A dual Kalman filtering algorithm for estimating the state of charge and health of sodium-ion batteries based on adaptive strong tracking algorithm and schmidt orthogonal transformation

Sodium-ion batteries (SIBs) have emerged as a promising energy storage technology due to their simple structure, scalability, and cost-effectiveness, garnering significant attention in recent years. Accurate estimation of the state of charge (SOC) and state of health (SOH) is critical for optimizing battery management and ensuring operational reliability. This study proposes a new joint estimation framework for SOC and SOH in SIB, based on the adaptive strong tracking algorithm of the fractional-order model and the double Kalman filtering algorithm of schmidt orthogonal transformation (ASTSOUKF-EKF). By obtaining the initial values of each parameter through the whale optimization algorithm and conducting modeling, it is proved that the fractional-order model effectively captures the complex ion dynamics of SIBs, and the maximum modeling error is less than 0.0707 V. To address the challenges of voltage sensitivity limitations and real-time state tracking, we integrate the improved adaptive strong Tracking Filter (ASTF) with the Unscented Kalman Filter (UKF), and utilize an adaptive algorithm to re-determine the value of the fading factor by using the relationship between prior residuals and posterior residuals, thereby enhancing the SOC estimation accuracy and dynamic response. Schmidt orthogonal transformation (SOT) is further incorporated to streamline computational processes during sampling point selection, while the extended Kalman filter (EKF) enables robust online parameter identification for accurate SOH monitoring. Experimental validation under diverse health states demonstrates the algorithm's superior performance, achieving an average SOC error <0.4% and SOH accuracy within 1%, with maximum average errors of 0.58%. This work establishes a methodological foundation for advanced battery management in SIBs, bridging critical gaps between theoretical modeling and practical implementation for next-generation energy storage systems.