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First Order Error Propagation of the Procrustes Method for 3D Attitude Estimation
February 2005 (vol. 27 no. 2)
pp. 221-229
The well-known Procrustes method determines the optimal rigid body motion that registers two point clouds by minimizing the square distances of the residuals. In this paper, we perform the first order error analysis of this method for the 3D case, fully specifying how directional noise in the point clouds affects the estimated parameters of the rigid body motion. These results are much more specific than the error bounds which have been established in numerical analysis. We provide an intuitive understanding of the outcome to facilitate direct use in applications.

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Index Terms:
Rigid body motion analysis, pose estimation, attitude estimation, Procrustes method, orthogonal Procrustes problem, perturbation analysis, error propagation, polar decomposition.
Citation:
Leo Dorst, "First Order Error Propagation of the Procrustes Method for 3D Attitude Estimation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 2, pp. 221-229, Feb. 2005, doi:10.1109/TPAMI.2005.29
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