An interpretable assessment of sensor’s orientation in the Quaternion domain

Magnetic and inertial measurement unit (MIMU) systems have been universally adopted in numerous navigation applications. These include domains such as aircraft, pedestrians, home automation, robots, etc. due to their advantages referring to price, size and accuracy. The fusion of the values recorded from magnetic and inertial sensors (magnetometer, accelerometer, gyroscope) can provide orientation with respect to the navigation path. Orientation can be given as either Euler angles or quaternions representing the rotation matrix associated with the orientation. The first is the commonest way since Euler angles can be easily interpreted in terms of yaw, pitch, and roll. However, their computation is ill-conditioned for some angulations due to a bad propagation of errors. Such intrinsic computational errors limit their use for free indoor, but equally affect the comparison and assessment of sensor fusion algorithms. In this paper, we present an assessment of orientation based on quaternion distances easy to interpret in terms of rotation axis and angle. We compare our approach to the standard assessment of orientation based on Euler angles in rotational trajectories around the three axes made using a Stäubli robotic arm. Results show the more superior reliability of the quaternion distance and the intrinsic artifacts of Euler angles for representing the whole space of rotations.