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Combination of 3D epoch-wise and permanent geodetic networks observed by GNSS

Ján Hefty, Ľubomíra Gerhátová (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The local, regional and global geodetic networks are recently almost exclusively observed by satellite radionavigation methods, such as the U.S. Global Positioning System (GPS), and the Russian navigation system GLONASS. The unprecedented accuracy of geodetic satellite positioning allows determination of the geocentric site coordinates at millimetre level. The paper points to complex adjustment model applied for combination of 3D coordinates observed in permanent and epoch-wise satellite networks....

Contribuciones a la generalización del problema de compensación por grupos de Helmert-Pranis Pranievich.

Ioan Popescu (1988)

Revista Matemática de la Universidad Complutense de Madrid

The paper presents in a generalized form the problem of the geodetic network adjustment by the Helmert-Pranis Pranievich groups method (groups with junction points included or not). The adjustment problem, as well as the cofactor matrix derivation for the partial-independent and linkage unknowns, was completely formulated by transformed weight matrix definition and usage. A complete sequence of the computing stages for the geodetic networks divided into groups without junction points was given for...

Generalized method of least squares collocation

Ludmila Kubáčková, Lubomír Kubáček (1982)

Aplikace matematiky

Two general solutions of the collocation problem of physical geodesy are given. Their mutual equivalency and equivalency of them to the classical solution in the regular case are proved. The regularity means the non-singularity of the covariance matrix of those random variables by outcomes of which the measured values of the gravitational field are generated.

Gravimetric quasigeoid in Slovakia by the finite element method

Zuzana Fašková, Karol Mikula, Róbert Čunderlík, Juraj Janák, Michal Šprlák (2007)

Kybernetika

The paper presents the solution to the geodetic boundary value problem by the finite element method in area of Slovak Republic. Generally, we have made two numerical experiments. In the first one, Neumann BC in the form of gravity disturbances generated from EGM-96 is used and the solution is verified by the quasigeoidal heights generated directly from EGM-96. In the second one, Neumann BC is computed from gravity measurements and the solution is compared to the quasigeoidal heights obtained by...

On inversions of van der Grinten projections

Tomáš Bayer, Milada Kočandrlová (2021)

Applications of Mathematics

Approximately 150 map projections are known, but the inverse forms have been published for only two-thirds of them. This paper focuses on finding the inverse forms of van der Grinten projections I--IV, both by non-linear partial differential equations and by the straightforward inverse of their projection equations. Taking into account the particular cases, new derivations of coordinate functions are also presented. Both the direct and inverse equations have the analytic form, are easy to implement...

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