In this paper, a satellite attitude estimation algorithm based on Strong Tracking Robust Adaptive Cubature Kalman Filter (STRACKF) is proposed for the problem of satellite attitude estimation in the process of fast swing sweep. Several fading factors were introduced into the traditional Cubature Kalman filter algorithm and their positions were determined. Huber function was used to correct the measurement model with errors, so as to improve the tracking performance and adaptability of the filter algorithm for attitude mutation. The algorithm combines quaternion and modified Rodriguez parameters to facilitate attitude updating and avoid singularity. The proposed STRACKF algorithm is simulated, and compared with traditional UKF and CKF algorithms, the simulation shows that STRACKF algorithm has higher attitude estimation accuracy and the ability to deal with attitude mutation.