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.
The article deals with the problem of geodetic monitoring of the technical condition of underwater gas pipeline crossings. The theoretical scheme of increasing the accuracy of depth determination is studied in detail. In this paper, the goal is to increase the accuracy of obtaining the depth of the gas pipeline. The accuracy of the planned position for the largest survey scale (1:500) is 0.75 meters and is achieved using satellite equipment, even without the use of a dynamic positioning system, which allows, if necessary, to increase the accuracy of the data obtained by determining the orientation angles of the vessel. Despite the high popularity of this complex, the accuracy of depth measurements does not correspond to regulatory documents, which raises the question of the need to change the method of measurement and data processing, since the performance of work on monitoring the technical condition of gas pipelines is an important and relevant task. In order to control the developed methodology and automate measurement processing, two programs were written in the Python 3.7 programming language in the Spyder environment.
The article considers the theoretical component of Newton’s second-order method, its main advantages and disadvantages when used in geodesy. The algorithm for determining the minimum of target functions by the Newton method of the second order was studied and analyzed in detail. Parameters of connection between flat rectangular coordinate systems are calculated. The task of determining the transition keys is relevant for geodesy. Comparative analysis of Newton’s method with the method of conjugated gradients was carried out. The algorithm for solving this problem was implemented in the Visual Basic for Applications software environment. The obtained data allow us to conclude that the Newton method can be used more widely in geodesy, especially in solving nonlinear optimization problems. However, the successful implementation of the method in geodetic production is possible only if the computational process is automated, by writing software modules in various programming languages to solve a specific problem.
The article provides general information on nonlinear methods of programming. The algorithm for determining the minimum of various target functions by Newton’s method of the second order is considered. The article presents the main advantages and disadvantages of the method. A circular approximation of the chimney measurement results is performed using Newton's method. The algorithm for solving these tasks was implemented in the Visual Basic for Applications software environment. The comparative analysis was held based on Newton’s method of the second order with the gradient methods for solving engineering and geodetic tasks. The data obtained allow considering the possibility of the further application of Newton’s method in geodesy, especially while solving nonlinear optimization problems. The development of modern technology allows to automate the computing process by writing specific software modules. This makes the process of calculating parameters convenient for the surveyor, as it relieves them from routine calculations.
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