An Approximate Estimation of the Accuracy of the Sides of a Solid Filling Triangulation Network

Abstract

State triangulations developed in the form of continuous networks based on first-class series extend a single coordinate system over the territory of a mining basin and serve as a basis for developing reference mine survey networks. Using the sides of the state triangulation network as initial ones, the mine surveyor must naturally be able to at least approximately estimate their accuracy. This applies mainly to filling networks of the second class, which still have to be used as a basis for developing mine networks and which in some cases can only with difficulty provide the required accuracy. In this case, the mine surveyor is primarily interested in the errors in the lengths of the sides of the base network involved in scaling the mine triangulation. To perform an accuracy analysis, the mine surveyor usually has only the coordinates of the points and a diagram of the base network. This makes it very laborious to use strict formulas of the least squares method for assessing the accuracy and pushes the mine surveyor to use approximate methods for calculating errors, often not tested in practice. In this article, we study the mechanism of accumulation of errors of the sides and, on this basis, provide an analysis and further development of approximate methods for estimating the accuracy of the sides of a continuous filling network. In this case, we limited ourselves to considering only the errors of the network sides that depend on the influence of errors in the measured values ​​involved in the adjustment of the network, and did not touch on the issues of the influence of errors in the initial data.