1 Afonin K.F.

Siberian State University of Geosystems and Technologies

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.
1.   Afonin K.F. Use of differential amendments to calculate geodesic latitudes by spatial rectangular coordinates. Vestnik SGUGiT, 2020, Vol. 25, no. 1,
2.   Balandin V.N., Bryn M.Ya., Imshenetskiy S.P., Matveev A.Yu., Yuskevich A.V. (2006) Algorithm for calculating the geodetic height by spatial rectangular coordinates. Geodesy and Cartography, 67(6), pp. 15–16.
3.   Boutkevitch A.V. (1967) On the transition from spatial rectangular coordinates to geodesic coordinates. Geodezia i Kartografia, 28(6), pp. 20-22.
4.   Kurchenko L. A., Taran V. V., Shlapak V. V. K voprosu o preobrazovanii geodezicheskikh pryamougol'nykh koordinat v krivolineinye. Izvestia vuzov «Geodesy and aerophotography», 2016, no. 3, pp. 29–33.
5.   Laping K. A. Vychislenie koordinat i vysot po izmerennym azimutam normal'nykh sechenii i uglam naklona khord na dvukh iskhodnykh punktakh. Izvestia vuzov «Geodesy and aerophotography», 1962, no. 1, pp. 3–8.
6.   Maksimova M. V. Preobrazovaniya koordinat pri inzhenerno-geodezicheskikh izyskaniyakh. Inzhenernye izyskaniya, 2013, no. 2, pp. 18–21.
7.   Medvedev P. A. Issledovaniya sposobov vychisleniya geodezicheskoi shiroty i vysoty tochek zemnoi poverkhnosti po pryamougol'nym koordinatam. Izvestia vuzov «Geodesy and aerophotography», 2016, no. 3, pp. 24–28.
8.   Medvedev P.A. (2016) Mathematical models transformations of spatial coordinates. Geodezia i Kartografia, (3), pp. 2–7. (In Russian). DOI: 10.22389/0016-7126-2016-909-3-2-7.
9.   Medvedev P. A., Novorodskaya M. V., Sharov S. A. Neiterativnyi algoritm vychisleniya geodezicheskoi shiroty po prostranstvennym pryamougol'nym koordinatam. Vestnik Omskogo gosudarstvennogo agrarnogo universiteta, 2017, no. 2 (26), pp. 60–64.
10.   Mustafin M.G., Tran Thanh Son (2018) Method for determining the normal heights from satellite data, taking into account the deviations of the plumb lines. Geodezia i Kartografia, 79(7), pp. 2-10. (In Russian). DOI: 10.22389/0016-7126-2018-937-7-2-10.
11.   Ogorodova L.V. (2011) Joint calculation of geodetic latitude and altitude of the Earth’s surface points. Geodezia i Kartografia, 72(9), pp. 11-15.
12.   Teleganov N. A., Elagin A. V. Vysshaya geodeziya i osnovy koordinatno-vremennyh sistem. Novosibirsk: SGGA, 2004, 238 p.
13.   Shanurov G.A., Manilova A.D. (2017) Mobile scanning complex positioning accuracy depending on the coordinate systems used. Geodezia i Kartografia, (1), pp. 13-17. (In Russian). DOI: 10.22389/0016-7126-2017-919-1-13-17.
14.   Shanurov G. A., Polovnyov O. V., Manilova A. D. Preobrazovaniya prostranstvennyh koordinat pri geodezicheskom obespechenii raboty skaniruyushchego kompleksa. Izvestia vuzov «Geodesy and aerophotography», 2015, no. 1, pp. 15-18.
15.   Younes J.A., Mustafin M.G. (2018) The characteristics of transforming coordinates from the geocentric system WGS-84 for the Mercator projection under low latitudes conditions. Geodezia i Kartografia, 79(10), pp. 2-6. (In Russian). DOI: 10.22389/0016-7126-2018-940-10-2-6.
16.   Bowring B. (1985) The accuracy of geodetic latitude and height equations. Survey Review, no. 28 (218), pp. 200-206.
17.   Bowring B. (1976) Transformation from spatial to geodetic coordinates. Survey Review, no. 23, pp. 323-327.
Afonin K.F., 
(2021) The method of using differential amendments to convert spatial rectangulars coordinates into those geodesic ones. Geodesy and cartography = Geodezia i Kartografia, 82(4), pp. 2-7. (In Russian). DOI: 10.22389/0016-7126-2021-970-4-2-7
Publication History
Received: 25.06.2020
Accepted: 24.02.2021
Published: 20.05.2021


2021 April DOI: