Multi-Timescale Estimation of SOE and SOH for Lithium-Ion Batteries with a Fractional-Order Model and Multi-Innovation Filter Framework

Based on a fractional-order equivalent circuit model, this paper proposes a multi-timescale collaborative State of Energy (SOE) and State of Health (SOH) estimation method (FOASTFREKF-EKF) for lithium batteries to mitigate the influence of model inaccuracies and battery aging on SOE estimation. Initially, a fractional-order equivalent circuit model is built, and its parameters are identified offline using the Starfish Optimization Algorithm (SFOA) to establish a high-fidelity battery model. An H∞ filter is then integrated to improve the algorithm’s resilience to external disturbances. Furthermore, an adaptive noise covariance adjustment mechanism is employed to reduce the effect of operational noise, and a time-varying attenuation factor is introduced to improve the algorithm’s tracking and convergence capabilities during abrupt system-state changes. A joint estimator is subsequently constructed, which uses an Extended Kalman Filter (EKF) for the online determination of battery parameters and SOH assessment. This approach minimizes the effect of varying model parameters on SOE accuracy while reducing computational load through multi-timescale methods. Experimental validation under diverse operating conditions shows that the proposed algorithm achieves root mean square errors (RMSE) of less than 0.21% for SOE and 0.31% for SOH. These findings demonstrate that the method provides high accuracy and reliability under complex operating conditions.