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CLOSED FORMULAS FOR TRANSFORMATION FROM SPATIAL GEOCENTRIC TO GEODETIC COORDINATES

Elena Peneva

Abstract

The calculation of geodetic coordinates ??,??,?? of points on the Earth's surface or in near-Earth space using the spatial geocentric coordinates ??,??,?? obtained by GNSS determinations, has wide application in geodetic practice. The direct problem consisting in determination of ??,??,?? with given ??,??,?? is solved with the established Helmert formulas. The inverse problem (determination of ??,??,?? from ??,??,??) is more complicated, the difficulty is related to the determination of ?? and ??. For the determination of the geodetic longitude ?? it is recommended to use formulas [7], and for the geodetic height ?? - formulas [2]. For the calculation of the geodetic latitude ?? two types of methods have been developed: iterative [3, 1] and direct [5,6,7,8]. Both methods involve a significant amount of computations. It should be noted that direct methods provide an accurate determination of B and H regardless of the location of point ?? and the value of ??. This paper proposes a new approach for the determination of the geodetic coordinates ?? and ?? from ??,??,?? using the reduced latitude ??. The proposed method is related to the solution of 4th degree equation concerning the reduced latitude. The solution of this 4th degree equation is solved using a 3rd degree resolvent equation. A formula for determining the geodetic height by the reduced latitude is given.

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DOI resolver: doi.org/10.5593/sgem2021/2.1/s09.42

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