Determination of the geodetic latitude and height by spatial geocentric coordinates

Abstract

The authors propose to derive the formulas given in [1, 2] for determining the height and latitude based on the Cartesian rectangular coordinates X, Y, Z, giving an accuracy for the geodetic height H of 1 mm for heights up to 50 km and for geodetic latitude B of 0,0001 arc seconds for H < 10 km. The formulas proposed in [1, 2] apply to all values of latitude and longitude (B and L). In [3], we propose two new formulas for H and B. In this paper, it is shown that the formulas proposed in [3] apply to points of ellipsoid surface and points with geodetic latitude of 0° and 90°. For the same formulas proposed in [3], the corrections are derived to ensure an accuracy of H of 1 mm at H ≤ 10 km, which apply to all values of B and L. Basing on the presented geometric conclusions, calculations and analyzes, a new solution for H and B respectively is proposed for given X, Y, Z, which provides an accuracy for H less than 1 mm for H ≤ 100 km and for B of 0,0001 arc seconds for H ≤ 50 km.