Mathematical Model for Processing Two-Dimensional Geodetic Networks Using Classical and Satellite Technologies
Mathematical Model for Processing Two-Dimensional Geodetic Networks Using Classical and Satellite Technologies

Summary/Abstract: GNSS technology has increasingly gained traction in the field of geodesy due to its numerous advantages. This paper proposes a case study where this technology was used to perform measurements on a geodetic network at the Râușor Dam between certain points where there were obstacles to performing measurements using the classical method (due to the positioning of the points, existing vegetation, or even the dam itself).To achieve the best possible ratio between the true value of the measured quantity and the obtained value, the data acquired from the network was processed to adjust for the inevitable errors that occur during the measurement process. Using the initial coordinates, the distances and orientations between the measured points were calculated. To formulate the correction equations and establish weights, coefficients for directions and distances were calculated, along with the variation in orientation and distance as a function of variations in planar coordinates and the free term, which are necessary elements. For the normalization of the linear equation system and solving the normal system, the matrix of the normal system N and its inverse Q were calculated, followed by calculating the vector of unknown parameters. With these elements, the necessary corrections for the measurements were calculated, resulting in the most probable coordinates of the new points.The novelty of this mathematical model lies in the combination of classical and satellite measurements by introducing a transformation parameter regarding rotation into the adjustment process. To verify if the adjusted elements meet the conditions of the functional model, a control of the results is performed after the adjustment. To conclude the observation processing, calculations for evaluating precision indicators are carried out, followed by the graphical representation of the error ellipse, which indicates the confidence domain in the 2D position of a point. Finally, the results obtained after processing the network are presented, including the most probable coordinates of the new points, the precision estimates of the unknown parameters, and the elements of the obtained ellipses.The case study demonstrated how GNSS technology offers advantages in this field (such as the lack of necessity for visibility between points), but also disadvantages, such as the lower precision of GNSS measurements compared to those made using classical methods. GNSS measurements are redundant, providing, in some cases, the ability to detect errors in the adjustment of classical measurements.

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