Weighted coordinate transformation formulated by standard least-squares theory
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2017
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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.
Ključne reči:
EIV model / Weighted total least-squares (WTLS) / Gauss-Markov model / Gauss-Helmert model / Similarity transformation / Affine transformationIzvor:
Survey Review, 2017, 49, 356, 328-345Izdavač:
- Taylor and Francis Ltd.
DOI: 10.1080/00396265.2016.1173329
ISSN: 0039-6265
WoS: 000407504800002
Scopus: 2-s2.0-84978477103
Institucija/grupa
GraFarTY - 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 . .