Constraint-augmented Kalman Filter for Magnetometer-free 3D Joint Angle Determination

Accurate three-dimensional (3D) intersegment joint angle measurement is an important biomechanical measure for a variety of applications. Although inertial and magnetic measurement units (IMMUs) are mobile alternatives to optical motion capture systems, the joint angle determination accuracy based on the IMMU is highly vulnerable to the magnetic distortion problem associated with magnetometer signals. This paper proposes a constraint-augmented Kalman filter (KF) for magnetometer-free 3D joint angle determination using inertial measurement unit (IMU) signals. The proposed KF uses two linear KFs consisting of a previously developed roll/pitch KF followed by a newly formulated yaw KF. In the yaw KF, the ball joint constraint provides a measurement equation for the yaw correction procedure, whereas magnetometers accomplish this procedure in most standalone algorithms. In the yaw KF, the yaw angle itself is not designated as a state because it is difficult to develop the equation in conjunction with the trigonometric functions. Instead, the sine and cosine of the yaw angle are designated as states in the form of algebraic variables. As the proposed approach does not rely on the magnetometer signals even for the 3D joint angle, it is completely free from the magnetic distortion problem. Experimental results utilizing a two-link mechanism connected by a ball joint verified that augmentation of the constraint successfully performed the role of correction. Accordingly, in magnetically undesirable conditions, the proposed IMU-based approach produced higher accuracy than the IMMU-based approaches. Furthermore, this paper investigated the residual of the constraint to provide an insight into how well each approach satisfies the kinematic constraint.