Abstract
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.
Highlights
Over the past thirty years, surveying and geodetic equipment has made a great leap forward
The second-order Newton’s method is an iterative method that applies a quadratic approximation to the original nonlinear objective function at each iteration
The authors of the article propose the creation of a software algorithm based on the second-order Newton’s method and on direct search methods, in particular the Powell method and the Davis–Sven–Kempy (DSK) method. The use of this software algorithm will enhance the positive aspects of the second-order Newton’s method, namely, to reduce the dependence on the preliminary values of the determined parameters. It would be convenient for the user to use an algorithm in which the number of iterations does not depend on the preliminary values of the parameters being determined
Summary
Over the past thirty years, surveying and geodetic equipment has made a great leap forward. Such a rapid development of technology allowed surveyors to receive and process an enormous amount of data about objects. The use of modern surveying and geodetic methods in the construction of buildings is especially important; this is noted in works [1,2], as well as when determining deformations [3]. An important element in the solution of any surveying and geodetic problems is the office processing of measurement results (rejection of gross errors, equalization, assessment of the accuracy of the solutions obtained). Redundancy of measurements increases the accuracy and plausibility of the obtained solutions; as the amount of information obtained increases, the complexity of data processing increases, as noted in articles [4,5]
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