Testing straightness of line objects using total least squares
Testiranje pravosti linijskih objekata primenom potpunog metoda najmanjih kvadrata
Апстракт
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.
Кључне речи:
errors in variables models / weighted total least squares / Gauss-Helmert's model / modeli sa greškama promenljivih / potpuni metod najmanjih kvadrata / Gauss-Helmertov modelИзвор:
Tehnika, 2017, 72, 2, 187-191Издавач:
- Savez inženjera i tehničara Srbije, Beograd
Институција/група
GraFarTY - JOUR AU - Popović, Jovan AU - Aleksić, Ivan R. AU - Božić, Branko AU - Milovanović, Branko AU - Todorović-Drakul, Miljana PY - 2017 UR - https://grafar.grf.bg.ac.rs/handle/123456789/841 AB - 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. AB - 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. PB - Savez inženjera i tehničara Srbije, Beograd T2 - Tehnika T1 - Testing straightness of line objects using total least squares T1 - Testiranje pravosti linijskih objekata primenom potpunog metoda najmanjih kvadrata EP - 191 IS - 2 SP - 187 VL - 72 DO - 10.5937/tehnika1702187P ER -
@article{ author = "Popović, Jovan and Aleksić, Ivan R. and Božić, Branko and Milovanović, Branko and Todorović-Drakul, Miljana", year = "2017", 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.", publisher = "Savez inženjera i tehničara Srbije, Beograd", journal = "Tehnika", title = "Testing straightness of line objects using total least squares, Testiranje pravosti linijskih objekata primenom potpunog metoda najmanjih kvadrata", pages = "191-187", number = "2", volume = "72", doi = "10.5937/tehnika1702187P" }
Popović, J., Aleksić, I. R., Božić, B., Milovanović, B.,& Todorović-Drakul, M.. (2017). Testing straightness of line objects using total least squares. in Tehnika Savez inženjera i tehničara Srbije, Beograd., 72(2), 187-191. https://doi.org/10.5937/tehnika1702187P
Popović J, Aleksić IR, Božić B, Milovanović B, Todorović-Drakul M. Testing straightness of line objects using total least squares. in Tehnika. 2017;72(2):187-191. doi:10.5937/tehnika1702187P .
Popović, Jovan, Aleksić, Ivan R., Božić, Branko, Milovanović, Branko, Todorović-Drakul, Miljana, "Testing straightness of line objects using total least squares" in Tehnika, 72, no. 2 (2017):187-191, https://doi.org/10.5937/tehnika1702187P . .