Three-dimensional (3D) similarity transformation is popularly applied for measurement datum transformation. In this study, a seamless partial errors-in-variables (EIV) model with equality constraints is established to describe the universal 3D similarity transformation problem (with arbitrary rotation angles and scale factor). Unlike the traditional transformation model, all of the random errors in the measured coordinates for common and non-common points, and their variance–covariance information can be considered. To obtain the least squares solution of this model, the constrained total least squares prediction (CTLSP) algorithm is derived using Gauss–Newton iteration and the Euler–Lagrange approach. Unnecessary matrix calculations in the application of the CTLSP algorithm for 3D datum transformation are avoided and the efficient iterative formulae are derived. Compared with the existing generalized total least squares prediction (GTLSP) algorithm, in which the transformation ...

中文翻译：

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无缝3D相似度转换的通用高效算法和精度评估

三维（3D）相似度转换广泛用于测量基准转换。在这项研究中，建立了具有相等约束的无缝局部变量误差（EIV）模型来描述通用3D相似度转换问题（具有任意旋转角度和比例因子）。与传统的转换模型不同，可以考虑对公共点和非公共点测量的坐标中的所有随机误差，以及它们的方差-协方差信息。为了获得该模型的最小二乘解，使用高斯-牛顿迭代法和欧拉-拉格朗日方法推导了约束总最小二乘预测（CTLSP）算法。避免了将CTLSP算法用于3D基准面转换时不必要的矩阵计算，并得出了有效的迭代公式。与现有的广义总最小二乘预测（GTLSP）算法相比，其中变换...