Case Study
Empirical Research of Interpolation Methods in Distortion Modeling for the Coordinate Transformation between Local and Global Geodetic Datums Downloaded from ascelibrary.org by Colorado University at Boulder on 01/04/16. Copyright ASCE. For personal use only; all rights reserved.
Marijan Grgi c1; Matej Varga2; and Tomislav Bašic3
Abstract: Conformal coordinate transformations very often are not accurate enough to be used for the coordinate transformations between local and global geodetic datums because of the inhomogeneity of the spatial data in different geodetic datums. Therefore, distortion modeling is used to improve the accuracy of the coordinate transformations. This paper presents empirical research on distortion modeling methods used to improve the coordinate transformation process from local to global geodetic datum and vice versa. Various models of distortion shifts in different grid resolutions were computed, evaluated, and compared with the official Croatian model of distortion shifts. Tested modeling methods are inverse distance to a power, kriging, minimum curvature, modified Shepard’s method, natural neighbor, nearest neighbor, polynomial regression, radial basis function, triangulation with linear interpolation, moving average, local polynomial, and least-squares collocation. Distortion model performance was evaluated using summary statistics derived from the back-interpolation for the independent control spatial data set. The present paper proposes the most appropriate method(s) of distortion modeling for the Croatian case and gives brief instructions on possible coordinate transformation improvements of the official Croatian coordinate transformation. DOI: 10.1061/(ASCE)SU.1943-5428.0000154. © 2015 American Society of Civil Engineers. Author keywords: Coordinate transformation; Empirical comparison; Global coordinate datum; Interpolation methods; Local coordinate datum; Distortion modeling; Hrvatski drzavni koordinatni sustav (HDKS); Hrvatski terestricki referentni sustav (HTRS96).
Introduction The rapid growth of using global navigation satellite systems (GNSS) in the geosciences for both scientific and engineering purposes has necessitated the replacement of local coordinate systems with global coordinate systems (Hofmann-Wellenhof et al. 2007). In 2004, the Republic of Croatia proposed the new geocentric geodetic datum Croatian Terrestrial Reference System (Hrvatski terestricki referentni sustav, HTRS96) and recommended it for adoption by 2010. Therefore, direct and inverse coordinate transformation procedures have had to be defined and standardized to ensure flawless coordinate transformation between the new and the old local Croatian State Coordinate System (Hrvatski drzavni koordinatni sustav, HDKS). Generally, the coordinate transformation process has to provide efficient methods of coordinate transformation that would maintain the accuracy and the shape of the original data (Collier 2002; Kutoglu and Ayan 2006). Because of the inhomogeneity of the spatial data in both HDKS and HTRS96 and, consequently, the systematic pattern of coordinate distortions in each datum, conformal coordinate transformations that use only coordinate shift, rotation, and 1
Research Assistant, Ph.D. Student, Faculty of Geodesy, Univ. of Zagreb, Kaciceva 26, 10000 Zagreb, Croatia (corresponding author). E-mail: mgrgic@ geof.hr 2 Research Assistant, Ph.D. Student, Faculty of Geodesy, Univ. of Zagreb, Kaciceva 26, 10000 Zagreb, Croatia. E-mail:
[email protected] 3 Full Professor, Faculty of Geodesy, Univ. of Zagreb, Kaciceva 26, 10000 Zagreb, Croatia. E-mail:
[email protected] Note. This manuscript was submitted on July 22, 2014; approved on August 17, 2015; published online on December 30, 2015. Discussion period open until May 30, 2016; separate discussions must be submitted for individual papers. This paper is part of the Journal of Surveying Engineering, © ASCE, ISSN 0733-9453. © ASCE
scaling [e.g., Helmert 7-parameter (7-p) transformation] did not satisfy the required accuracy (Bašic 2006). Therefore, conformal transformations had to be extended for the distortion corrections that are usually interpolated from the models of coordinate shifts. In accordance with a widely accepted practice, the grid-based coordinate transformation, which integrates Helmert 7-p transformation and grid distortion modeling, was developed as the official coordinate transformation process in Croatia. Such grid-based transformation processes already have been adopted in many countries, such as the United States (Dewhurst 1990), Canada (Junkins and Farley 1995), Australia (Collier 2002), Austria (Imrek 2005), Germany (Kempe et al. 2006), United Kingdom (Ordnance Survey 2013), Netherlands (Broekman et al. 2013), and so on. Fig. 1 shows the coordinate transformation process from local to global geodetic datum and vice versa for the Croatian case. The grid-based transformation model includes 7-p transformation and coordinate corrections from the grid of coordinate shifts for planar coordinates. The grid of coordinate shifts was derived from the distortion residuals of common points by the least-squares collocation method traditionally used in physical geodesy (Herzfeld 1992). This transformation model was integrated into the T7D stand-alone software application (created by the University of Zagreb Faculty of Geodesy and Croatian State Geodetic Administration) (Bašic 2006) used in geodesy, surveying, photogrammetry, cartography, and related professions. Although the defined transformation model is already in use, external quality evaluation of the model was never performed. Furthermore, distortion modeling was done only using the leastsquares collocation method in a one-grid resolution (distortion grid cell size), and its performance was never compared with the other modeling methods. Also, in most countries, only a few methods were considered, such as multiple regression (Applebaum 1982),
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