Total leastsquares determination of body segment attitude
To examine segment and joint attitudes when using imagebased motion capture, it is necessary to determine the rigid body transformation parameters from an inertial reference frame to a reference frame fixed in a body segment. Determine the rigid body transformation parameters must account for errors in the coordinates measured in both reference frames, a total leastsquares problem. This study presents a new derivation that shows that a singular value decompositionbased method provides a total leastsquares estimate of rigid body transformation parameters. The total leastsquares method was compared with an algebraic method for determining rigid body attitude (TRIAD method). Two cases were examined: case 1 where the positions of a marker cluster contained noise after the transformation, and case 2 where the positions of a marker cluster contained noise both before and after the transformation. The white noise added to position data had a standard deviation from zero to 0.002 m, with 101 noise levels examined. For each noise level, 10000 criterion attitude matrices were generated. Errors in estimating rigid body attitude were quantified by computing the angle, error angle, required to align the estimated rigid body attitude with the actual rigid body attitude. For both methods and cases, as the noise level increased the error angle increased, with errors larger for case 2 compared with case 1. The singular value decomposition (SVD)based method was superior to the TRIAD algorithm for all noise levels and both cases, and provided a total leastsquares estimate of body attitude.
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Work Title  Total leastsquares determination of body segment attitude 

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Publication Date  March 4, 2021 
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Deposited  July 24, 2022 
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