Study on the Influence of Reference Data on the Processing of Geodetic Monitoring Networks
Study on the Influence of Reference Data on the Processing of Geodetic Monitoring Networks

Summary/Abstract: The purpose of this work is twofold. Initially, it started with the desire to study potential displacements of characteristic points located on the Pecineagu Dam. Subsequently, we realized that determining the generalized inverse is an important and current topic, so we decided to pursue both aspects in parallel: monitoring the behavior of the characteristic points on the dam and determining the generalized inverse using three methods. The motivation for this study stems from the importance of dams for both the population and nature, serving multiple roles such as flood protection, irrigation, electricity production, and more.The initial data consisted of the provisional coordinates of the new points and measurements of distances and directions conducted within a local network. This network is formed by six new points (6, 7, 8, Ro, 12, 13) included in the geodetic network located at the Pecineagu Dam, a 107-meter-high rockfill dam on the Dâmbovița River in Argeș. Initially, we calculated the coefficients for distances and directions as well as the orientation angle of each station, which were later used in developing the stochastic functional model. The next step was outlining the three methods we used for determining the generalized inverse.The first method involved determining the generalized inverse using the "pinv" function integrated into the Octave application. To extract the A, P, and l matrices from the functional model, we applied the first equivalence rule, aiming to eliminate the unknowns associated with the stations orientation angles, replacing each unknown with a sum equation.The second method involved applying the S transformation with a partial minimum condition. To determine the generalized inverse using the transformation matrix S, it was necessary to first apply a reduction to the network's center of gravity regarding the coordinates. At this stage, the initial functional model was used without applying the equivalence rule.The third method was applying the "pinv" function using the initial functional model without applying the equivalence rule.After determining the generalized inverse, we proceeded with determining the corrections, applying them, and calculating the precisions and the elements of the error ellipses. As can be observed from the results, methods 1 and 2 yielded the same final matrices (both Q and x), while applying the "pinv" function without eliminating the orientation unknowns of the stations resulted in different outcomes that cannot be further used in the continuation of the adjustment. After calculating the characteristic elements of the ellipses, the precision was significantly better in the 2020 stage compared to the 2023 stage. Regarding the monitoring of the characteristic points between 2020-2023, the Fischer test was passed marginally, prompting me to also apply the Student's test. The result indicated that point 12 had displaced in both directions, while point 13 displaced only in the East direction.

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