Abstract: We investigate the computational complexity of tracking 3D orientation (3DO) using gyroscope angular velocity measurements around its three sensitivity axes. These three rotations, obtained at every measurement step, are simultaneous and, due to rotation non-commutativity, interpreting them as sequential, i.e., Euler rotations, yields a systematic error in the estimated 3DO. As this error grows with the angle of rotation, an efficient approach for its reduction is to shorten the measurement interval, demanding a larger number of measurement and hence computational steps. We show that from the computational complexity point of view, for similar levels of result accuracy, the simultaneous interpretation of gyroscope measurements is superior to the sequential. Experimental results obtained using a dedicated microcontroller and relying on a specially developed, computationally optimized implementation, show that for the largest rotation angle considered, i.e., 3.67°, execution time for the simultaneous interpretation is 12 times shorter than for the sequential. Aiming to achieve computational efficiency and relevant comparison of both interpretations, rotation matrices were used when calculating 3DO after each measurement step and the rotation quaternions were used when combining multiple consecutive measurements in a single rotation composite.