MATHEMATICAL MODELS OF GAUSS-KRUGER COORDINATE SYSTEM STUDY AIMED AT CALCULATING OF GEODETIC COORDINATES BY FLAT RECTANGULAR COORDINATES
A study of mathematical models of Gauss-Krüger coordinates in order to calculate 18 degree0meridional zones of geodetic coordinates. They are latitude B and longitude difference l= L - L<sub>0</sub> found usingflat rectangular coordinates x , y. Particularly, the algorithms, recommended by All-Union-State Standard (GOST 32453-2017, Global Navigation Satellite System. Coordinate system. Methods of coordinate transformation of points for determination.), and enacted as a National Standard of the Russian Federation of 1st July 2018, are analyzed. Optimal coordinate calculation algorithms of B and L on the parameters of any ellipsoid with improved convergence are developed. Derivation is carried out by selecting spherical terms in rows of determined quantities, represented by powers of the y coordinate, followed by replacing their sums using spherical trigonometry formulae. For such transformations laws of the transverse-cylindrical projection of the sphere on the plane are used. For accuracy assessment of the results according to the derived algorithms, theoretical studies are presented and formulae are obtained. For calculation of the latitude B by the arc length of the meridian X , an optimal high-precision algorithm is proposed. This work is considered an option for improving the Gauss-Krüger coordinate system formulae recommended by the All-Union State standard.