This paper proposes a new method of deriving 9-parameter affine 3D datum transformations by ordinary least-squares. Unlike previous methods, it covers all versions of the transformation. Initially, an ‘average’ scale factor is computed by distance analysis. Removing the scaling effect, the ‘RIGOPT’ subroutine is applied to optimise the rigid transformation that consists of 3 translations and 3 rotations. Using an equivalent enlargement hypothesis, the number of scale factors is increased to 3 by a short series of single-search-direction optimisations. The minimisation of residuals is verified by enclosing-interval analysis. The case studies cover datasets in Western Australia, Great Britain and Sweden.

本文提出了一种通过普通最小二乘法导出 9 参数仿射 3D 基准变换的新方法。与以前的方法不同，它涵盖了转换的所有版本。最初，通过距离分析计算“平均”比例因子。消除缩放效应，应用“RIGOPT”子程序来优化由 3 次平移和 3 次旋转组成的刚性变换。使用等效放大假设，通过一系列短的单搜索方向优化，比例因子的数量增加到 3。通过封闭区间分析验证了残差的最小化。案例研究涵盖西澳大利亚、英国和瑞典的数据集。