Cubature Kalman filter (CKF) has recently drawn much attention due to its more stable performance than the unscented Kalman filter (UKF). This third-degree cubabure rule based nonlinear filter may not be accurate enough in many estimation problems. In this paper, a more general class of CKFs with arbitrary high-degree estimation accuracy is proposed. It can be shown that the conventional CKF is a special case of the proposed method. A target tracking problem is used to test the performance of the proposed filters. It will be shown that the high-degree CKFs can achieve better performance than the extended Kalman filter, the unscented Kalman filter, and the conventional third-degree CKF. In addition, it can maintain a close performance to the Gauss-Hermite quadrature filter with less computation load.