Proceedings, XXth congress: Proceedings, XXth congress

Altan, M. Orhan

Bibliographic data

Multivolume work

Persistent identifier:: 1663674213

Title:: Proceedings, XXth congress

Sub title:: Istanbul, 12 - 23 July 2004

Year of publication:: 2004

Place of publication:: Istanbul

Publisher of the original:: [Verlag nicht ermittelbar]

Identifier (digital):: 1663674213

Language:: English

Additional Notes:: Erscheinungsdatum des Originals ist aus dem Copyrightjahr ermittelt.; Auch bezeichnet als XXth International Congress for Photogrammetry and Remote Sensing

Editor:: Altan, M. Orhan

Corporations:: International Society for Photogrammetry and Remote Sensing, Congress, 20., 2004, Istanbul; International Society for Photogrammetry and Remote Sensing, Commission Primary Data Acquisition

Adapter:: International Society for Photogrammetry and Remote Sensing, Congress, 20., 2004, Istanbul; International Society for Photogrammetry and Remote Sensing, Commission Primary Data Acquisition

Founder of work:: International Society for Photogrammetry and Remote Sensing, Congress, 20., 2004, Istanbul; International Society for Photogrammetry and Remote Sensing, Commission Primary Data Acquisition

Other corporate:: International Society for Photogrammetry and Remote Sensing, Congress, 20., 2004, Istanbul; International Society for Photogrammetry and Remote Sensing, Commission Primary Data Acquisition

Document type:: Multivolume work

Volume

Persistent identifier:: 166368779X

Title:: Proceedings, XXth congress

Scope:: IV, 226 Seiten

Year of publication:: 2004

Place of publication:: Istanbul

Publisher of the original:: [Verlag nicht ermittelbar]

Identifier (digital):: 166368779X

Illustration:: Illustrationen, Diagramme

Signature of the source:: ZS 312(35,B8)

Language:: English

Additional Notes:: Erscheinungsdatum des Originals ist aus dem Copyrightjahr ermittelt.

Usage licence:: Attribution 4.0 International (CC BY 4.0)

Editor:: Altan, M. Orhan

Corporations:: International Society for Photogrammetry and Remote Sensing, Congress, 20., 2004, Istanbul; International Society for Photogrammetry and Remote Sensing

Adapter:: International Society for Photogrammetry and Remote Sensing, Congress, 20., 2004, Istanbul; International Society for Photogrammetry and Remote Sensing

Founder of work:: International Society for Photogrammetry and Remote Sensing, Congress, 20., 2004, Istanbul; International Society for Photogrammetry and Remote Sensing

Other corporate:: International Society for Photogrammetry and Remote Sensing, Congress, 20., 2004, Istanbul; International Society for Photogrammetry and Remote Sensing

Publisher of the digital copy:: Technische Informationsbibliothek Hannover

Place of publication of the digital copy:: Hannover

Year of publication of the original:: 2019

Document type:: Volume

Collection:: Earth sciences

Chapter

Title:: APPROACH OF THE HUNGARIAN GEOID SURFACE WITH SEQUENCE OF NEURAL NETWORKS P. Zaletnyik, L. Völgyesi, B. Paláncz

Document type:: Multivolume work

Structure type:: Chapter

bul 2004 Sensing, navand: | remote Remote ng and e PC. ns Inc., al web- nik.com iparison In: XX. analysis tute for de, The ted by ermany. Karsten ‘ing this APPROACH OF THE HUNGARIAN GEOID SURFACE WITH SEQUENCE OF NEURAL NETWORKS P. Zaletnyik ^ * , L. Vólgyesi * , B. Paláncz " * Department of Geodesy and Surveying, Budapest University of Technology and Economics, H-1521 Budapest, Hungary, e-mail: volgyesi@eik.bme.hu, zaletnyikp@hotmail.com ? Department of Photogrammetry and Geoinformatics, Budapest University of Technology and Economics, H-1521 Budapest, Hungary, e-mail: palanez@epito.bme.hu KEY WORDS: Neural, Artificial Intelligence, Surface, Data Mining, Geodesy ABSTRACT For global data representation, like the approximation of a surface, algebraic or trigonometric polynomials may be used. However, polynomial approaches are limited concerning their accuracy. In the last decade neural networks were applied very successfully in many fields of data mining and representation. In this research sequence of neural networks has been employed to high accuracy regression in 3D as data representation in form z = f(x,y). The first term of this series of networks estimates the values of the dependent variable as it is usual, while the second term estimates the error of the first network, the third term estimates the error of the second network and so on. Assuming that the relative error of every network in this sequence is less than 100%, the sum of the estimated error can be reduced very significantly and effectively. To illustrate this method the geoid of Hungary was estimated. To approach this surface, a RBF neural network has been employed with 35 neurons having Gaussian activation functions. We used this type of network, because the radial basis type activation function proved to be the most efficient in case of function approximation problems. According to our experience, the iteration process is converging rapidly, and after 3-4 iteration steps there were no further significant change in the values. Comparing the results of the first network with the fourth network the value of standard deviations was reduced with about 30 percents. And comparing these results with the polynomial approach the improvement is more significant, it is about 60 percents. These computations were carried out with the symbolic-numeric integrated system Mathematica. 1. INTRODUCTION N=h-H : (1) Nowadays the GPS measurements are one of the most frequently used technique in geodesy. With this technique where N = geoid height ellipsoidal height can be reckoned. However in the engineering h = ellipsoidal height practice orthometric heights (height above sea level) are used. H = orthometric height. The orthometric heights are determined by levelling. Transforming the GPS-derived ellipsoidal heights to The transformation of ellipsoidal heights to orthometric ones orthometric heights it is important to know the distance between requires that the geoid height must refer to the same reference the ellipsoidal and the geoid surface, called the geoid height or ellipsoid (to the WGS-84 ellipsoid). geoid undulation. With the spreading of the GPS measurements the need for a In geodesy two types of Earth’s figure are distinguished. One of good geoid model has been increased. The geoid can be them is the physical or topographic earth’ surface, that is the calculated from different types of input data. The simplest real surface of the Earth with the mountains, seas and plains. method is to use GPS and levelling points, where both the The other is the mathematical or the theoretical figure of the ellipsoidal and orthometric heights are given. Another Earth. This is the shape of the free water surface be balanced by possibility and the most commonly used technique for precise the gravity field only, this surface is one of the equipotential determination of geoid is using the gravimetric solution, carried surfaces of the gravity. The equipotential surface at the mean out by the Stokes-integral. sea level (MSL) is called geoid. In Hungary considerable investigations are in progress for the The geoid is the reference surface of the orthometric heights, determination of the separation of the geoid: lithospheric geoid but the reference surface of the GPS measurements is an solution (Papp and Kalmar 1996), gravimetric solution HGR97 ellipsoid, the WGS-84. The geoid height can be computed with (Kenyeres 1999), HGTUB98 and HGTUB2000 solution (Téth a simple subtraction: and Rózsa 2000). The HGTUB2000 geoid heights were used for our investigations. This gravimetric solution was based on terrestrial gravity data, height data and the EGM96 geopotential model, and was computed with the 1D Spherical FFT method * Corresponding author. 119

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