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Izravnava po metodi najmanjših kvadratov z upoštevanjem pogreškov pri neznankah
ID Marjetič, Aleš (Author)

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Abstract
V članku obravnavamo postopek izračuna vrednosti neznank pod pogojem minimalne vsote kvadratov popravkov opazovanj (metoda najmanjših kvadratov) z upoštevanjem pogreškov pri neznankah. Problem so že predstavili številni avtorji, predvsem na področju regresijske analize in računanja transformacijskih parametrov. Predstavljen je pregled teoretičnih osnov metode najmanjših kvadratov in njene razširitve z upoštevanjem pogreškov pri neznankah neznank v matriki modela. Metodo, ki jo lahko poimenujemo "popolna" metoda najmanjših kvadratov, v prispevku predstavimo na primeru prilagajanja regresijske premice nizu točk in na primeru izračuna transformacijskih parametrov za prehod med starim in novim slovenskim državnim koordinatnim sistemom. Z rezultati na podlagi ustreznih statistik potrdimo primernost obravnavane metode za izvajanje tovrstnih strokovnih nalog.

Language:Slovenian
Keywords:izravnava po metodi najmanjših kvadratov, TLS, SVD, pogreški, transformacija
Typology:1.02 - Review Article
Organization:FPP - Faculty of Maritime Studies and Transport
Year:2021
Number of pages:Str. 205-218
Numbering:Letn. 65, št. 2
PID:20.500.12556/RUL-132741 This link opens in a new window
UDC:528.4
ISSN on article:0351-0271
DOI:10.15292/geodetski-vestnik.2021.02.205-218 This link opens in a new window
COBISS.SI-ID:69451779 This link opens in a new window
Publication date in RUL:02.11.2021
Views:1331
Downloads:135
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Record is a part of a journal

Title:Geodetski vestnik : glasilo Zveze geodetov Slovenije
Shortened title:Geod. vestn.
Publisher:Zveza geodetov Slovenije
ISSN:0351-0271
COBISS.SI-ID:5091842 This link opens in a new window

Secondary language

Language:English
Title:Least-squares adjustment taking into account the errors in variables
Abstract:
In this article, we discuss the procedure for computing the values of the unknowns under the condition of the minimum sum of squares of the observation residuals (least-squares method), taking into account the errors in the unknowns. Many authors have already presented the problem, especially in the field of regression analysis and computations of transformation parameters. We present an overview of the theoretical foundations of the least-squares method and extensions of this method by considering the errors in unknowns in the model matrix. The method, which can be called %the total least-squares method%, is presented in the paper for the case of fitting the regression line to a set of points and for the case of calculating transformation parameters for the transition between the old and the new Slovenian national coordinate systems. With the results based on relevant statistics, we confirm the suitability of the considered method for solving such tasks.

Keywords:east-squares adjustment, TLS, SVD, errors, transformation

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