State of charge (SOC) is a vital parameter which helps make full use of battery capacity and improve battery safety control. In this paper, an improved adaptive dual unscented Kalman filter (ADUKF) algorithm is adopted to realize co-estimation of the battery model parameters and SOC. Notably, the covariance matching method that can adapt the system noise covariance and the measurement noise covariance is used to improve the estimation accuracy. Besides, singular value decomposition (SVD) is utilized to deal with the non-positive error covariance matrix in both unscented Kalman filters, further enhancing the stability of estimation algorithm. Verification results under Dynamic Stress test and Federal Urban Driving Schedule test indicate that improved ADUKF can achieve more accurate SOC estimates with error band controlled within 2.8%, while that of traditional dual unscented Kalman filter (DUKF) can only be controlled within 5%. Moreover, robustness analysis is also conducted and the validation results present that the proposed algorithm can still provide precise SOC prediction results under some disturbances, such as erroneous initial SOC, inaccurate battery capacity, and various ambient temperatures.