Pregledni rad

Parameter estimation and accuracy analysis of the free geodetic network adjustment using singular value decomposition

Branko Božić ; University of Belgrade, Faculty of Civil Engineering, Department of Geodesy and Geoinfomatics, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia
Kornelija Ristić ; University of Belgrade, Faculty of Civil Engineering, Department of Geodesy and Geoinfomatics, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia
Marko Pejić ; University of Belgrade, Faculty of Civil Engineering, Department of Geodesy and Geoinfomatics, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia

Sažetak

In order to determine the vector of the coordinates of the free geodetic networks by the least square adjustment, it is necessary to solve a singular system of linear equations and to find the inverse of a singular matrix. It is well known that there is a unique inverse of a regular square matrix. The main question is how to find the inverse of a singular matrix. This paper describes the traditional approach to the solving of the singular problem in opposition to the singular value decomposition (SVD). To exemplify, a free two-dimensional (2D) geodetic network was used to obtain and compare both the traditional and the SVD solutions. The analysis of the two approaches to the problem solving is of particular interest to this work. The advantages of the SVD approach are summarized and suggested to be used more frequently.

Ključne riječi

geodetic networks; least square method; linear systems; singular value decomposition

Hrčak ID:

120400

URI

https://hrcak.srce.hr/120400

Datum izdavanja:

26.4.2014.

Podaci na drugim jezicima: hrvatski

Posjeta: 3.409 *