Потпуни метод најмањих квадрата у функцији решавања геодетских проблема
Total Least Sqares Method for Solving Geodetic Tasks.
Popović, Jovan M.
Faculty:University of Belgrade, Faculty of Civil Engineering
Aleksić, Ivan R.
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Doktorska teza je posvećena primeni tehnike potpune metode najmanjeg kvadrata...A doctoral thesis deals with the application of Total Least Squares (TLS) techniques for parameters estimation of mathematical models for various geodetic problems. Total Least Squares is a relatively new technique of parameters model estimation. The first research in the field of mathematics dating from the early eighties and the first applications appeared in various nongeodetic disciplines. Studies on possibility of applications in the parameters estimation of geodetic models are of later date, there are about ten years ago (Kupferer, 2005 Schaffrin, 2006). Research is developing towards adjustment TLS geodetic problems in the sense finding a solution that include different accuracy and mutual correlation of data (measurement results). In order to achieve this, rather than solutions obtained by decomposition of the extended matrix model on the singular values (SVD), solutions based on the minimization of Lagrange's objective function (Euler-Lagrange's method) are developed...
Keywords:Matematičko modeliranje,Gauss-Markov-ljev metod, Gauss-Helmert-ov metod, Potpuni metod najmanjeg kvadrata; Mathematic modelling, Gauss-Markov model, Gauss-Helmert model, Total Least Squares (TLS).