CONVERSION BETWEEN AUSTRIAN AND HUNGARIAN MAP PROJECTION SYSTEMS

Conversion between Austrian and Hungarian map projection systems is presented here. The conversion may be performed in two steps: first any kind of map projection systems should be transformed into WGS-84 ellipsoidal co-ordinates in one country, and then from WGS-84 ellipsoidal co-ordinates should be transformed into the desired system for the other country. A computer programme has been developed to carry out all the possible transformations between the two countries. Using our method and software the transformation between Austrian and Hungarian map projection systems can be performed with a few centimeters accuracy for a few ten kilometers range of common border

INTERPOLATION OF DEFLECTION OF THE VERTICAL BASED ON GRAVITY GRADIENTS

In this paper, the significance of interpolation of deflection of the vertical by means of tor- sion balance measurements is pointed out, followed by outlining its fundamentals. There- after, its practical methods of solution will be presented

Renaissance of Torsion Balance Measurements in Hungary

In the 20th century, a large amount of torsion balance measurements have been carried out around the world. The measurements still provide a good opportunity to detect the lateral underground mass inhomogeneities and the geological fault structures using the so called edge eects in gravity gradients. Hitherto almost 60000 torsion balance measurements were made in Hungary mainly for geophysical purposes. Only the horizontal gradients were used for geophysical prospecting, the curvature gradients measured by torsion balance remained unused. However, curvature gradients are very useful data in geodesy, using these gradients precise deflections of the vertical can be calculated by interpolation and using astrogeodetic determination of the geoid the fine structure of the geoid can be derived. In our test area a geoid with few centimeters accuracy was determined based on the curvature data. Based on the horizontal and the curvature gradients of gravity the full Eötvös tensor (including the vertical gradients) can be derived by the 3D inversion method. In our earlier research works additional new torsion balance measurements were necessary. Applying the new technical opportunities we reconstructed and modernized our older instruments, and additional torsion balance measurements have been made to study the linearity of gravity gradients

TEST INTERPOLATION OF DEFLECTION OF THE VERTICAL IN HUNGARY BASED ON GRAVITY GRADIENTS

A program package for computers was developed to test empirical methods of interpolation of deflection of the vertical which can be used to determine deflections of the vertical by any method of interpolation either along triangulation chains or in networks covering arbitrary large areas. In the course of our test computations in Hungary first we compared different empirical methods of interpolation then we tried to get an answer to the question whether the reliability of interpolated data can be increased by introducing appropriate weighting. Another important object of our investigations was to determine optimal geometrical arrangement for interpolation networks

GPS AS THE DEVICE OF JUNCTION OF TRIANGULATION NETWORKS

Conversion between Hungarian and Austrian map projection systems is presented in this paper. The conversion may be performed in two steps: at first any kind of map projection systems should be transformed into WGS-84 ellipsoidal co-ordinates in one country, and then from WGS-84 ellipsoidal co-ordinates should be transformed into the desired system of the other country. An algorithm and a computer program have been developed to carry out this transformation

A nehézségi erőtér potenciálfüggvényének inverziós rekonstrukciója Eötvös-inga adatok alapján

A nehézségi erőtér potenciálfüggvényének inverziós rekonstrukciójára teszünk javaslatot. A javasolt módszerrel lehetőség nyílik Eötvös-inga mérési adatok felhasználásával függővonal-elhajlás meghatározására, az eddig alkalmazott interpolációs módszerek pontosságát felülmúló számítások elvégzésére és a korábban alkalmazott eljárások során felmerülő bizonyos problémák áthidalására

Eötvös Loránd munkásságának geodéziai jelentősége

Eötvös Loránd fizikus, geofizikus kiemelkedő tudósa és közéleti személyisége volt Magyarországnak, munkássága számos területen kapcsolódik a geodézia tudományterületéhez. 1848-ban született és 100 évvel ezelőtt 1919. április 8-án hunyt el. Halálának 100. évfordulója alkalmából számtalan magyarországi és külföldi rendezvényen emlékezünk meg a munkásságáról. A világhírnevet hozó legjelentősebb eredményei a torziós ingájához kapcsolódnak. Arad környékén az ingájával végzett mérések felhasználásával Eötvös Loránd foglalkozott a világon elsőként gradiens-mérések alapján végezhető függővonal-elhajlás interpolációval és a nehézségi erőtér szintfelületének részletes meghatározásával. A geoid finomszerkezetének meghatározáshoz szükséges magyarországi gravitációs adatbázisnak kiemelten fontos és értékes részét képezik a korábbi Eötvös-inga mérések. Az alábbiakban az Eötvös-évforduló előtt tisztelegve áttekintjük a műszerének rövid történetét, megismerkedünk a torziós inga működésének alapelvével, méréseinek jelentőségével és geodéziai felhasználási lehetőségeivel

A Numeric-Symbolic Solution of GNSS Phase Ambiguity

Solution of the Global Navigation Satellite Systems (GNSS) phase ambiguity is considered as a global quadratic mixed integer programming task, which can be transformed into a pure integer problem with a given digit of accuracy. In this paper, three alter-native algorithms are suggested. Two of them are based on local and global linearization via McCormic Envelopes, respectively. These algorithms can be effective in case of simple configuration and relatively modest number of satellites. The third method is a locally nonlinear, iterative algorithm handling the problem as {-1, 0, 1} programming and also lets compute the next best integer solution easily. However, it should keep in mind that the algorithm is a heuristic one, which does not guarantee to find the global integer optimum always exactly. The procedure is very powerful utilizing the ability of the numeric-symbolic abilities of a computer algebraic system, like Wolfram Mathematica and it is properly fast for minimum 4 satellites with normal configuration, which means the Geometric Dilution of Precision (GDOP) should be between 1 and 8. Wolfram Alpha and Wolfram Clouds Apps give possibility to run the suggested code even via cell phones. All of these algorithms are illustrated with numerical examples. The result of the third one was successfully compared with the LAMBDA method, in case of ten satellites sending signals on two carrier frequencies (L1 and L2) with weighting matrix used to weight the GNSS observation and computed as the inverse of the corresponding covariance matrix

SUPPORT VECTOR CLASSIFIER VIA MATHEMATICA

In this case study a Support Vector Classifier function has been developed in Mathematica. Starting with a brief summary of support vector classification method, the step by step implementation of the classification algorithm in Mathematica is presented and explained. To check our function, two test problems, learning a chess board and classification of two intertwined spirals are solved. In addition, an application to filtering of airborne digital land image by pixel classification is demonstrated using a new SVM kernel family, the KMOD, a kernel with moderate decreasing

OPTIMAL TOPOGRAPHIC - ISOSTATIC CRUST MODELS FOR GLOBAL GEOPOTENTIAL INTERPRETATION

The topographic-isostatic potential of the earth's crust can be computed easily using average crustal density parameters, a global isostatic model and a numerical dataset of mean continental and oceanic heights. In lack of the detailed data for density, crustal thickness and isostatic compensation, a least squares estimation is suggested to determine global horizontal variation of crustal parameters. These variations can be determined using a minimum principle to yield a minimum variance high frequency residual geoid. The basic mathematical tool for the determina- tion of such parameter variation functions is the Clebsch-Gordan product-sum conversion formula of spherical harmonics. Computer programs were developed based on the above mentioned mathematical algorithm to determine optimal linear topographic-isostatic crust models (OLTM). Previ- ous calculations detected significant global density variations inside the crust with respect to the simple Airy model of uniform crustal parameters. The result would perhaps show us a better insight into the global isostatic behaviour of the crust