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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:

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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.

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