State of charge (SOC) is one key status to indicate the safety and reliability of lithium-ion batteries in electric vehicles (EVs). Cubature Kalman filter (CKF) is an intensively considered model-based approach for SOC estimation because of its merits in accuracy, convergence rate, and robustness compared with other Kalman filter methods. Nevertheless, CKF suffers from a non-positive definite error covariance matrix because of abnormal perturbations, inaccurate initial values and limited computer word length, causing the divergence of the CKF and the failure of SOC estimation. To address this issue, this paper introduces three typical matrix decomposition strategies, namely, singular value decomposition (SVD), UR decomposition and LU decomposition, to replace the Cholesky decomposition in the traditional CKF. The second-order RC equivalent circuit model is utilized to simulate the dynamics of a lithium-ion battery. The theoretical errors of the methods are formulated by F-norms. The results indicate that three matrix decomposition strategies can overcome the problem of a non-positive definite error covariance matrix and improve the convergence rate of the CKF. In particular, the UR decomposition exhibits the best comprehensive performance because it has a moderate convergence rate and computational cost, and it is robust against the initial error covariance matrix.