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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-4626f6b9-d036-4981-a4d5-16013ce06ec1

Czasopismo

Reports on Geodesy and Geoinformatics

Tytuł artykułu

Least squares collocation alternative to Helmert's transformation with Hausbrandt's post-transformation correction

Autorzy Ligas, M.  Banasik, P. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
Abstrakty
EN The paper presents a least squares collocation - based alternative to Helmert’s transformation with Hausbrandt’s post-transformation correction. The least squares collocation is used as an exact predictor i.e. it honors the data, thus the problem of zero residuals on transformation control points is overcome and zero residuals are assured by the method applied. Despite the fact that the procedure is presented for Helmert’s transformation it may easily be copied to any other form of coordinate transformation. A numerical example is provided within the content of the paper.
Słowa kluczowe
PL kolokacja metodą najmniejszych kwadratów   transformacja Helmerta   funkcja kowariancji   kowariancja   korekta posttransformacyjna  
EN least squares collocation   Helmert's transformation   covariance function   post-transformation correction  
Wydawca Wydział Geodezji i Kartografii Politechniki Warszawskiej
Czasopismo Reports on Geodesy and Geoinformatics
Rocznik 2014
Tom Vol. 97
Strony 23--34
Opis fizyczny Bibliogr. 11 poz., rys., tab.
Twórcy
autor Ligas, M.
  • AGH University of Science and Technology, Faculty of Mining Surveying and Environmental Engineering, Department of Geomatics, 30 Mickiewicza Av., 30–059 Krakow, Poland, ligas@agh.edu.pl
autor Banasik, P.
  • AGH University of Science and Technology, Faculty of Mining Surveying and Environmental Engineering, Department of Geomatics, 30 Mickiewicza Av., 30–059 Krakow, Poland, pbanasik@agh.edu.pl
Bibliografia
[1] Christensen R. (2011) Plane answers to complex questions: the theory of linear models, Springer
[2] Ghilani C.D. (2010) Adjustment computations – spatial data analysis, 5th edition, Wiley, New Jersey
[3] Goldberger A.S. (1962) Best Linear Unbiased Prediction in the Generalized Linear Regression Model, Journal of the American Statistical Association, 57(298), 369-375
[4] Hardy R.L. (1977) Least squares prediction, Photogrammetric Engineering and Remote Sensing, 43(4), 475-492
[5] Hausbrandt S. (1970) Rachunek wyrównawczy i obliczenia geodezyjne, PPWK Warszawa
[6] Krarup T., (1969): A contribution to the mathematical foundation of physical geodesy, Geodaetisk Institut, Kobenhavn
[7] Kraus K., Mikhail E. M. (1972), Linear least-squares interpolation, Twelfth Congress of the International Society of Photogrammetry, Ottawa, Canada, July 23 – August 5, 1972, Presented paper, Commission III
[8] Mikhail E.M. (with contributions by F. Ackermann) (1976), Observations and least squares, IEP – A Dun – Donnelley Publisher, New York
[9] Moritz H. (1972) Advanced least-squares methods, Reports of the Department of Geodetic Science, Report No. 175, The Ohio State University
[10] Moritz, H., (1980) Advanced Physical Geodesy, Herbert Wichmann Verlag, Karlsruhe
[11] Robinson G. K. (1991) That BLUP is a good thing: the estimation of random effects, Statistical Science, 6(1), 15-32
Kolekcja BazTech
Identyfikator YADDA bwmeta1.element.baztech-4626f6b9-d036-4981-a4d5-16013ce06ec1
Identyfikatory
DOI 10.2478/rgg-2014-0009