naslovnica

IF JCR (2020): 0.551
IF SNIP (2020): 0.417
ISSN: 0351-0271
e-ISSN: 1581-1328
COBISS.SI ID: 5091842
UDK: 528=863
Zveza geodetov Slovenije
Publisher:
Association of Surveyors of Slovenia
Zemljemerska ulica 12, SI-1000 Ljubljana
E-mail: info@geodetski-vestnik.com
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Izravnava po metodi najmanjših kvadratov z upoštevanjem pogreškov pri neznankah

Least-squares adjustment taking into account the errors in variables

Author(s):

Aleš Marjetič

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:

least-squares adjustment, TLS, SVD, errors, transformation

DOI: 10.15292/geodetski-vestnik.2021.02.205-218

Citation:

Aleš Marjetič (2021). Izravnava po metodi najmanjših kvadratov z upoštevanjem pogreškov pri neznankah. | Least-squares adjustment taking into account the errors in variables. Geodetski vestnik, 65 (2), 205-218. DOI: 10.15292/geodetski-vestnik.2021.02.205-218

ISSN: 0352-3551
EISSN: 1581-0267
COBISS: 3664386
UDK: (05) 532;556;626/628.6
Zveza geodetov Slovenije
Publisher:
Association of Surveyors of Slovenia
Zemljemerska ulica 12, SI-1000 Ljubljana
E-mail: info@geodetski-vestnik.com
CC