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Due to the huge amount of redundant data, the problem arises of finding a single integral solution that will satisfy numerous possible accuracy options. Mathematical processing of such measurements by traditional geodetic methods can take significant time and at the same time does not provide the required accuracy. This article discusses the application of nonlinear programming methods in the computational process for geodetic data. Thanks to the development of computer technology, a modern surveyor can solve new emerging production problems using nonlinear programming methods—preliminary computational experiments that allow evaluating the effectiveness of a particular method for solving a specific problem. The efficiency and performance comparison of various nonlinear programming methods in the course of trilateration network equalization on a plane is shown. An algorithm of the modified second-order Newton’s method is proposed, based on the use of the matrix of second partial derivatives and the Powell and the Davis–Sven–Kempy (DSK) method in the computational process. The new method makes it possible to simplify the computational process, allows the user not to calculate the preliminary values of the determined parameters with high accuracy, since the use of this method makes it possible to expand the region of convergence of the problem solution.

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During the construction and operation of buildings and structures, it is extremely important to ensure the accuracy of their geometrical parameters in nature. At the same time, accuracy requirements are constantly increasing. At the same time, studying such issues as consideration of geological factors, for example, consideration of the structural features of the buildings and structures foundations has remained virtually in the same state for decades. In the guidelines for observing the deformations of the basements and foundations of buildings and structures the earth’s surface is taken as homogeneous array, and it is recommended when observing deformations, to carry out laying initial benchmarks for industrial and civil objects at a distance of 50–100 m. A number of studies show that a homogeneous array should be considered as a special case. In fact, in the construction of various objects, heterogeneity of the soil massif in the form of stratification, as well as the presence of zones of tectonic disturbances are often encountered. The latter, in the form of faults and geopathic zones, are already taken into account in urban planning activities, medicine, and other areas. Without taking them into account, the creation of a geodetic center base during construction can lead to significant errors, due to the uneven deformation of the structure near fault zones. There is a need to assess the impact of these zones during construction and their consideration when creating a geodetic center base. Here it is necessary to emphasize the fact that ensuring the removal of the structure’s geometrical parameters into nature is the task of the geodetic service in any circumstances. The next important point in construction is to minimize the error of projecting geocentric coordinates onto a plane. This is especially true when using satellite coordinates. In the traditional approach, the coordinate basis for construction is normatively oriented to the use of the Gauss-Kruger projection. With extended objects in the latitudinal direction and remoteness from the axial meridian of the six-degree zone, the use of this projection causes transformation errors. When creating a geodesic framework according to satellite coordinates determinations, it is highly advisable to use local to-center topocentric flat surfaces, which allow a significant reduction in the distortion of the transformation. The authors discuss the solution of identified issues and provide specific examples.