Weighted total least-squares joint adjustment with weight correction factors

Wang, Leyang; Yu, Hongkai

doi:10.1080/03610918.2018.1468450

Cited by 4 publications

(1 citation statement)

References 30 publications

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“…Recently most of all works on WTLS method focus on methods and applications for linear regression model fit, curved line fit and coordinate transformation (Deng, 2019;Fang, 2014;Fang, 2015;San, 2014;[20] Wang, 2016;Wang, 2019a;2019b). But due to the lack of general method to determine cofactor matrix of coefficient matrix of function model, it is restricted in practical application.…”

Section: Introductionmentioning

confidence: 99%

Study on triangulation network adjustment by Total Least Square Method

Kim,

2024

Advances in Geodesy and Geoinformation

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Generally, Least Squares (LS) Method treats only random errors of observation vector in adjustment function models. However, both observation vector and elements of coefficient matrix of adjustment function model contain random errors. Therefore, there is no guarantee that the result of adjustment by LS method is the global optimal solution. Total Least Square (TLS) method is a primary estimation method that treats random errors of observation vector and coefficient matrix in adjustment functional models. Since TLS method take into account both random errors of observation vector and coefficient matrix based on errors-in-variables model, it is possible to improve the accuracy compared with the result of LS method. So TLS method has been applied to different fields of science and technology including signal and image processing, computer vision,communication engineering and geodesy. However, weighted total least square (WTLS) method has been not applied in geodetic network adjustment problem compared with other fields widely. So the purpose of this paper is to summarize the algorithm of WTLS briefly and to propose an application method in adjustment of triangulation network. Key problem in application of WTLS to adjustment of geodetic network is to determine the weight matrix (or cofactor matrix) for elements of coefficient matrix in adjustment function model. In this paper proposed a method to determine cofactor matrix for errors of coefficient matrix in triangulation network, and verifies the effectiveness of suggested method through example applied to triangulation network.

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