Two innovations are presented for coordinate time-series computation. First, an improved solution is given to a century-old problem, that is the non-iterative computation of conventional geodetic (CG: latitude, longitude, height) coordinates from geocentric Cartesian (GC: x, y, z) coordinates. The accuracy is 1 nm for heights < 500 km and < 10⁻¹⁵ rad for latitude at any point, terrestrial or outer space. This can be 3 orders of magnitude more accurate than published non-iterative methods. Secondly, CG time series are transformed into a practical system of “graticule distance” (GD: easting, northing, height) curvilinear coordinates that, unlike the commonly used system of topocentric Cartesian (TC: east, north, up) coordinates, is global in nature without arbitrary specification of GC reference coordinates for every geodetic station. Since 2011, Nevada Geodetic Laboratory has publicly produced time series for 20,000 GPS stations in GD form that have been cited by hundreds of studies. The GD system facilitates direct comparison of positions for co-located stations. Users of GD time series are able: (1) to resolve different historical station names that have been assigned to the same physical benchmark and (2) to resolve different physical benchmarks that have been assigned the same name. This benefits historical reconstruction of benchmark occupation and local site tie analysis for reference frame integrity. GD coordinates have archival value, in that inversion back to GC coordinates is practically exact. For geodetic stations, GD time series closely emulate TC time series with rates agreeing to 0.01 mm/yr, and so can be used interchangeably.

坐标时间序列计算提出了两项​​创新。首先，对一个百年难题给出了改进的解决方案，即从地心笛卡尔（GC：x、y、z）坐标非迭代计算常规大地测量（CG：纬度、经度、高度）坐标。对于高度 < 500 km 的精度为 1 nm，对于陆地或外太空任何点的纬度精度为 < 10 ^-15 rad。这比已发布的非迭代方法准确 3 个数量级。其次，CG时间序列被转换为实用的“经纬网距离”（GD：东向、北向、高度）曲线坐标系，与常用的地心笛卡尔（TC：东、北、上）坐标系不同，它是全球性的在自然界中，没有为每个大地测量站任意指定 GC 参考坐标。自 2011 年以来，内华达大地测量实验室以 GD 形式公开制作了 20,000 个 GPS 站的时间序列，已被数百项研究引用。 GD 系统有助于直接比较同一地点的站点的位置。 GD时间序列的用户能够：（1）解析已分配给相同物理基准的不同历史站名称；（2）解析已分配相同名称的不同物理基准。这有利于基准占用的历史重建和本地站点关联分析以确保参考框架的完整性。 GD 坐标具有档案价值，因为反演回 GC 坐标实际上是准确的。对于大地测量站，GD 时间序列与 TC 时间序列密切相似，速率一致为 0.01 毫米/年，因此可以互换使用。