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 takes into account both random errors of observation vector and coefficient matrix based on errors-in-variables (EVI) model, it is possible to improve the accuracy more than the result of LS method. Therefore, 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 applied less widely to geodetic network adjustment problems than to other fields.
Kim Jung Hyang, a researcher at the Faculty of Earth Science and Technology, has proposed an application method for the adjustment of triangulation network, based on the brief summarization of the algorithm of WTLS.
The key problem in the application of WTLS to the adjustment of geodetic network is to determine the weight matrix (or cofactor matrix) for the elements of coefficient matrix in the adjustment function model.
He proposed a method to determine cofactor matrix for errors of coefficient matrix and observation vector in triangulation network, and verified the effectiveness of the proposed method through an example applied to the simulation triangulation network.
You can find more information in his paper “Study on triangulation network adjustment by Total Least Square Method” in “ADVANCES IN GEODESY AND GEOINFORMATION” (SCI).
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