On the Interpretation of 3D Gyroscope Measurements

We demonstrate that the common interpretation of angular velocities measured by a 3D gyroscope as being sequential Euler rotations introduces a systematic error in the sensor orientation calculated during motion tracking. For small rotation angles, this systematic error is relatively small and can be mistakenly attributed to different sources of sensor inaccuracies, including output bias drift, inaccurate sensitivities, and alignments of the sensor sensitivity axes as well as measurement noise. However, even for such small angles, due to accumulation over time, the erroneous rotation interpretation can have a significant negative impact on the accuracy of the computed angular orientation. We confirm our findings using real-case measurements in which the described systematic error just worsens the deleterious effects typically attributed to an inaccurate sensor and random measurement noise. We demonstrate that, in general, significant improvement in the angular orientation accuracy can be achieved if the measured angular velocities are correctly interpreted as simultaneous and not as sequential rotations