Dual-Timescale Hysteresis Modeling with a Square-Root Central Difference Kalman Filter for Robust State-of-Charge Estimation of Strongly Hysteretic Lithium-Ion Batteries

Abstract Accurate state-of-charge (SOC) estimation is essential to the battery management system but becomes difficult when the open-circuit voltage (OCV) is strongly path dependent, as in lithium-rich and conversion-type chemistries, or almost flat, as in LiFePO4. This study couples a second-order equivalent circuit model with a dual-timescale hysteresis description—a fast, current-weighted direction state plus a slow random-walk magnitude state that absorbs ageing- and temperature-induced drift—and recovers the state by a square-root central difference Kalman filter (SRCDKF) whose deterministic sigma points and QR covariance propagation remain well conditioned where the OCV slope is near zero. Three evidence levels are used. Genuine 0.1C galvanostatic curves of a lithium-rich/MnO@C coin cell give a mean hysteresis width of 0.457 V, and a 0.1C/1C rate gap anchors the ohmic-resistance order (about 18.5 ohm for a 2 mAh cell). A labeled synthetic test shows that under a +30% magnitude mismatch the proposed filter holds 0.58% SOC error whereas fixed-magnitude and extended Kalman (EKF) baselines diverge. On public CALCE data it reaches 1.01% mean error over six unseen NMC profiles and 0.40–2.16% over A123 LiFePO4 profiles at 0, 25 and 50 °C, against 3.70% and 4.85–12.49% (worst case 20.63%) for a same-model EKF. A Monte-Carlo study shows this ranking to be invariant to ±50% errors in the representative RC parameters, while capacity must be measured independently. At 0.3–0.4 ms per step the estimator is real-time feasible.