Estimating Relative Angles Using Two Inertial Measurement Units Without Magnetometers

Inertial measurement units (IMUs) are used in biomechanical and clinical applications for quantifying joint kinematics. This study aimed to assist researchers new to IMUs and wanting to develop an inexpensive IMU system to estimate the relative angle between IMUs, while understanding the different algorithms for estimating angular kinematics. Thus, there were three subgoals: 1) to present a low-cost and convenient IMU system utilizing two 6-axis IMUs for computing the relative angle between the IMUs; 2) to examine seven methods for estimating the angular kinematics of an IMU; and 3) to provide an open-source code and working principles of these methods. The raw gyroscopic and accelerometer data were preprocessed. The seven methods included gyroscopic integration (GI), accelerometer inclination (AC), basic complementary filter (BCF), Kalman filter (KF), digital motion processor (DMP, a proprietary algorithm), Madgwick filter (MW), and Mahony filter (MH). An apparatus was designed to test nine conditions that computed angles for rotation about three axes (roll, pitch, yaw) and three movement speeds (50°/s, 150°/s, 300°/s). Each trial lasted 25 min. The root-mean-squared error (RMSE) between the gold-standard value measured from the apparatus’ encoder and the value calculated from each of the seven methods was determined. For roll and pitch, all methods accurately quantified angles (RMSE < 6°) at all speeds. For yaw, all methods except AC and DMP displayed RMSE < 6° at all speeds. AC could not be used for yaw angle computation, and DMP displayed RMSE >6°. Researchers can utilize appropriate methods based on their study’s application.