Open AccessLeast-squares adjustment taking into account the errors in variables
Author(s) -
Aleš Marjetič
Publication year - 2021
Publication title -
geodetski vestnik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.254
H-Index - 11
eISSN - 1581-1328
pISSN - 0351-0271
DOI - 10.15292/geodetski-vestnik.2021.02.205-218
Subject(s) - least squares function approximation , total least squares , transformation (genetics) , computation , generalized least squares , non linear least squares , mathematics , matrix (chemical analysis) , explained sum of squares , set (abstract data type) , field (mathematics) , least trimmed squares , linear least squares , residual sum of squares , regression , statistics , algorithm , computer science , linear model , biochemistry , chemistry , materials science , estimator , pure mathematics , composite material , gene , programming language
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.