State-of-Energy Estimation of a Lithium Iron Phosphate Battery Usingan Iterated CKF–EKF Algorithm

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.