Geoid height computation in strip-area project by using least-squares collocation

Abstract

GPS/leveling technique is the most effective engineering method for the determination of heights and height differences. This method is based on the principal of conversion of ellipsoid heights to orthometric heights. For transformation, polynomial surface models are generally used for study region or area. The accuracy of results depends on the location and distribution of selected reference stations with known ellipsoidal and orthometric heights. Especially, in the strip area projects (highway, railway, channel etc.) polynomial curve model is used instead of polynomial surface model due to reference stations disturbing along a route. In this research, Least Squares Collocation (LSC) methods used in determining the geoid heights of a strip area were examined. For this purpose, GPS/leveling data of Bozkurt-Dinar (Afyonkarahisar) train project which is approximately 75 km was used in order to examine LSC methods. The ground control stations of the project were classified as reference and test for the purpose of this research. The geoid heights of test stations were calculated by curve polynomial with different degrees. Additionally geoid heights at the same points were calculated using polynomial curve fitting based on LSC which is suggested by this research. The geoid heights by computed using LSC approach when compared to polynomial curve method were observed to yield better results. ARTICLE INFO

En Küçük Kareler Kollokasyon ve Kriging Yöntemleri ile Lokal Jeoid Belirleme

“…Jeoid belirleme yöntemleri, eldeki mevcut verilere ve kullanılan modellere göre sınıflandırılabilir (Sjöberg,1994;Bolat 2013 (Demirel, 1977;Doğanalp ve Selvi, 2015;Doğanalp, 2016 (Tscherning ve Rapp, 1974;Moritz, 1976;Musyoka, 1999;Krynski ve Lyszkowicz, 2006…”

“…En Küçük Kareler Kollokasyon (EKKK) yöntemi; matematiksel modeli bir kısmı olan fonksiyonel modelin sinyal adı verilen sapmaları içermesi durumda, en uygun kestirim değerlerinin en küçük kareler yöntemine göre belirlendiği bir enterpolasyon yöntemidir (Demirel, 1977). Bu yöntemin birçok kullanım alanı olduğu gibi jeodezik çalışmalarda da sıklıkla kullanılmıştır (Doğanalp, 2016;Doğanalp ve Selvi, 2015;Jarmolovski, 2013).…”

“…Bu fonksiyon lineer, polinomal, spline, trigonometrik olabilir (Demirel, 1977;. Doğanalp ve Selvi, 2015;Doğanalp, 2016). Bu çalışmada polinomsal enterpolasyon trend olarak seçilmştir.…”

Geoid undulation prediction using Gaussian Processes Regression: A case study in a local region in Turkey

“…where ℎ is the ellipsoidal height, is the orthometric height, and is the geoid undulation or geoid height. The geoid undulation determined by the GNSS/leveling technique can also be used as data in the determination of the geoid via various estimation techniques such as the interpolation, least-squares collocation (LSC) and geophysical gravity data inversion (GGI) methods (Kotsakis and Sideris, 1999;Tscherning et al, 2001;Erol et al, 2008;Trojanowicz, 2012Trojanowicz, , 2015Doganalp and Selvi, 2015;Doganalp, 2016;Karaaslan et al, 2016;Tusat and Mikailsoy, 2018;Trojanowicz et al, 2020). Several soft-computing methods have been applied as alternative techniques to produce accurate results in the prediction of geoid undulation, including the artificial neural network (ANN), least square support vector machines (LS-SVM), and adaptive neuro-fuzzy inference systems (ANFIS).…”

Local geoid determination using a generalized regression neural network and interpolation methods: A case study in Kars, Turkey

“…Creating and selecting the most appropriate and realistic model in geoid determination is extremely important for the practitioners using such models. In the literature to date, many interpolation and least square collocation methods have been used for the geometric modeling of local geoids (Zhan-ji and Yongqi, 1999;Yanalak and Baykal, 2001; Doganalp and Selvi, 2015;Doganalp, 2016;Karaaslan, et al, 2016;Şişman and Elevli, 2018;Yılmaz and Kuru, 2019;Yılmaz, 2019).…”