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:

Orientation Errors

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

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where q is the vector of generalized coordinates, w_i's are the weights corresponding to each IMU orientation, and θ_i's are the angle component of the orientation errors expressed by an axis-angle representation.