Optimization Method Based on Minimization M-Order Central Moments Used In Surveying Engineering Problems

Sławomir Cellmer

University of Warmia and Mazury in Olsztyn

Andrzej Bobojć




Abstract

A new optimization method presented in this work – the Least m-Order Central Moments method, is a generalization of the Least Squares method. It allows fitting a geometric object into a set of points in such a way that the maximum shift between the object and the points after fitting is smaller than in the Least Squares method. This property can be very useful in some engineering tasks, e.g. in the realignment of a railway track or gantry rails. The theoretical properties of the proposed optimization method are analyzed. The computational problems are discussed. The appropriate computational techniques are proposed to overcome these problems. The detailed computational algorithm and formulas of iterative processes have been derived. The numerical tests are presented, in order to illustrate the operation of proposed techniques. The results have been analyzed, and the conclusions were then formulated.


Keywords:

the Least Squares method, the Newton method, objective function, m-estimation, surveying engineering

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Published
2021-05-31 — Updated on 2021-06-15

Cited by

Cellmer, S., & Bobojć, A. (2021). Optimization Method Based on Minimization M-Order Central Moments Used In Surveying Engineering Problems. Technical Sciences, 24(1), 39–49. https://doi.org/10.31648/ts.6555

Sławomir Cellmer 
University of Warmia and Mazury in Olsztyn
Andrzej Bobojć 




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