The 3D similarity coordinate transformation is fundamental and frequently encountered in many areas of work such as geodesy, engineering surveying, LIDAR, terrestrial laser scanning, photogrammetry, machine vision, etc. The algorithms of 3D similarity transformation are divided into two categories. One is a closed-form algorithm that is straightforward and fast. However, it cannot provide the accuracy information for the transformation parameters. The other category of algorithm is iterative, and this can offer the accuracy information for the transformation parameters. However, the latter usually needs a good initial value of the unknown. Considering the accuracy information for transformation parameters is essential or indispensable from the viewpoint of uncertainty, this contribution proposes a weighted total least squares (WTLS) iterative algorithm of the 3D similarity coordinate transformation based on Gibbs vectors. It is fast in terms of fewer iterations, reliable and does not need good initial values of transformation parameters. Two cases including the registration of LIDAR points with big rotation angles and a geodetic datum transformation with small rotation angles are demonstrated to validate the new algorithm.

中文翻译：

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基于Gibbs向量的3D相似坐标变换的WTLS迭代算法

3D 相似坐标变换是大地测量、工程测量、激光雷达、地面激光扫描、摄影测量、机器视觉等许多工作领域中的基础和经常遇到的。3D 相似变换的算法分为两类。一种是简单且快速的封闭形式算法。但是，它无法提供转换参数的准确度信息。另一类算法是迭代的，它可以为转换参数提供准确度信息。然而，后者通常需要一个良好的未知初始值。从不确定性的角度考虑变换参数的精度信息是必不可少的或不可缺少的，该贡献提出了一种基于 Gibbs 向量的 3D 相似坐标变换的加权总最小二乘 (WTLS) 迭代算法。它在迭代次数少、可靠且不需要良好的转换参数初始值方面很快。演示了两种情况，包括大旋转角度的激光雷达点的配准和小旋转角度的大地基准变换，以验证新算法。