Simultaneous estimation of state-of-charge and state-of-temperature in lithium-ion batteries using a coupled electro-thermal model

In this paper, we propose a coupled electro-thermal model for simultaneous estimation of state-of-charge (SoC) and internal state-of-temperature (SoT) in lithium-ion battery cell. The electrical sub-model employs a temperature-aware first-order equivalent circuit model (ECM) whose parameters and the V OC ( SoC , T ) map are identified across eight temperatures from −25°C to 45°C, capturing strong thermo-electrochemical nonlinearities. For accuracy at low SoC, V OC ( SoC , T ) is modeled by two 10th-order polynomials split at 7% SoC. SoC is inferred with a Kalman filter, then used to compute the cell heat input d q cell / dt , which includes Joule heating and an entropic term ∂ V OC / ∂ T ; d q cell / dt drives a compact autoregressive with extra input (ARX) thermal model whose coefficients depend on ambient temperature to yield SoT. In experiments on a Samsung 18650-35E cell, the method achieves RMSE of 0.0079°C between the ARX thermal model’s SoT estimate and an independently measured temperature reference obtained using a micro T-type thermocouple (~80 µm in diameter) embedded inside the cell, substantially lower than a recent Pearson-correlation deep model (0.097°C), while achieving SoC RMSE = 1.96% with markedly lower computational burden than UKF variants, making it suitable for low-cost battery management system (BMS). The ECM terminal-voltage RMSE remains small (lowest at −5°C: 0.074; highest at 45°C: 0.363), reflecting temperature-dependent dynamics captured by the model. Overall, the novelty lies in: (i) full temperature-dependence of ECM parameters and V OC ( SoC , T ) over a wide thermal range, (ii) an ARX-based SoT estimator explicitly fed by physics-informed d q cell / dt , and (iii) a single-Kalman Filter–ARX pipeline that balances accuracy and real-time applicability on resource-constrained hardware.