*Article* **Research on a High-Precision State-of-Charge Estimation Method Based on Forgetting Factor Recursive Least Squares and Adaptive Extended Kalman Filter Applied to LiFePO4 Battery**

**Yihui Xia, Zhihao Ye \*, Liming Huang, Lucheng Sun and Yunxiang Jiang**

School of Electrical Engineering, Naval University of Engineering, Wuhan 430033, China; xiayihui2005@163.com (Y.X.); huangliming1998@163.com (L.H.); d23380807@nue.edu.cn (L.S.); jiangyunxaing@163.com (Y.J.) **\*** Correspondence: yxyx928@126.com

**Abstract:** The state-of-charge (SOC) estimation accuracy is closely associated with the estimation method and the battery parameter identification performance. The battery parameter identification method based on forgetting factor recursive least squares (FFRLS) has the advantages of high parameter identification accuracy and fast dynamic response speed. On this basis, the performance of two SOC estimation methods, the extended Kalman filter (EKF) and adaptive extended Kalman filter (AEKF) are compared and studied. The results show that AEKF has better steady-state and dynamic SOC estimation performance, but the estimation accuracy and dynamic response performance are still not objective. To further improve the performance of SOC estimation, a joint SOC estimation method based on FFRLS-AEKF is proposed, and the SOC estimation experimental results with FFRLS-AEKF and AEKF are conducted. The experimental results show that the proposed joint SOC estimation method based on FFRLS-AEKF has a better steady-state and dynamic performance of SOC estimation. The maximum absolute error of the proposed algorithm is 4.97%. As the battery working time increases, the SOC estimation accuracy continues to converge to the true value, and the average absolute error is reduced to 2.5%. The proposed method and theoretical analysis are proven to be correct and feasible.

**Keywords:** LiFePO4 battery; high precision; FFRLS; AEKF; SOC estimation
