This paper proposes a new method of deriving rigorously-conformal 7-parameter 3D coordinate transformations between geodetic datums. The problem of linearisation is reduced by distance analysis which provides an estimate of scale-change. The resulting 6-parameter transformation is linearised to enable an initial least-squares estimate of the rotation parameters. The 6-parameter transformation is then re-linearised to obtain a least-squares estimate of the corrections to the rotations. The validity of the scale-change estimate can be tested and is verified in almost all cases. The exception is transformations covering very small areas where short distances maximise the impact of measurement errors in the control data. Even there, the method can be adapted to optimise the transformation. The method can also be used to obtain pseudo-optimal conformal transformations that provide a closest fit to published Bursa-Wolf transformations.

本文提出了一种导出大地基准之间严格共形的7参数3D坐标变换的新方法。通过距离分析减少了线性化的问题，距离分析提供了标度变化的估计。对所得的6参数变换进行线性化，以实现旋转参数的初始最小二乘估计。然后将6参数变换重新线性化，以获得对旋转的校正的最小二乘估计。几乎在所有情况下，都可以测试并验证比例尺变化估计的有效性。唯一的例外是覆盖范围很小的区域中的转换，在这些区域中，短距离使控制数据中测量误差的影响最大化。即使在此，该方法也可以适用于优化转换。