Processing of measures measured in underground polygonations

The information, which is the concrete basis for solving geodetic and topographic problems, comes from measurement observations made on quantities that are mainly angles and distances. The quality of the observations has an important role in achieving the objectives for which they are executed, in conditions of efficiency and safety. As topographically, underground works are conducted using polygonal paths, the methods used for processing measurements are of great interest. The quality of the observations obtained from the measurements is a direct function of the volume of the observations and the accuracy of the instruments and techniques for their processing. It is necessary, on the basis of the purpose for which the measurements are made, to establish the appropriate values in terms of size and accuracy, taking into account the economic aspect of the volume of necessary and sufficient observations required. Considering the importance of underground polygons in the management of mining, hydrotechnical works, roads, etc., it is necessary to process the measured quantities (angles, distances) by rigorous methods based on the theory of small squares. Underground polygons can be simple or networked [1]. However, as the networks are formed by simple polygonal routes, such a route will be analyzed (Figure 1). Fig. 1. Polygonal path. * Corresponding author: larisafilip@yahoo.com © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). MATEC Web of Conferences 342, 02018 (2021) https://doi.org/10.1051/matecconf/202134202018 UNIVERSITARIA SIMPRO 2021

The coordinates of points A, B, P, Q are known as given quantities and angles , respectively distances as natural quantities.
To determine the coordinates of the points 1, 2, … , 1, it is necessary and important to process the measured quantities in order to obtain their probable values.
For this purpose, it is observed that there are three quantities measured in addition to the required number, respectively the distance and angles , . As a result, three geometric conditions must be met [2]: -a condition of guidelines -two coordinate conditions The conditions are expressed by the equations: For the first group, the system of normal equations is [3]: and corrections are obtained with the equalities: For the second group, the coefficients must be transformed. Thus, the correction coefficients will be B and C obtained with the equalities: But according to the scheme 1: The system of normal equations for the system of error equations of group II is [3]: 0 0 (10) By solving the system(10) the correlates are obtained , that: Total corrections are obtained: In topographic practice, there are frequent cases when the angles of the polygons are measured with high precision. This is achieved by small non-concluding on the orientations and consequently small corrections of the angles.
In such a situation the measured angles are considered with the same precision, and the non-closing on the orientations is distributed in equal parts on all the measured angles.
With the angles thus corrected (compensated) the orientations of the sides are calculated and together with them the coordinates of the points of the polygon.
It turns out that only the sides can be further processed compensated. There will be only two conditions for which there are two equations of form: cos cos ⋯ cos 0 (13) sin sin ⋯ sin 0 Weights are introduced for sides of different lengths, but we consider the above artifice and consequently in the following calculations we do not use weights. For the system (13) of normal equations is:

1, 2, … ,
In practice there is often a particular case regarding the geometric shape of the polygonal path [4]. There are polygonal paths developed in the AB direction with the measured angles close to200 . For such routes the orientations of the sides and direction they are equal. The mentioned equations are multiplied by cos and sin after which by assembly it results: As a result, the system of error equations has the form: ⋯ cos sin 0 Analyzing the system of error equations (20) it is found that in the first two equations there are errors of angles and in equation 3 errors of sides. The conclusion is that in polygons made in one direction, the errors of lengths act distinctly from the errors of angles.
Moreover, in the system of normal equations the correlation coefficients and are equal to zero.
It is also found that the terms free and are obtained with relationships: By analyzing the polygonal paths performed on the processing of the measured quantities, methods are established that have the role of contributing to the increase of safety in the execution of the underground objectives.