The unscented Kalman filter (UKF) is a filtering algorithm that gives sufficiently good estimation results for estimation problems of nonlinear systems even when high nonlinearity is in question. However, in the case of system uncertainty the UKF becomes inaccurate and diverges in time. In other words, if any change occurs in the process noise covariance, which is known a priori, the filter fails. This study introduces a novel adaptive fading UKF algorithm based on the correction of process noise covariance (Q-adaptation) for the case of mismatches with the model. By the use of a newly proposed adaptation scheme for the conventional UKF algorithm, change in the noise covariance is detected and corrected. Differently from most of the existing adaptive UKF algorithms, covariance is not updated at each step; it has only been corrected when the change in the process noise covariance is detected, and that brings about a noteworthy reduction in the computational burden. The proposed algorithm is tested as a part of the attitude estimation algorithm of a picosatellite, a satellite type for which computational convenience is necessary because of the design limitations. In this sense, different change scenarios for the process noise covariance are taken into consideration.