Inertial Sensor-Based Motion Calibration for 1-DoF Joint Angle Estimation

This study presents a simple and accurate method for estimating joint angles with one degree of freedom using two inertial measurement units. The approach leverages quaternion-based computations and eigenvalue decomposition to determine the rotation axes, requiring only a single calibration movement, and was validated through simulation and real-case experiments. In simulations, the proposed approach achieved a mean squared error of 1.1838 degrees, demonstrating robustness to sensor misalignment and varying noise levels. A real-world validation was conducted on a healthy subject performing elbow flexion-extension, using Xsens DOT units at 60 Hz and an OptiTrack motion capture system at 100 Hz, with sensor signals interpolated for direct comparison. The results showed strong agreement between both methods, with a root mean squared error of 4.8922 degrees, ranging from 2.6995 to 5.9759 degrees during resting phases. The method's efficiency and minimal calibration requirements make it ideal for biomechanics, rehabilitation, and robotics. Its calibration-by-motion approach is particularly useful for applications such as cycling-based knee analysis, where the motion of interest inherently serves as calibration, although elbow joint studies may require a separate calibration step to avoid interference from shoulder movement.