The IMU IK tool (available as of OpenSim 4.2) goes through each time step (frame) of motion and computes generalized coordinate values which positions the model in a pose that "best matches" experimental IMU orientations. Mathematically, the "best match" is expressed as a weighted least squares problem, whose solution aims to minimize orientation errors. The topics covered in this section include:
An orientation error is the orientation difference between the experimental IMU and the corresponding model's IMU, quantified by the the angle when representing the orientation difference by an axis-angle representation.
Weighted Least Squares Equation
The weighted least squared problem solved by IMU IK is
where q is the vector of generalized coordinates, wi's are the weights corresponding to each IMU orientation, and θi's are the angle component of the orientation errors expressed by an axis-angle representation.