A complete solution of an improved universal 3D coordinate similarity transformation model

• 作者: Leyang Wang Jianqiang Sun Qiwen Wu
• 来源期刊: 大地测量与地球动力学（英文版）
• 年，卷（期）: 2021,（2）
• 页码范围: 125-132
• 页数: 8页
• 语种: 英文

摘要

When linearizing three-dimensional(3D)coordinate similarity transformation model with large rota-tions,we usually encounter the ill-posed normal matrix which may aggravate the instability of solutions.To alleviate the problem,a series of conversions are contributed to the 3D coordinate similarity trans-formation model in this paper.We deduced a complete solution for the 3D coordinate similarity transformation at any rotation with the nonlinear adjustment methodology,which involves the errors of the common and the non-common points.Furthermore,as the large condition number of the normal matrix resulted in an intractable form,we introduced the bary-centralization technique and a surrogate process for deterministic element of the normal matrix,and proved its benefit for alleviating the con-dition number.The experimental results show that our approach can obtain the smaller condition number to stabilize the convergence of the interested parameters.Especially,our approach can be implemented for considering the errors of the common and the non-common points,thus the accuracy of the transformed coordinates improves.