Uncertainty of spatial straightness in 3D measurement

The least-square method is commonly employed to verify the spatial straightness in actual three-dimensional measurement process, but the uncertainty of the verification result is usually not given by the coordinate measuring machines. According to the basic principle of spatial straightness least-square verification and the uncertainty propagation formula given by ISO/TS 14253-2, a calculation method for the uncertainty of spatial straightness least-square verification is proposed in this paper. By this method, the coefficients of the line equation are regarded as a statistical vector, so that the line equation, the result of the spatial straightness verification and the uncertainty of the result can be obtained after the expected value and covariance matrix of the vector are determined. The method not only assures the integrity of the verification result, but also accords with the requirement of the new generation of GPS standards, which can improve the veracity of verification