Taking into account the influence of errors of initial points when assessing the accuracy of mine survey triangulation networks

Abstract

When using formulas of the theory of errors and the method of least squares for assessing the accuracy of triangulation networks, it is necessary to strive for the most complete consideration of all sources of errors that affect the accuracy of determining the elements of the network. This applies primarily to the influence of errors in the initial data, the issue of taking into account which has repeatedly attracted the attention of geodesists and mine surveyors. In the existing works devoted to this issue, the most detailed solution is based on the direct application of the main formula of the theory of errors to the function of interest to us, which is preliminarily expressed through directly measured quantities (see article). The strict formulas given in the mentioned works, however, are difficult to apply to the analysis of the accuracy of mine survey triangulations, which are usually rigid networks of the lowest construction queues and have a significant amount of initial data. The use of these formulas is associated with the production of very cumbersome calculations that do not have sufficient clarity and hide from the calculator the mechanism of accumulation of errors in the network, thereby complicating the transition to approximate methods of assessing accuracy. To solve some specific problems of assessing the accuracy of network elements encountered in mine surveying practice, it is possible to derive special formulas that solve these problems much more simply and clearly.