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http://dx.doi.org/10.7848/ksgpc.2022.40.4.315

TLS (Total Least-Squares) within Gauss-Helmert Model: 3D Planar Fitting and Helmert Transformation of Geodetic Reference Frames  

Bae, Tae-Suk (Dept. Geoinformation Engineering, Sejong University)
Hong, Chang-Ki (Dept. Geoinformatics Engineering, Kyungil University)
Lim, Soo-Hyeon (Geoinformation Engineering, Sejong University)
Publication Information
Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography / v.40, no.4, 2022 , pp. 315-324 More about this Journal
Abstract
The conventional LESS (LEast-Squares Solution) is calculated under the assumption that there is no errors in independent variables. However, the coordinates of a point, either from traditional ground surveying such as slant distances, horizontal and/or vertical angles, or GNSS (Global Navigation Satellite System) positioning, cannot be determined independently (and the components are correlated each other). Therefore, the TLS (Total Least Squares) adjustment should be applied for all applications related to the coordinates. Many approaches were suggested in order to solve this problem, resulting in equivalent solutions except some restrictions. In this study, we calculated the normal vector of the 3D plane determined by the trace of the VLBI targets based on TLS within GHM (Gauss-Helmert Model). Another numerical test was conducted for the estimation of the Helmert transformation parameters. Since the errors in the horizontal components are very small compared to the radius of the circle, the final estimates are almost identical. However, the estimated variance components are significantly reduced as well as show a different characteristic depending on the target location. The Helmert transformation parameters are estimated more precisely compared to the conventional LESS case. Furthermore, the residuals can be predicted on both reference frames with much smaller magnitude (in absolute sense).
Keywords
GNSS (Global Navigation Satellite System); VLBI (Very Long Baseline Interferometry); IVP (InVariant Point); TLS (Total Least-Squares); GHM (Gauss-Helmert Model);
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