1 Medvedev P.A.

Omsk State Agrarian University named after P.A. Stolypin

Statement that calculation of spatial geodetic coordinates latitude B and H height according to the given rectangular geocentric coordinates X, Y, Z may be done by iterative method only, expressed in scientific publications by L. V. Ogorodova is analyzed. Different approaches and solution methods of this task, suggested by Russian and foreign scientists are considered for the purpose to refute this conclusion. It is shown that geodetic latitude is calculated not only by consecutive approximations but directly according to the algorithms divided into approximate and precise. Their comparative characteristic is also given. For the calculation of geodetic height, the formula expressed through the initial data and geodetic latitude (it’s fault) is used. Noniterative precision algorithms for the direct definition of spatial geodetic coordinates B, L, H on initial rectangular geocentric coordinates X, Y, Z is obtained on the basis of iterative algorithm by the method of permutation and identical transformations.
1.   Izotov A.A. (1969) Преобразование пространственных прямоугольных координат в геодезические координаты. Геодезия и картография, (5), pp. 6–7.
2.   Medvedev P.A. (1995) Вычисление широты методом касательных при переходе от пространственных прямоугольных координат к геодезическим. Геодезия и картография, (12), pp. 4–6.
3.   Medvedev P.A. Analiz preobrazovanij prostranstvennyh pryamougol'nyh koordinat v geodezicheskie. Omsk: izd. OmGAU, 2000, 104 p.
4.   Medvedev P.A. (2014) The analyses of transformation of the spatial coordinates of ground points. Geodezia i Kartografia, (4), pp. 2-8. (In Russian). DOI: 10.22389/0016-7126-2014-886-4-2-8.
5.   Morozov V.P. Kurs sferoidicheskoj geodezii. Izd. 2-e, pererab. i dop. M.: Nedra, 1979, 295 p.
6.   Ogorodova L.V. Prostoj i nadyozhnyj sposob vychisleniya geodezicheskoj shiroty i vysoty tochek poverhnosti Zemli po pryamougol'nym koordinatam. Izv. vuzov. Geodeziya i aehrofotos"yomka, 2014, no. 2, pp. 63–66.
7.   Okunev L.Ya. Vysshaya algebra. M.: Prosveshchenie, 1996, 336 p.
8.   Penev P., Peneva E. Preobrazovanie pryamougol'nyh geocentricheskih koordinat v geodezicheskie bez primeneniya iteracij. Izv. vuzov. Geodeziya i aehrofotos"emka, 2012, no. 3, pp. 34–38.
Medvedev P.A., 
(2016) Precision algorithms for the direct calculation of spatial geodetic coordinates by rectangular coordinates. Geodesy and cartography = Geodezia i Kartografia, (11), pp. 2–6. (In Russian). DOI: 10.22389/0016-7126-2016-917-11-2-6
Publication History
Received: 29.12.2015
Accepted: 26.02.2016
Published: 21.12.2016


2016 November DOI: