Linear conform transformation: Errors in both coordinate systems

Lubomír Kubáček; Ludmila Kubáčková; Jan Ševčík

Applications of Mathematics (2002)

  • Volume: 47, Issue: 4, page 361-380
  • ISSN: 0862-7940

Abstract

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Linear conform transformation in the case of non-negligible errors in both coordinate systems is investigated. Estimation of transformation parameters and their statistical properties are described. Confidence ellipses of transformed nonidentical points and cross covariance matrices among them and identical points are determined. Some simulation for a verification of theoretical results are presented.

How to cite

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Kubáček, Lubomír, Kubáčková, Ludmila, and Ševčík, Jan. "Linear conform transformation: Errors in both coordinate systems." Applications of Mathematics 47.4 (2002): 361-380. <http://eudml.org/doc/33120>.

@article{Kubáček2002,
abstract = {Linear conform transformation in the case of non-negligible errors in both coordinate systems is investigated. Estimation of transformation parameters and their statistical properties are described. Confidence ellipses of transformed nonidentical points and cross covariance matrices among them and identical points are determined. Some simulation for a verification of theoretical results are presented.},
author = {Kubáček, Lubomír, Kubáčková, Ludmila, Ševčík, Jan},
journal = {Applications of Mathematics},
keywords = {linear conform transformation; regression model with constraints; regression model with constraints},
language = {eng},
number = {4},
pages = {361-380},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Linear conform transformation: Errors in both coordinate systems},
url = {http://eudml.org/doc/33120},
volume = {47},
year = {2002},
}

TY - JOUR
AU - Kubáček, Lubomír
AU - Kubáčková, Ludmila
AU - Ševčík, Jan
TI - Linear conform transformation: Errors in both coordinate systems
JO - Applications of Mathematics
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 47
IS - 4
SP - 361
EP - 380
AB - Linear conform transformation in the case of non-negligible errors in both coordinate systems is investigated. Estimation of transformation parameters and their statistical properties are described. Confidence ellipses of transformed nonidentical points and cross covariance matrices among them and identical points are determined. Some simulation for a verification of theoretical results are presented.
LA - eng
KW - linear conform transformation; regression model with constraints; regression model with constraints
UR - http://eudml.org/doc/33120
ER -

References

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  1. Criterion of accuracy at linear conform tranformation, Geodetický a kartografický obzor 8 (1962), 181–187. (Czech) (1962) 
  2. 10.1007/BF02585752, Studia Geoph. et Geod. 10 (1966), 124–136. (1966) DOI10.1007/BF02585752
  3. Some statistical aspects of the estimation of parameters of a linear conform transformation, Apl. Mat. 15 (1970), 190–206. (1970) MR0261753
  4. About the generalization of an orthogonal regression, Apl. Mat. 20 (1975), 87–95. (1975) MR0375650
  5. 10.1007/BF01613249, Studia Geoph. et Geod. 21 (1977), 227–235. (1977) DOI10.1007/BF01613249
  6. 10.1007/BF01627899, Studia Geoph. et Geod. 22 (1978), 224–230. (1978) DOI10.1007/BF01627899
  7. Foundations of Estimation Theory, Elsevier, Amsterdam-Oxford-New York-Tokyo, 1988. (1988) MR0995671
  8. Nonlinear error propagation law, Appl. Math. 41 (1996), 329–345. (1996) MR1404545
  9. Foundations of Experimental Data Analysis, CRC Press, Boca Ratton-Ann Arbor-London-Tokyo, 1992. (1992) MR1244322
  10. Unified theory of linear estimation, Sankhya, Ser.  A 33 (1971), 371–394. (1971) Zbl0236.62048MR0319321
  11. Weak nonlinearity in model which arises from the Helmert transformation, Appl. Math, Submitted. 

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