Joint Battery State of Charge Estimation Method Based on a Fractional-Order Model with an Improved Unscented Kalman Filter and Extended Kalman Filter for Full Parameter Updating

State estimation of batteries is crucial in battery management systems (BMSs), particularly for accurately predicting the state of charge (SOC), which ensures safe and efficient battery operation. This paper proposes a joint SOC estimation method based on a fractional-order model, utilizing a multi-innovation full-tracking adaptive unscented Kalman filter (FOMIST-AUKF-EKF) combined with an extended Kalman filter (EKF) for online parameter updates. The fractional-order model more effectively represents the battery's dynamic characteristics compared to traditional integer-order models, providing a more precise depiction of electrochemical processes and nonlinear behaviors. It offers superior modeling for long-memory effects, complex dynamics, and aging processes, enhancing adaptability to aging and nonlinear characteristics. Comparative results indicate a maximum end-voltage error reduction of 0.002 V with the fractional-order model compared to the integer-order model. The multi-innovation technology increases filter robustness against noise by incorporating multiple historical observations, while the full-tracking adaptive strategy dynamically adjusts the noise covariance matrix based on real-time data, thus enhancing estimation accuracy. Furthermore, EKF updates battery parameters (e.g., resistance and capacitance) in real time, correcting model errors and improving SOC prediction accuracy. Simulation and experimental validation show that the proposed method significantly outperforms traditional UKF-based SOC estimation techniques in accuracy, stability, and adaptability. Specifically, under varying conditions such as NEDC and DST, the method demonstrates excellent robustness and practicality, with maximum SOC estimation errors of 0.27% and 0.67%, respectively.