The study and analysis of approximate methods of equalization is of great practical importance. It is obvious that in all cases, approximate methods of equalization give results less accurate compared to the results that can be obtained by equalization by the method of least squares (provided that it is correctly applied). Therefore, the practical use of approximate methods is due only to the desire to reduce the labor intensity of equalization calculations.

In connection with the development in recent years of methods of light-location and radiolocation, interest in the problem of processing geodetic networks with measured side lengths has increased significantly. In this paper we consider the question of equalization of a continuous network with measured side lengths, dividing it into sections and simultaneously using the methods of conditional and mediocre measurements. This method of equalization can be applied in the case when due to the peculiarities of the network construction it is more reasonable to process one part of it by the method of conditional and the other — by the method of mediocre measurements.

Experimental work on the use of radar system of RGSC for justification of regional gravimetric survey in sparsely populated areas of the USSR showed that ground radio stations in some cases can not be located in sufficient proximity to the reference geodetic points, winterization of radio stations and therefore reduces the effectiveness of radio geodesic methods.

When creating a survey base by radio-geodetic methods, the coordinates of points are usually determined from the solution of linear serifs on two measured distances with the use of formulas ...

The article studies the relationship between the errors in the position of two mine triangulation points rigidly inserted into the existing base network, with their separate and joint adjustment. The solution to this problem is of considerable interest to mine surveying practice when replenishing the existing mine triangulation network with new points as mining operations develop. In this case, when inserting new points, the mine surveyor is forced to accept previously determined points as initial ones, due to which sometimes a significant number of stages in constructing the network arises and its accuracy is reduced to a certain extent. The mine surveyor must be able to quantitatively assess the loss of accuracy of network elements caused by separate adjustment of existing and newly determined points, and on this basis decide on the choice of one or another scheme for inserting points and the most appropriate use of the reference network when solving mine surveying and other engineering problems. If the mine network points are determined simultaneously, then preference, of course, should be given to their joint adjustment, since under normal conditions it always increases the weight to a certain extent elements of the network. But even in this case, the results obtained in the article are of interest, since they shed new light on the issue of the relationship between the weights of network elements in separate and joint equalization of the points being determined and allow a more correct assessment of the merits of the latter.

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.

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.

The method of multi-group equalization by the method of indirect observations, proposed by I. Yu. Pranis-Pranevich, has now received very wide application in the Soviet Union in equilibration of large filling networks of class II. This method is not entirely rigorous and leads to results somewhat different from the results obtained with strict joint equalization of the network by the method of indirect observations in corrections to directions. In this article, we will give a quantitative estimate of the distortions in the network arising from the non-rigor of the multi-group equalization method, and we will show that without significantly complicating the equalization calculations, these distortions can be almost completely eliminated.