Physics‑Informed LSTM and EKF Fusion for Robust Battery SoC Estimation

Reliable state‑of‑charge estimation remains difficult in the presence of long‑term ageing, open‑circuit‑voltage hysteresis, and variable operating profiles. We investigate a hybrid estimator that marries a first‑principles equivalent‑circuit model with sequence learners, coupled through a residual‑aware fusion rule. Using a minute‑resolution ageing dataset from a lithium‑titanate (LTO) cell (236,282 samples across 2500 cycles), we identify phase‑aware OCV‑to‑SoC lookup tables for charge and discharge, deploy an extended Kalman filter with soft half‑cycle anchoring, and train LSTM, 1D‑CNN, and Transformer baselines with physics‑informed regularization promoting Coulomb consistency and concordance between OCV and terminal voltage. The phase‑aware EKF attains MAE 0.04535 and RMSE 0.05057 on cycle‑wise averages. A stitched LSTM yields MAE 0.03023 and RMSE 0.05192. Residual‑weighted fusion of EKF and LSTM produces MAE 0.03049 and RMSE 0.03991, which represents a 21% reduction relative to EKF while preserving the LSTM’s low bias. A coarse parameter sweep over the circuit model confirms expected early‑life behavior, namely lower resistance and a longer polarization time constant. At the window level, a physics‑informed LSTM achieves MAE 0.0184. The fusion is model‑agnostic, requires no retraining of the base estimators, and adds negligible computational overhead. We release phase‑aware OCV tables, a trained LSTM, and configuration files for seamless one‑command reproduction.