Network adjustment

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Under network adjustment is in the Geodesy the application of the compensation calculation understood in geodetic measurements to coordinates in a network of points and to determine the best possible way to adapt to all available measurements.

The network, which is usually made up of triangles , angles and lines, is put into a computational model and the measurements are balanced using the least squares method . Prior to this, the approximate coordinates of the points involved must be determined, which serve to linearize the observation equations that are to be used for the compensation. The approximate coordinates are obtained from a preliminary calculation of the network, an earlier survey of the area or graphically from a map.

The mathematical process is usually an adjustment based on mediating observations . It minimizes the effect of the (inevitable) small measurement errors by limiting them to the smallest possible sum of squares. Are these measurement deviations randomly distributed, i. H. without systematic components, the balanced network is the theoretically achievable optimum. In a small-scale network, the measurement deviations are on average below 0.001  gon or 3 " , in first-order networks far below 1", which corresponds to a few millimeters per kilometer. In this way, point coordinates with accuracies in the centimeter range are achieved even in the case of extensive networks.

The better the network design ( symmetrical shape, sufficient overdetermination ), the more the advantages of network equalization come into play. It improves accuracy by an average of 30 to 60 percent and also increases reliability. Weakly integrated power supply units (e.g. brackets or imprecise sections) can be identified and, if necessary, supplemented by subsequent measurements.

The least squares method was developed by Carl Friedrich Gauß when he came across unexpected discrepancies in the measurements during the Hanoverian land survey in the Harz region . In 1799 he used the method for measuring the degree between Altona and Gotha in order to compensate for the triangular contradictions in the angle measurements of the triangulation . The quality of his results later enabled him to determine the refraction coefficient of the atmosphere; its value of 13% of the earth's curvature is still considered the standard for long net visors .

The Gaussian principle is still the most important compensation principle in geodetic measurements, but has been converted to the more modern notation of matrix calculation in the formula apparatus . For more complex tasks, it can be expanded to include collocation in order to be able to process non-geometric measured variables "in one go".

Before the age of  EDP , graphic compensation methods were also used, the principles of which were developed at the end of the 19th century. They take into account the influence of small angular errors on the point coordinates due to perpendiculars , which are plotted on the overview plan of the network across the respective sight.

For leveling and height networks, on the other hand, an iterative method of adjustment was developed, which was named military height adjustment . All measured height differences are written in a table and the contradictions (mm..cm per km) are smoothed out by systematic changes .

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Literature and web links