局部区域三维坐标变换的两步解法

Two Step Method for 3D Coordinate Transformation in Local Area

摘要:

在局部区域三维坐标变换中，布尔萨模型的旋转参数和平移参数存在相关性，容易出现解算模型病态问题.为此提出将旋转参数和平移参数分开解算的两步解法，在去掉平移参数后采用最小二乘法估计旋转参数，再用加权整体最小二乘法估计尺度参数和平移参数.该方法既可避免解算复杂的病态整体最小二乘问题，也顾及了原系统坐标误差影响.模拟实验表明：与最小二乘法和整体最小二乘法比较，两步法提高了尺度参数和平移参数的估计精度，特别是尺度参数，外围坐标变换精度明显提高.

Abstract:

Because the rotation parameters and the translation parameters are related, the ill posed problem will easily occur in the solution model in 3D coordinate transformation in the data of local area based on the Bursa Wolf model. The errors of the original system were not taken into account by the common regularization solution. In this paper, a two step approach was proposed for solving this problem, which first computed the rotation parameters with the least square adjustment after the translation parameters were centered by an idempotent matrix. Then, the weighted total least squares adjustment was employed to estimate the scale and the translation parameters with a new four parameter model. The suggested method not only considers the error of the original system but also avoids solving the complex ill posed total least squares problem. A simulation experiment was conducted to test the new method. The result shows that the proposed method can improve the relative accuracy of the scale and the translation parameters, particularly of the scale parameter, and significantly improve the transformation accuracy of external points.