State-of-Energy Estimation of a Lithium Iron Phosphate Battery Usingan Iterated CKF–EKF Algorithm
5 affiliations
- 1School of Chemistry and Environmental Engineering, Wuhan Textile University, Wuhan 430073, China
- 2School of Environment and Chemical Engineering, Shanghai University, Shanghai 200444, China
- 3State Key Laboratory of Light Superalloys, Wuhan University of Technology, Wuhan 430070, China
- 4Hubei Key Laboratory of Advanced Technology for Automotive Components, Wuhan University of Technology, Wuhan 430070, China
- 5Camel Group Wuhan Optics Valley R&D Center Co., Ltd., Wuhan 430073, China
Abstract
Accurate state-of-energy (SOE) estimation on the flat voltage plateau of lithium iron phosphate (LFP) batteries depends on observation calibration and initialization. This study implements an iterated cubature Kalman filter–extended Kalman filter (CKF–EKF) with a joint state–parameter covariance and five damped voltage relinearizations. On one 25,251-sample Dynamic Stress Test (DST) of a 27 Ah cell at nominal 25 °C, its calibrated full-record mean absolute error/root mean square error (MAE/RMSE) is 0.8340/0.8514 percentage points (pp); the score includes the supervised development prefix. The earlier-protocol experiment in which a fixed-RC adaptive EKF reached 0.1260 pp is restored beside that comparison, together with the non-adaptive estimators of the same archived table, which reach 0.1260 and 0.1259 pp without adapting anything; that value is the floor set by the initial 20 pp step under that protocol. To remove the protocol difference, every architecture is also scored over the entire shared 129-member noise-candidate bank: the lowest full-record RMSE attainable by a fixed-RC adaptive EKF is 1.3753 pp, and at the archived noise setting itself, that baseline gives 7.1988 pp against 1.1885 pp for the hybrid. The DST evaluation is one continuous full-history replay; a no-history interior restart is not tested. Two similar-cell, 20-segment stepped discharges at approximately 1C and nominal 25 °C, with long rests and each target cell’s measured usable energy supplied, yield RMSE 0.6868/0.7995 pp and signed mean errors of −0.6851/−0.7975 pp, an offset traced to a 2–3 mV mismatch of the transferred observation curve. These are conditional transfer tests, not additional DST validations. Fixed-settings ablations characterize the parameter block and iteration within the proposed implementation. The evidence is limited to the tested temperature, cell condition, load profiles and known-energy calibration. One additional dynamic profile, temperature variation and aging remain unvalidated.
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BibTeX
@article{xiao2026stateofenergy,
title = {{State-of-Energy Estimation of a Lithium Iron Phosphate Battery Usingan Iterated CKF–EKF Algorithm}},
author = {Mingming Xiao and Mofan Li and Jianqiang Kang and Zhong Tian},
journal = {Batteries},
year = {2026},
month = oct,
doi = {10.3390/batteries12100397},
url = {https://www.mdpi.com/2313-0105/12/10/397},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - State-of-Energy Estimation of a Lithium Iron Phosphate Battery Usingan Iterated CKF–EKF Algorithm
AU - Mingming Xiao
AU - Mofan Li
AU - Jianqiang Kang
AU - Zhong Tian
PY - 2026
DA - 2026/10/04
JO - Batteries
DO - 10.3390/batteries12100397
UR - https://www.mdpi.com/2313-0105/12/10/397
AB - Accurate state-of-energy (SOE) estimation on the flat voltage plateau of lithium iron phosphate (LFP) batteries depends on observation calibration and initialization. This study implements an iterated cubature Kalman filter–extended Kalman filter (CKF–EKF) with a joint state–parameter covariance and five damped voltage relinearizations. On one 25,251-sample Dynamic Stress Test (DST) of a 27 Ah cell at nominal 25 °C, its calibrated full-record mean absolute error/root mean square error (MAE/RMSE) is 0.8340/0.8514 percentage points (pp); the score includes the supervised development prefix. The earlier-protocol experiment in which a fixed-RC adaptive EKF reached 0.1260 pp is restored beside that comparison, together with the non-adaptive estimators of the same archived table, which reach 0.1260 and 0.1259 pp without adapting anything; that value is the floor set by the initial 20 pp step under that protocol. To remove the protocol difference, every architecture is also scored over the entire shared 129-member noise-candidate bank: the lowest full-record RMSE attainable by a fixed-RC adaptive EKF is 1.3753 pp, and at the archived noise setting itself, that baseline gives 7.1988 pp against 1.1885 pp for the hybrid. The DST evaluation is one continuous full-history replay; a no-history interior restart is not tested. Two similar-cell, 20-segment stepped discharges at approximately 1C and nominal 25 °C, with long rests and each target cell’s measured usable energy supplied, yield RMSE 0.6868/0.7995 pp and signed mean errors of −0.6851/−0.7975 pp, an offset traced to a 2–3 mV mismatch of the transferred observation curve. These are conditional transfer tests, not additional DST validations. Fixed-settings ablations characterize the parameter block and iteration within the proposed implementation. The evidence is limited to the tested temperature, cell condition, load profiles and known-energy calibration. One additional dynamic profile, temperature variation and aging remain unvalidated.
SN - 2313-0105
ER -