Robust Solution for Coordinate Transformation Based on Coordinate Component Weighting

This study proposed classifying and weighting the coordinate components to improve the precision of the coordinate transformation. A coordinate transformation model should avoid the participation of angle parameters to reduce the error caused by the linearization process when describing the rotation matrix. Based on Rodrigues' formula, the coordinate transformation model and the calculation method for the initial values of the parameters were given. It is difficult to reasonably determine the pretest information for robust estimation, so the median function was used to classify and estimate the error in the coordinate components to determine the threshold value of the weight function in each direction. The third scheme of the Institute of Geodesy and Geophysics (IGG3) weight function was used as the equivalent weight function. The parametric adjustment method with additional constraints was adopted to solve the transformation parameters. The simulation test and case analysis were conducted using the tunnel control network of particle accelerator engineering as an example. The results show that the method in this study is not affected by empirical parameters when determining the weight, its robustness is stronger than the traditional robust estimation method, and the coordinate transformation precision is higher.