The state of charge estimation is an important part of the battery management system, the estimation accuracy of which seriously affects the working performance of the lithium ion battery pack. The unscented Kalman filter algorithm has been developed and applied to the iterative calculation process. When it is used to estimate the SOC value, there is a rounding error in the numerical calculation. When the sigma point is sampled in the next round, an imaginary number appears, resulting in the estimation failure. In order to improve the estimation accuracy, an improved adaptive square root - unscented Kalman filter method is introduced which combines the QR decomposition in the calculation process. Meanwhile, an adaptive noise covariance matching method is implied. Experiments show that the proposed method can guarantee the semi-positive and numerical stability of the state covariance, and the estimation accuracy can reach the third-order precision. The error remains about 1.60% under the condition of drastic voltage and current changes. The conclusion of this experiment can provide a theoretical basis of the state of charge estimation in the battery management of the lithium ion battery pack.