Partially-conformal variations of the Standard Molodensky datum transformation

Abstract: Standard Molodensky is a recognised method of transforming coordinates between geodetic datums. Although less accurate than some other methods, it has the merit of being direct. That is to say it can be applied to geodetic coordinates, without involving Cartesian coordinates that give rise to difficulties in computing latitude. This paper considers the use of Standard Molodensky when at least one of the datums is 2D+1D in nature, meaning that that horizontal and vertical positions are obtained by different methods. This was generally the case before 3D positioning by satellites and is a widespread characteristic of local datums that are still used. The 2D+1D property weakens the argument for 3D conformality, and invites the possibility that different translation parameters might be used for horizontal and vertical shifts. The possibility of including a Z-rotation as a 7th parameter is also considered. Besides being ideal for those who favour the simplicity of Standard Molodensky, the variations introduced in this paper offer significant improvements in accuracy such as error reductions of 75%, 69% and 99% in the three selected case studies.摘要：标准莫洛坚斯基（Standard Molodensky）是目前公认的大地基准面（geodetic datums）间坐标转换方法。尽管其精度不及部分其他同类方法，但优势在于计算过程直接——可直接应用于大地坐标（geodetic coordinates），无需引入会给纬度计算带来困难的笛卡尔坐标系（Cartesian coordinates）。本文针对至少一个基准面为二维加一维（2D+1D）结构的场景展开研究，探讨了标准莫洛坚斯基方法的适配应用。此类场景在卫星三维定位普及前普遍存在，也是当前仍在使用的局部基准面（local datums）的典型特征，即水平位置与垂直位置通过不同手段获取。二维加一维的特性削弱了三维保形性（3D conformality）的论证基础，同时为水平、垂直偏移采用差异化平移参数提供了可行性。此外，本文还探讨了将Z轴旋转（Z-rotation）作为第七参数（7th parameter）纳入转换模型的可能性。本文提出的改进变体，既契合了偏好标准莫洛坚斯基方法简洁性的用户需求，又在精度上实现了显著提升：在三个选定的案例研究中，误差分别降低了75%、69%与99%。