Coordinate Transformation Uncertainty Analysis in Large-Scale Metrology

3-D coordinate transformation, which is based on aligning two sets of common reference points, is frequently applied in large-scale combined measurement to unify coordinate frames and tie individual measurement systems together. However, it introduces uncertainty into the final measurement results. This uncertainty must be quantified to make the results complete. This paper presents a novel approach to the uncertainty analysis of 3-D coordinate transformation based on the weighted total least squares adjustment. This approach takes full account of the uncertainty characteristics of measuring instruments and is simple in calculation. In this approach, the transformation uncertainty of a point in a world frame is analyzed carefully. The simulations show that the transformation uncertainty has a distribution of concentric ellipsoids and is affected by the measurement uncertainties and layout of common points. Besides, strategies for minimizing transformation uncertainty are recommended. The experimental results from a laser tracker prove that this proposed approach is valid under normal instrument operating conditions and that these strategies are feasible and efficient.

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