Open AccessPSEUDONORMAL OPTIMIZATION METHOD AND GEODESIC EQUATION CALCULATIONS
Author(s) -
А. Г. Барлиани,
Galina A. Nefedova,
Irina V. Karnetova
Publication year - 2020
Publication title -
vestnik sgugit
Language(s) - English
Resource type - Journals
ISSN - 2411-1759
DOI - 10.33764/2411-1759-2020-25-3-5-13
Subject(s) - moore–penrose pseudoinverse , least squares function approximation , triangulation , computer science , mathematics , algorithm , mathematical optimization , geodesic , parametric statistics , matrix (chemical analysis) , mathematical analysis , inverse , statistics , estimator , materials science , geometry , composite material
The purpose of this paper is a comparative analysis of the methods of least squares and pseudonormal optimization on the example of equalization and estimation of the accuracy of the first-class triangulation link. Pseudonormal optimization is radically different from the traditional method of least squares optimization, since it leads to complex and cumbersome procedures for equalizing and evaluating the accuracy of the results of processing geodesic constructions due to complex formulas. A recurrent method of sequential formation of a pseudoinverse matrix of parametric correction equations is presented, which allows avoiding the time-consuming computational process of composing and solving normal equations. A mathematical algorithm for estimating the accuracy of the equalized parameters is considered. The analysis of the equation works has shown that the pseudonormal optimization method allows calculating the values of the equalized coordinates 4 times more accurately than the least squares optimization.