Parameter estimation and accuracy analysis of the free geodetic network adjustment using singular value decomposition
Article (Published version)
MetadataShow full item record
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.
Keywords:geodetic networks / least square method / linear systems / singular value decomposition
Source:Tehnički vjesnik / Technical Gazette, 2014, 21, 2, 451-456
- Faculty of Mechanical Engineering in Slavonski Brod, Faculty of Electrical Engineering in Osijek, Faculty of Civil Engineering in Osijek