The method of using differential amendments to convert spatial rectangulars coordinates into those geodesic ones

Abstract

The article is devoted to considering the technological aspects of the application of differential amendments for the transition from spatial rectangular coordinates to geodesic. It is shown that the coordinate provision of the territories is impossible to imagine at present without the use of GNSS technologies. But they allow to get only spatial rectangular coordinates of defined points. It is noted how the vast majority of users need other coordinates-flat rectangular coordinates in the projection of Gauss–Kruger, which can be calculated only by geodesic latitudes and longitudes. The national and foreign literature describes more than a dozen ways to calculate geodesic coordinates by spatial rectangular coordinates. These methods can be divided into three groups. The first group uses iterative methods and algorithms, the second group uses non-iteter methods. The third group is characterized by the calculation and introduction of amendments to the approximate value of geodesic latitude. It is possible to reduce the number of technological operations that allow to solve the problem without losing the accuracy of calculated geodesic coordinates. There are numerical examples showing the feasibity of the proposed technology at maximum ground points.