Precision algorithms for the direct calculation of spatial geodetic coordinates by rectangular coordinates

Owing to the widespread use of GNSS technologies in geodetic practice, the problem arises of transition from rectangular spatial coordinates of points to spatial geodetic coordinates, which are necessary for the transition to flat rectangular coordinates in the Gauss-Kruger projection. The authors proposed five algorithms for converting rectangular coordinates of points in the plane of the meridian ellipse into geodetic heights and latitudes. The first two algorithms are geometrically related to the intersection point of the ellipse with the normal passing through the point at which the rectangular spatial coordinates were obtained. The formulas of the other three algorithms are based on the geometric relationships of the point of intersection of the meridian ellipse with the straight line connecting the point with the center of curvature of the meridian. As a result of the experiments, deviations of the calculated latitudes and heights from the reference values of the given grid of geodetic coordinates were obtained. The formulas were tested not only for points under and on the earth's surface, but also outside the earth at different heights up to an altitude of 20,000 km.

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Calculation of the plane rectangular coordinates, meridian rapprochement and Gauss projection scale in the 6th grid zone using geodetic coordinates

Geodesy and Cartography ◽

10.22389/0016-7126-2014-884-2-11-13 ◽

2014 ◽

Vol 884 (2) ◽

pp. 11-13 ◽

Cited By ~ 2

Author(s):

V.N. Balandin ◽

◽

M.J. Bryn ◽

I.V. Menchikov ◽

Yu.G. Firsov ◽

...

Keyword(s):

Geodetic Coordinates ◽

Rectangular Coordinates

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Transformation of the spatial rectangular coordinates into the geodetic coordinates

Bulletin Géodésique ◽

10.1007/bf02526103 ◽

1967 ◽

Vol 83 (1) ◽

pp. 21-26 ◽

Cited By ~ 2

Author(s):

M. Pick

Keyword(s):

Geodetic Coordinates ◽

Rectangular Coordinates

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Conversion of geodetic coordinates into flat (2-dimensinal) coordinates PL-UTM for the purposes of navigation

Zeszyty Naukowe Akademii Marynarki Wojennej ◽

10.5604/0860889x.1237622 ◽

2017 ◽

pp. 45-60 ◽

Cited By ~ 1

Author(s):

Wacław Morgaś ◽

Zdzisław Kopacz

Keyword(s):

Prime Minister ◽

The State ◽

State System ◽

Inverse Transformation ◽

Coordinate Systems ◽

Geodetic Coordinates ◽

Rectangular Coordinates ◽

Relevant Calculation

This paper presents mathematical interdependences in converting geodetic coordinates into flat rectangular coordinates and inverse transformation recommended in the Ordinance by Prime Minister on the State System of Spatial References. It especially presents formulas contained in works by M. Hooijberg (1997) Practical Geodesy and R. Kadaj (2001) Projection Formulas and Parameters of Coordinate Systems. G-1.10.In order to illustrate uses of the presented formulas relevant calculation examples based on the reference ellipsoids WGS 84 and GRS 80 are included.

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Gravimetric and Astrogeodetic Reference Systems in Space and Time

International Astronomical Union Colloquium ◽

10.1017/s0252921100050995 ◽

1975 ◽

Vol 26 ◽

pp. 161-179

Author(s):

H. Moritz

Keyword(s):

Final Section ◽

Temporal Variations ◽

Reference Ellipsoid ◽

Earth Tides ◽

Plate Motion ◽

Reference Systems ◽

Natural Coordinates ◽

Geodetic Coordinates ◽

Rectangular Coordinates ◽

Definition Of

AbstractThis paper is concerned with conceptual aspects of terrestrial reference systems to be used in connection with gravimetric and astrogeodetic methods. Two principal kinds of reference systems are discussed: natural coordinates, based on the gravity field (geoid and plumb lines), and geodetic coordinates, which numerically approximate the natural coordinates but are based on a reference ellipsoid instead of the geoid and are, therefore, directly related to spatial rectangular coordinates.The discussion includes temporal variations due to Earth tides, and problems posed by the definition of the origin because of polar motion and by the change of station position due to plate motion, etc., as well as questions raised by the definition of reference ellipsoids, including effects of the atmosphere. A final section deals briefly with references for gravity observations.

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