) Improved particle swarm optimization-adaptive dual extended Kalman filtering for accurate battery state of charge and state of energy joint estimation with efficient core factor feedback correction. Energy 322: 135686. https://doi.org/10.1016/j.energy.2025.135686

[17]

Jiang Z, Zhang Y, Gao R (2025) An improved electrochemical-thermal coupling model for state-of-charge estimation of lithium-ion battery. Energy 333: 137486. https://doi.org/10.1016/j.energy.2025.137486

[18]

Li Z, Zhang X, Gao W (2024) State of health estimation of lithium-ion battery during fast charging process based on BiLSTM-Transformer. Energy 311: 133418. https://doi.org/10.1016/j.energy.2024.133418

[19]

Li F, Zuo W, Zhou K, et al. (2024) State-of-charge estimation of lithium-ion battery based on second order resistor-capacitance circuit-PSO-TCN model. Energy 289: 130025. https://doi.org/10.1016/j.energy.2023.130025

[20]

Yuan B, Zhang B, Yuan X, et al. (2024) Study on the estimation of the state of charge of lithium-ion battery. Electrochim Acta 491: 144297. https://doi.org/10.1016/j.electacta.2024.144297

[21]

Li N, Zhang X, Wang R, et al. (2025) SR-CKF algorithm-based state-of-charge estimation of lithium-ion batteries for energy storage over a wide temperature range. J Energy Storage, 125: 116849. https://doi.org/10.1016/j.est.2025.116849

[22]

Wang D, Yang Y, Gu T (2023) A hierarchical adaptive extended Kalman filter algorithm for lithium-ion battery state of charge estimation. J Energy Storage 62: 106831. https://doi.org/10.1016/j.est.2023.106831

[23]

Ding F (2023) Least squares parameter estimation and multi-innovation least squares methods for linear fitting problems from noisy data. J Comput Appl Math 426: 115107. https://doi.org/10.1016/j.cam.2023.115107

[24]

Huang C (2023) An online condition-based parameter identification switching algorithm for lithium-ion batteries in electric vehicles. IEEE Trans Veh Technol 72: 1701-1709. https://doi.org/10.1109/TVT.2022.3210688

[25]

Hou J, Liu J, Chen F, et al. (2023) Robust lithium-ion state-of-charge and battery parameters joint estimation based on an enhanced adaptive unscented Kalman filter. Energy 271: 126998. https://doi.org/10.1016/j.energy.2023.126998

[26]

Wang J, Song J, Li Y, et al. (2024) State of charge estimation for lithium-ion battery based on improved online parameters identification and adaptive square root unscented Kalman filter. J Energy Storage 77: 109977. https://doi.org/10.1016/j.est.2023.109977

[27]

Yang J, Fang W, Chen J, et al. (2022) A lithium-ion battery remaining useful life prediction method based on unscented particle filter and optimal combination strategy. J Energy Storage 55: 105648. https://doi.org/10.1016/j.est.2022.105648

[28]

Jiang Z, Qin S, Wei Y, et al. (2021) An immune genetic extended kalman particle filter approach on state of charge estimation for lithium-ion battery. Energy 230: 120805. https://doi.org/10.1016/j.energy.2021.120805

[29]

Ananda S, Lakshminarasamma N, Radhakrishna, et al. (2022) Lithium-ion cell sorting and cell performance modeling for spacecraft battery. IEEE Trans Ind Appl 58: 6536-6545. https://doi.org/10.1109/TIA.2022.3179459

[30]

Li N, He F, Ma W, et al. (2022) An indirect state-of-health estimation method based on improved genetic and back propagation for online lithium-ion battery used in electric vehicles. IEEE Trans Veh Technol 71: 12682-12690. https://doi.org/10.1109/TVT.2022.3196225

[31]

Zhang F, Xing Z, Wu M (2023) State of health estimation for Li-ion battery using characteristic voltage intervals and genetic algorithm optimized back propagation neural network. J Energy Storage 57: 106277. https://doi.org/10.1016/j.est.2022.106277

[32]

Liu Y, Zhao W, Yin G (2024) Forgetting-Factor regrets for online convex optimization. IEEE Trans Autom Control 69: 5034-5048. https://doi.org/10.1109/TAC.2023.3340120

[33]

Cao R, Zhang Z, Shi R, et al. (2025) Model-constrained deep learning for online fault diagnosis in Li-ion batteries over stochastic conditions. Nat Commun 16: 1651. https://doi.org/10.1038/s41467-025-56832-8

[34]

Liu Z, He H, Xie J, et al. (2022) Self-discharge prediction method for lithium-ion batteries based on improved support vector machine. J Energy Storage 55: 105571. https://doi.org/10.1016/j.est.2022.105571

[35]

Ren X, Liu S, Yu X, et al. (2021) A method for state-of-charge estimation of lithium-ion batteries based on PSO-LSTM. Energy 234: 121236. https://doi.org/10.1016/j.energy.2021.121236

[36]

Sharma S, Garg A, Panigrahi B (2024) Predicting state-of-charge using gradient-boosted SVR ensemble technique for lithium ion battery used in EVs. IEEE Trans Transp Electrification 10: 4441-4454. https://doi.org/10.1109/TTE.2023.3310159

[37]

Shi J, Rivera A, Wu D (2022) Battery health management using physics-informed machine learning: Online degradation modeling and remaining useful life prediction. Mech Syst Signal Process 179: 109347. https://doi.org/10.1016/j.ymssp.2022.109347

