In satellite mission, attitude control system plays an important role, and precise attitude control presents high attitude determination requirements. The TRIAD (TRIaxial Attitude Determination) method, which is widely used for satellite attitude determination, requires two sensor signals. However, when the reference vector direction to be observed in these sensors is close, the attitude determination error increases. Thus, in this case, attitude estimation is required, and the state estimator of nonlinear objects is widely used for extended Kalman and unscented Kalman filters. In this paper, we propose a method for determining satellite attitude using an unscented Kalman filter with high estimation accuracy compared to an extended Kalman filter. To reduce the amount of computation in the unscented Kalman filter and to ensure the real-time of the estimation, we use the unscented Kalman filtering method with a new sigma point selection. Compared with the traditional unscented Kalman filter, it ensures better real-time and higher accuracy.