Robust Joint Estimation of State of Charge and State of Health in Lithium-Ion Batteries Using a Fractional-Order Model and Observer-Assisted, History-Enhanced Kalman Filtering

Accurate and reliable joint estimation of state of charge (SOC) and state of health (SOH) is a core requirement for next-generation battery management systems (BMSs). In this context, this study develops an innovative joint estimation algorithm that combines a fractional-order sliding-mode adaptive multi-innovation unscented Kalman filter with an extended Kalman filter (FOSMOAMIUKF+EKF). The proposed method is based on a fractional-order model, and the Crested Porcupine Optimizer (CPO) is introduced for the first time to identify the model parameters accurately. On this basis, an adaptive multi-innovation unscented Kalman filtering framework integrated with a fractional-order sliding mode observer is developed. The sliding mode observer effectively suppresses model uncertainties and non-Gaussian disturbances by exploiting its variable structure characteristics. The multi-innovation mechanism enhances convergence speed and mitigates impulsive noise through the accumulation of historical innovations, while the adaptive noise estimation dynamically matches time-varying noise statistics. Consequently, the proposed framework overcomes the limitations of conventional Kalman filtering, which relies on accurate models and Gaussian noise assumptions, thereby significantly improving the robustness and accuracy of SOC estimation. In parallel, an EKF is employed to estimate SOH, thereby updating the actual capacity used in the SOC estimator. Experiments show low SOC/SOH errors under varied conditions, noise.