L. Bányai Geodetic and Geophysical Research Institute of the Hungarian Academy of Sciences POB 5 H-9401 Sopron Hungary

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The theoretical and practical background of the similarity transformation together with the simultaneous estimation of local geoid undulations is presented.The mean features of the traditional network adjustment on the local ellipsoids are summarized and the different Hungarian networks and known geoid solutions are shortly described as the basic data of the test computations.The eigenvalue and eigenvector decomposition revealed that the seven parameter similarity transformation cannot be applied together with the simultaneous local geoid estimation because the rotations about the X and Y axes significantly destroy the condition of the normal equations.However, the replacement of the rotations about the X, Y and Z axes by the rotation about the ellipsoidal normal of the datum point can provide a very well conditioned solution, which takes into account the special role of the datum point of the astro-geodetic network adjustment.Based on the unit weights of the input data an optimal adjustment strategy is demonstrated from a computational point of view, where the five transformation parameters can be estimated together with a very large number of local geoid undulations. The geoid has to be known in the global reference system. The geoid unknowns describe only the relative position of this known geoid with respect to the local reference system.The application of the available and the simultaneously estimated local geoid solutions proved that neglecting local geoid heights has a most significant impact on the scale parameter, while it has no significant effects on the horizontal residuals from the statistical point of view.The small scale difference (1 ppm) and the small rotation (-0.5 arc sec) about the datum point and its ellipsoidal normal of the Hungarian local system with respect to the global GPS system demonstrate the high quality of the traditional measurements as well.

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Acta Geodaetica et Geophysica
Language English
Size B5
Year of
per Year
per Year
Founder Magyar Tudományos Akadémia
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó Springer
Nature Switzerland AG
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Chief Executive Officer, Akadémiai Kiadó
ISSN 2213-5812 (Print)
ISSN 2213-5820 (Online)

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