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Weighted coordinate transformation formulated by standard least-squares theory

Authorized Users Only
2017
Authors
Mihajlović, Dragan
Cvijetinović, Željko
Article (Published version)
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Abstract
This paper presents a universal model of weighted coordinate transformation, i.e. transformation considering the errors of coordinates in both coordinate systems. It is intrinsically one of the typical examples of 'error-in-variables' (EIV) models. The proposed method of LS theory application on weighted coordinate transformation does not impose any constraints on the form of functional relationship among stochastic variables. Since the basic idea is to generalise Gauss-Markov model (GMM) by introduction of so-called 'total residuals', the proposed procedure is named 'Generalised Gauss-Markov model'. Formulation of expressions for estimation of unknown transformation parameters is theoretically confirmed using the Gauss-Helmert model (GHM) and three different modifications of the GMM. The proposed procedure is in its essence a strict solution to total least-squares (unweighted) and weighted total least-squares problem in coordinate transformation. This thesis is experimentally confirme...d by comparison of its results with those found in four characteristic examples from the literature.

Keywords:
EIV model / Weighted total least-squares (WTLS) / Gauss-Markov model / Gauss-Helmert model / Similarity transformation / Affine transformation
Source:
Survey Review, 2017, 49, 356, 328-345
Publisher:
  • Taylor and Francis Ltd.

DOI: 10.1080/00396265.2016.1173329

ISSN: 0039-6265

WoS: 000407504800002

Scopus: 2-s2.0-84978477103
[ Google Scholar ]
3
2
URI
https://grafar.grf.bg.ac.rs/handle/123456789/879
Collections
  • Radovi istraživača / Researcher's publications
  • Катедра за геодезију и геоинформатику
Institution/Community
GraFar
TY  - JOUR
AU  - Mihajlović, Dragan
AU  - Cvijetinović, Željko
PY  - 2017
UR  - https://grafar.grf.bg.ac.rs/handle/123456789/879
AB  - This paper presents a universal model of weighted coordinate transformation, i.e. transformation considering the errors of coordinates in both coordinate systems. It is intrinsically one of the typical examples of 'error-in-variables' (EIV) models. The proposed method of LS theory application on weighted coordinate transformation does not impose any constraints on the form of functional relationship among stochastic variables. Since the basic idea is to generalise Gauss-Markov model (GMM) by introduction of so-called 'total residuals', the proposed procedure is named 'Generalised Gauss-Markov model'. Formulation of expressions for estimation of unknown transformation parameters is theoretically confirmed using the Gauss-Helmert model (GHM) and three different modifications of the GMM. The proposed procedure is in its essence a strict solution to total least-squares (unweighted) and weighted total least-squares problem in coordinate transformation. This thesis is experimentally confirmed by comparison of its results with those found in four characteristic examples from the literature.
PB  - Taylor and Francis Ltd.
T2  - Survey Review
T1  - Weighted coordinate transformation formulated by standard least-squares theory
EP  - 345
IS  - 356
SP  - 328
VL  - 49
DO  - 10.1080/00396265.2016.1173329
ER  - 
@article{
author = "Mihajlović, Dragan and Cvijetinović, Željko",
year = "2017",
abstract = "This paper presents a universal model of weighted coordinate transformation, i.e. transformation considering the errors of coordinates in both coordinate systems. It is intrinsically one of the typical examples of 'error-in-variables' (EIV) models. The proposed method of LS theory application on weighted coordinate transformation does not impose any constraints on the form of functional relationship among stochastic variables. Since the basic idea is to generalise Gauss-Markov model (GMM) by introduction of so-called 'total residuals', the proposed procedure is named 'Generalised Gauss-Markov model'. Formulation of expressions for estimation of unknown transformation parameters is theoretically confirmed using the Gauss-Helmert model (GHM) and three different modifications of the GMM. The proposed procedure is in its essence a strict solution to total least-squares (unweighted) and weighted total least-squares problem in coordinate transformation. This thesis is experimentally confirmed by comparison of its results with those found in four characteristic examples from the literature.",
publisher = "Taylor and Francis Ltd.",
journal = "Survey Review",
title = "Weighted coordinate transformation formulated by standard least-squares theory",
pages = "345-328",
number = "356",
volume = "49",
doi = "10.1080/00396265.2016.1173329"
}
Mihajlović, D.,& Cvijetinović, Ž.. (2017). Weighted coordinate transformation formulated by standard least-squares theory. in Survey Review
Taylor and Francis Ltd.., 49(356), 328-345.
https://doi.org/10.1080/00396265.2016.1173329
Mihajlović D, Cvijetinović Ž. Weighted coordinate transformation formulated by standard least-squares theory. in Survey Review. 2017;49(356):328-345.
doi:10.1080/00396265.2016.1173329 .
Mihajlović, Dragan, Cvijetinović, Željko, "Weighted coordinate transformation formulated by standard least-squares theory" in Survey Review, 49, no. 356 (2017):328-345,
https://doi.org/10.1080/00396265.2016.1173329 . .

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