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Geodesy and Cartography

The Journal of Committee on Geodesy of Polish Academy of Sciences

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Kriging approach for local height transformations

Marcin Ligas
  • Corresponding author
  • AGH University of Science and Technology Faculty of Mining Surveying and Environmental Engineering Department of Geomatics, 30 Mickiewicza Al., 30-059 Krakow, Poland
  • Email:
/ Marek Kulczycki
  • AGH University of Science and Technology Faculty of Mining Surveying and Environmental Engineering Department of Geomatics, 30 Mickiewicza Al., 30-059 Krakow, Poland
  • Email:
Published Online: 2014-06-13 | DOI: https://doi.org/10.2478/geocart-2014-0002

Abstract

In the paper a transformation between two height datums (Kronstadt’60 and Kronstadt’86, the latter being a part of the present National Spatial Reference System in Poland) with the use of geostatistical method - kriging is presented. As the height differences between the two datums reveal visible trend a natural decision is to use the kind of kriging method that takes into account nonstationarity in the average behavior of the spatial process (height differences between the two datums). Hence, two methods were applied: hybrid technique (a method combining Trend Surface Analysis with ordinary kriging on least squares residuals) and universal kriging. The background of the two methods has been presented. The two methods were compared with respect to the prediction capabilities in a process of crossvalidation and additionally they were compared to the results obtained by applying a polynomial regression transformation model. The results obtained within this study prove that the structure hidden in the residual part of the model and used in kriging methods may improve prediction capabilities of the transformation model.

Streszczenie

W artykule przedstawiono lokalną transformację między dwoma układami wysokości (Kronsztadt’60 oraz Kronsztadt’86, ostatni z nich będący obecnie częścią Państwowego Systemu Odniesień Przestrzennych w Polsce) z wykorzystaniem metod geostatystycznych - kriging. Ze względu na fakt, iż różnice wysokości między dwoma układami na punktach dostosowania wykazywały silny trend pod uwagę wzięto tylko te metody, które uwzględniają tego typu niestacjonarność procesu. Zastosowano dwie metody: hybrydową (Analiza Trendu Powierzchniowego z interpolacją reszt do modelu za pomocą krigingu zwyczajnego) oraz kriging uniwersalny. Przedstawiono rys teoretyczny obydwu metod. Dokonano porównania wyżej wymienionych metod pod względem ich zdolności predykcyjnych w procesie kroswalidacji modeli a zarazem otrzymane wyniki skonfrontowano z wynikami otrzymanymi z regresji wielomianowej. Otrzymane wyniki dowodzą, iż struktura ukryta w rezydualnej części modelu używana przez kriging może podnieść zdolności predykcyjne modelu transformacji

Keywords: kriging; polynomial regression; height transformation

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About the article

Received: 2013-08-30

Accepted: 2014-03-03

Published Online: 2014-06-13

Published in Print: 2014-06-01


Citation Information: Geodesy and Cartography, ISSN (Online) 2300-2581, ISSN (Print) 2080-6736, DOI: https://doi.org/10.2478/geocart-2014-0002.

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© by Marcin Ligas. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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