For the measurement of large-scale components in aircraft assembly, the evaluation of coordinate transformation parameters between the coordinate frames of individual measurement systems to the assembly frame is an essential task, which is usually completed by registration of the enhanced reference system (ERS) points. This paper aims to propose an analytical method to evaluate the uncertainties of transformation parameters considering both the measurement error and the deployment error of ERS points.
For each measuring station, the measured coordinates of ERS points are first roughly registered to the assembly coordinate system using the singular value decomposition method. Then, a linear transformation model considering the measurement error and deployment error of ERS points is developed, and the analytical solution of transformation parameters’ uncertainties is derived. Moreover, the covariance matrix of each ERS points in the transformation evaluation is calculated based on a new uncertainty ellipsoid model and variance-covariance propagation law.
For the transformation of both single and multiple measuring stations, the derived uncertainties of transformation parameters by the proposed analytical method are identical to that obtained by the state-of-the-art iterative method, but the solution process is simpler, and the computation expenses are much less.
The proposed uncertainty evaluation method would be useful for in-site measurement and optimization of the configuration of ERS points in the design of fixture and large assembly field. It could also be applied to other registration applications with errors on both sides of registration points.
