A representative method involves: generating measured angular velocities and measured axial accelerations; calculating a resulting deviation associated with movements and rotations in a spatial reference frame by: providing a previous quaternion corresponding to time T−1 based on the measured axial accelerations corresponding to time T−1 and the measured angular velocities corresponding to time T−1; converting the measured angular velocities corresponding to time T based on the previous quaternion into a current quaternion and predicted axial accelerations; comparing the predicted axial accelerations with the measured axial accelerations corresponding to time T to obtain a first comparison result; obtaining an updated quaternion associated with time T based on the current quaternion and the first comparison result, and using the updated quaternion as a next occurrence of the previous quaternion; and providing the resulting deviation based on the updated quaternion; and, providing content based on the resulting deviation in the spatial reference frame.