To improve the state-of-charge (SOC) estimation accuracy of sodium-ion batteries under complex operating conditions, this paper proposes a particle swarm optimization-based heterogeneous adaptive extended Kalman filter. A hardware-in-the-loop (HIL) validation platform is also established to reproduce the sampling-chain constraints of a practical battery management system. In addition, a second-order equivalent circuit model (ECM) serves to characterize battery dynamics and generate validation data. Within this framework, the degradation in estimation performance from the theoretical environment to practical hardware execution is quantitatively analyzed. The feasibility of using ECM-generated data for SOC estimation algorithm validation is also evaluated. Using measured Federal Urban Driving Schedule data at 25 °C, the proposed method achieves high estimation accuracy and stable convergence in both environments. Specifically, the mean absolute error and root-mean-square error in the theoretical environment are 0.11% and 0.25%, respectively. Under HIL conditions, the corresponding values are 0.60% and 0.63%. Additional tests under different temperatures and composite disturbance conditions further verify the adaptability and robustness of the proposed algorithm. The results also show that practical hardware constraints introduce non-negligible performance degradation. In addition, ECM-generated data remain highly consistent with measured data in terms of error-evolution trends. Therefore, ECM-generated data can serve as a feasible validation data source for SOC estimation algorithm performance evaluation and rapid validation.
Li et al. (Tue,) studied this question.