Overcoming non-Gaussian noise in battery state of charge estimation: A hybrid fractional-order and maximum correntropy Kalman filter approach

Accurate state of charge (SOC) estimation is critical for electric vehicles and grid storage, yet non-Gaussian noise severely degrades traditional algorithms. To overcome limitations of existing Kalman filters, including susceptibility to interference, low accuracy, and poor robustness under non-Gaussian noise, this paper proposes a fractional-order model based maximum correntropy criterion extended Kalman filter (FOM-MCCEKF). This study first develops a second-order circuit model by employing constant phase elements (CPE) instead of ideal capacitors, allowing for more precise modeling of battery. Then, an adaptive genetic algorithm (AGA) is utilized to determine parameters, reducing terminal voltage root mean squared error (RMSE) by 19 %–30 % compared to traditional models and minimizing modeling errors at the source. Finally, we propose a novel SOC estimation algorithm that combines fractional-order modeling with the maximum correntropy criterion (MCC). The algorithm demonstrates strong robustness under complex non-Gaussian noise environments, such as a mixture of Gaussian and uniform noise. Even under severe disturbances, the RMSE of the SOC estimation remains stably controlled below 0.05. Experimental results demonstrate that the proposed FOM-MCCEKF establishes new benchmarks for SOC estimation: Reduces SOC RMSE by 30 %–50 % vs. Fractional-Order EKF (FOEKF) and 50 %–70 % vs. standard MCCEKF in harsh conditions, achieves rapid convergence within 30 s despite large initial errors, and maintains high accuracy (<3 % error) across dynamic operating conditions. This work addresses critical challenges in battery diagnostics, providing a high-precision, robust, and fast-converging SOC estimation framework for next-generation energy storage systems.