Open AccessOptimization method based on minimization m-Order central moments used in surveying engineering problems
Author(s) -
Sławomir Cellmer,
Andrzej Bobojć
Publication year - 2021
Publication title -
technical sciences
Language(s) - English
Resource type - Journals
eISSN - 2083-4527
pISSN - 1505-4675
DOI - 10.31648/ts.6555
Subject(s) - generalization , mathematical optimization , minification , least squares function approximation , set (abstract data type) , property (philosophy) , computer science , computational complexity theory , algorithm , optimization problem , method of moments (probability theory) , mathematics , mathematical analysis , philosophy , statistics , epistemology , estimator , programming language
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.