This study discusses simultaneous adaptation of the process and measurement noise covariance matrixes for a nontraditional attitude filtering algorithm. The nontraditional attitude filtering algorithm integrates the singular value decomposition (SVD) method with the unscented Kalman filter (UKF) to estimate the attitude of a nanosatellite. The SVD method uses magnetometer and Sun sensor measurements as the first stage of the algorithm and estimates the attitude of the nanosatellite, giving one estimate at a single frame. Then these estimated attitude terms are used as input to an adaptive UKF. The conventional UKF and the proposed adaptive UKF were compared with demonstrations of the attitude and attitude rate estimation of the satellite. Specifically, the Q (process noise covariance)-adaptation method is proposed. In the case of process noise increment, which may be caused by the changes in the environment or satellite dynamics, the performance of the Q-adaptive UKF was investigated.