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Title: CLOSED FORMULAS FOR TRANSFORMATION FROM SPATIAL GEOCENTRIC TO GEODETIC COORDINATES
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CLOSED FORMULAS FOR TRANSFORMATION FROM SPATIAL GEOCENTRIC TO GEODETIC COORDINATES
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1314-2704
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English
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21
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2.1
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• Prof. DSc. Oleksandr Trofymchuk, UKRAINE
• Prof. Dr. hab. oec. Baiba Rivza, LATVIA |
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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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conference
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21st International Multidisciplinary Scientific GeoConference SGEM 2021
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21st International Multidisciplinary Scientific GeoConference SGEM 2021, 16 - 22 August, 2021
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Proceedings Paper
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STEF92 Technology
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SGEM International Multidisciplinary Scientific GeoConference
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SWS Scholarly Society; Acad Sci Czech Republ; Latvian Acad Sci; Polish Acad Sci; Serbian Acad Sci & Arts; Natl Acad Sci Ukraine; Natl Acad Sci Armenia; Sci Council Japan; European Acad Sci, Arts & Letters; Acad Fine Arts Zagreb Croatia; Croatian Acad Sci
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129-136
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16 - 22 August, 2021
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website
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cdrom
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7894
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geodetic coordinates; geocentric coordinates; coordinate transformation; direct method
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