Testing straightness of line objects using total least squares

Abstract

The paper presents the adaptation (fitting) of a set of points, with an estimated two-dimensional positions, to the straight line model of the by the application of the Weighted Total Least Squares, WTLS. The traditional method to solve this problem by using an iterative algorithm of the conditional adjustment with the parameters (Gauss-Helmert's model) is also shown. In the example of testing the straightness of the rail of the crane, a comparison of the efficiency of the two algorithms is performed by means of result of parameter estimation and to the number of required iterations to final solution.

U radu je prikazano adaptiranje (fitovanje) skupa tačaka, sa ocenjenim dvodimenzionalnim pozicijama, na model prave linije primenom težinskog potpunog metoda najmanjih kvadrata (Weighted Total Least Squares, WTLS). Prikazan je takođe i tradicionalni postupak rešavanja ovog problema primenom iterativnog algoritma uslovnog izravnanja sa parametrima, odnosno Gauss-Helmertovog modela. Na primeru testiranja pravosti kranske šine, izvršeno je upoređivanje efikasnosti ova dva algoritma u pogledu rezultata ocenjivanja parametara izravnavajuće prave i brzine konvergencije ka finalnom rešenju.