Hybrid modeling for state of charge estimation in battery electric vehicles: balancing accuracy, efficiency, and interpretability

The transition to electrified transportation increases demands on battery management systems, making accurate state of charge (SOC) estimation essential for fuel-gauge functionality, safety supervision, and energy management. Existing SOC estimation methods span conventional, model-based, data-driven, and hybrid approaches; however, practical deployment requires accuracy, causal operation, low computational burden, and embedded real-time compatibility. For lithium iron phosphate (LFP) batteries, SOC estimation is complicated by a flat open-circuit voltage characteristic, path-dependent voltage response, and hysteresis, which limit voltage-to-SOC observability. Although LFP SOC estimation has advanced through extended Kalman filter (EKF) algorithms and correction schemes, compact embedded-oriented frameworks retaining a low-order physics-based observer while using machine learning to model structured residual errors remain underexplored. This study introduces a lightweight hybrid framework that integrates a 2-RC Thevenin model into the EKF algorithm, with sparse Gaussian process regression for sample-level residual correction. It preserves observer interpretability and low computational burden while adding a causal learned correction term. A reliability-aware Bayesian fusion stage moderates the correction by component reliability. On unseen cells drawn close to the training distribution, the proposed framework reduced mean SOC RMSE from 1.12% for the EKF to 0.39%, whereas a weaker, less uniform response under stronger secondary-domain shift highlighted the importance of training-domain coverage. The main contribution is demonstrating lightweight EKF residual error as a structured, learnable, and computationally feasible correction term within online SOC-estimation constraints, improving accuracy while preserving a physics-based backbone. The open-source implementation provides a reusable baseline for retraining, recalibration, and domain-adaptation studies.