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Adjustment of Planned Surveying and Geodetic Networks Using Second-Order Nonlinear Programming Methods

Department of Engineering Geodesy, Saint-Petersburg Mining University, 199106 Saint-Petersburg, Russia
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Author to whom correspondence should be addressed.
Academic Editor: Demos Tsahalis
Computation 2021, 9(12), 131; https://doi.org/10.3390/computation9120131
Received: 8 November 2021 / Revised: 29 November 2021 / Accepted: 1 December 2021 / Published: 3 December 2021
(This article belongs to the Section Computational Engineering)
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. View Full-Text
Keywords: nonlinear programming; optimization methods; geodetic computations; Newton’s method; trilateration network; conjugate gradient method nonlinear programming; optimization methods; geodetic computations; Newton’s method; trilateration network; conjugate gradient method
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MDPI and ACS Style

Mustafin, M.; Bykasov, D. Adjustment of Planned Surveying and Geodetic Networks Using Second-Order Nonlinear Programming Methods. Computation 2021, 9, 131. https://doi.org/10.3390/computation9120131

AMA Style

Mustafin M, Bykasov D. Adjustment of Planned Surveying and Geodetic Networks Using Second-Order Nonlinear Programming Methods. Computation. 2021; 9(12):131. https://doi.org/10.3390/computation9120131

Chicago/Turabian Style

Mustafin, Murat, and Dmitry Bykasov. 2021. "Adjustment of Planned Surveying and Geodetic Networks Using Second-Order Nonlinear Programming Methods" Computation 9, no. 12: 131. https://doi.org/10.3390/computation9120131

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