[38]

Liu M, Zhou X, Yang L, et al. (2023) A novel Kalman-filter-based battery internal temperature estimation method based on an enhanced electro-thermal coupling model. J Energy Storage 71: 108241. https://doi.org/10.1016/j.est.2023.108241

[39]

Wang C, Yang M, Wang X, et al. (2025) A review of battery SOC estimation based on equivalent circuit models. J Energy Storage 110: 115346. https://doi.org/10.1016/j.est.2025.115346

[40]

Su S, Li W, Mou J, et al. (2023) A hybrid battery equivalent circuit model, deep learning, and transfer learning for battery state monitoring. IEEE Trans Transp Electrification 9: 1113-1127. https://doi.org/10.1109/TTE.2022.3204843

[41]

Zhu G, Hu M, Qiu C, et al. (2025) Integer variable-order equivalent circuit model and switching strategy for lithium-ion power batteries for vehicles based on information criterion under dynamic and static working conditions. Energy 322: 135694. https://doi.org/10.1016/j.energy.2025.135694

[42]

Hong Z, Wang Y, Jin Z (2025) Diagnosis of battery external short circuits based on an improved second-order RC fault model and recursive least squares identification method. Energy 319: 134880. https://doi.org/10.1016/j.energy.2025.134880

[43]

Xiong R, Pan Y, Shen W, et al. (2020) Lithium-ion battery aging mechanisms and diagnosis method for automotive applications: Recent advances and perspectives. Renewable Sustainable Energy Rev 131: 110048. https://doi.org/10.1016/j.rser.2020.110048

[44]

Monirul I, Qiu L, Ruby R (2024) Accurate SOC estimation of ternary lithium-ion batteries by HPPC test-based extended Kalman filter. J Energy Storage 92: 112304. https://doi.org/10.1016/j.est.2024.112304

[45]

Yan Y, Wang B, Wang C, et al. (2024) Adaptive maximum available energy evaluation for lithium battery in hydrogen-electric hybrid unmanned aerial vehicle applications considering dynamic ambient temperature and aging level. Energy Convers Manage 314: 118685. https://doi.org/10.1016/j.enconman.2024.118685

[46]

Wei L, Lin T, Wang Y (2025) CCEM: Cell-to-Cell Extension Model for low-cost joint estimation of SOC and temperature in supercapacitor series modules. J Energy Storage 119: 116316. https://doi.org/10.1016/j.est.2025.116316

[47]

Paul T, Wang S, Zhang H, et al. (2023) An ASTSEKF optimizer with nonlinear condition adaptability for accurate SOC estimation of lithium-ion batteries. J Energy Storage 70: 108098. https://doi.org/10.1016/j.est.2023.108098

[48]

Fan Y, Zhang Z, Yang G, et al. (2025) A comparative study of modeling and parameter identification for lithium-ion batteries in energy storage systems. Measurement 243: 116263. https://doi.org/10.1016/j.measurement.2024.116263

[49]

Yang B, Wang D, Sun X, et al. (2023) Offline order recognition for state estimation of Lithium-ion battery using fractional order model. Appl Energy 341: 120977. https://doi.org/10.1016/j.apenergy.2023.120977

[50]

Duan Z, Hong X, Li H, et al. (2024) Simulating the uneven temperature distributions within large-sized lithium-ion batteries using a thermal resistance network model. J Energy Storage 101: 113732. https://doi.org/10.1016/j.est.2024.113732

[51]

Peng J, Meng J, Wu J, et al. (2023) A comprehensive overview and comparison of parameter benchmark methods for lithium-ion battery application. J Energy Storage 71: 108197. https://doi.org/10.1016/j.est.2023.108197

[52]

Wang Y, Cheng Y, Xiong Y, et al. (2022) Estimation of battery open-circuit voltage and state of charge based on dynamic matrix control-extended Kalman filter algorithm. J Energy Storage 52: 104860. https://doi.org/10.1016/j.est.2022.104860

[53]

Wu J, Lei D, Liu Z, et al. (2024) A fusion algorithm of multidimensional element space mapping architecture for SOC estimation of lithium-ion batteries under dynamic operating conditions. Energy 311: 133467. https://doi.org/10.1016/j.energy.2024.133467

[54]

Zhou Z, Duan B, Li C, et al. (2025) Life-cycle state-of-charge estimation for lithium-ion battery considering coulomb efficiency and capacity decay. IEEE Trans Transp Electrification 11: 6335-6343. https://doi.org/10.1109/TTE.2024.3506778

[55]

Tang A, Huang Y, Liu S, et al. (2023) A novel lithium-ion battery state of charge estimation method based on the fusion of neural network and equivalent circuit models. Appl Energy 348: 121578. https://doi.org/10.1016/j.apenergy.2023.121578

[56]

Xu M, Zhang E, Wang S, et al. (2024) Dynamic ultrasonic response modeling and accurate state of charge estimation for lithium ion batteries under various load profiles and temperatures. Appl Energy 355: 122210. https://doi.org/10.1016/j.apenergy.2023.122210

[57]

Zhang Y, Lai X, Zhang X, et al. (2025) Fusion of stress and electrical signals for high-accuracy joint estimation of SOC and SOH in lithium-ion batteries. Energy 331: 137063. https://doi.org/10.1016/j.energy.2025.137063

PDF (1758KB)

0

Accesses

0

Citation

Detail

Sections
Recommended

/

〈 〉