Physics-guided residual Kalman learning for state-of-charge estimation of lithium iron phosphate batteries

Abstract: Accurate state of charge (SOC) estimation of lithium iron phosphate (LFP) batteries remains challenging because of their flat open-circuit-voltage (OCV)-SOC characteristics, temperature-dependent dynamics, and sensitivity to initialization errors. Here, we propose a physics-guided residual Kalman learning (PRKL) framework for electrochemical-model-based SOC estimation. PRKL combines a control-oriented single-particle-model-based extended Kalman filter (EKF), which provides recursive physical state propagation, with a gated recurrent unit (GRU) residual learner that compensates structured EKF errors using electrochemical states and measurement features. The framework is evaluated on a public graphite/LFP dataset covering three dynamic drive cycles, eight temperatures from -10 to 50 degrees C, and initialization offsets up to 20 percent. Using dynamic stress test (DST) and federal urban driving schedule (FUDS) cycles for training and the supplemental federal test procedure (US06) cycle for cross-profile testing within the same cell dataset, PRKL achieves a global average root mean square error (RMSE) of 1.19 percent, corresponding to a 77 percent reduction relative to the physics-only EKF. These results show that electrochemical state information can guide residual learning and improve recursive SOC estimation for LFP batteries. The present validation supports cross-profile robustness within the studied dataset and provides a basis for future cross-cell, ageing-aware, and embedded-platform validation.