Estimating Relative Angles Using Two Inertial Measurement Units Without
Magnetometers
Abstract
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 inexpensive IMU
system to estimate the relative angle between IMUs, while understanding
the different algorithms for estimating angular kinematics. Thus, there
were three sub-goals: 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 open-source code and working principles of
these methods. The raw gyroscopic and accelerometer data were
pre-processed. The seven methods included gyroscopic integration (GI),
accelerometer inclination (AC), Basic Complementary filter (BCF), Kalman
filter (KF), Digital Motion Processor (DMPTM, 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 minutes. 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 method 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.