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.
