• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.40 no.4
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• pp.315-324
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• 2022

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).

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.28 no.1
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• pp.153-160
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• 2010

It is necessary to determine accurate 3-dimensional coordinates of the building corner points that could be control or check points in order to verify the accuracy of 3D digital maps in the near future. The usual process of obtaining the coordinates of the building corner points is to set up the ground control points with a GPS and then to practice terrestrial survey such as distance or angle measurements. However, since an error in the ground control points can be propagated through the terrestrial survey into the final coordinates of the buildings, accurately should be considered as much as possible. The actual effect of the GPS-derived ground control point error on the estimates of the unknowns through the terrestrial survey is mathematically analyzed, and the simulation data is tested numerically. The error of the ground control points is tested in the cases of 1-4 cm for the horizontal components and 2-8 cm for the vertical component. The vertical component error is assigned twice the horizontal ones because of the characteristics of the GPS survey. The distance measurement is assumed for convenience and the precision of the estimated coordinates of the building corner points is almost linearly increased according to the errors of the ground control points. In addition, the final estimates themselves can vary by the simulated random errors depending on the precision of the survey instrument, but the precision of the estimates is almost independent of survey accuracy.