Case Study
Dec 30, 2015

Empirical Research of Interpolation Methods in Distortion Modeling for the Coordinate Transformation between Local and Global Geodetic Datums

Publication: Journal of Surveying Engineering
Volume 142, Issue 2

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.

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References

Andrei, C. O. (2006). “3D affine coordinate transformations.” M.Sc. thesis, Royal Institute of Technology, Stockholm, Sweden.
Applebaum, L. T. (1982). “Geodetic datum transformation by multiple regression equations.” Proc., 3rd Int. Geodetic Symp. on Satellite Doppler Positioning, Defense Mapping Agency, Las Cruces, NM, 207–223.
Arya, S., Mount, D. M., Netanyahu, N. S., Silverman, R., and Wu, A. Y. (1998). “An optimal algorithm for approximate nearest neighbor searching fixed dimensions.” J. ACM, 45(6), 891–923.
Bašić, T. (2006). “Jedinstveni transformacijski model i novi model geoida Republike Hrvatske.” Izvješće o znanstveno-stručnim projektima, State Geodetic Administration, Zagreb, Croatia (in Croatian).
Blais, J. A. R. (1982). “Synthesis of Kriging estimation methods.” Manuscripta Geod., 7(4), 325–352.
Briggs, I. C. (1974). “Machine contouring using minimum curvature.” Geophysics, 39(1), 39–48.
Broekman, R., Marel, H., and Huisman, L. (2013). “National report of the Netherlands.” IAG Subcommission for Europe (EUREF) Symp., Budapest, Hungary.
Bursa, M. (1962). “The theory for the determination of the non-parallelism of the minor axis of the reference ellipsoid and the inertial polar axis of the Earth, and the planes of the initial astronomic and geodetic meridians from observations of artificial Earth satellites.” Stud. Geophys. Geod, 6, 209–214.
Collier, P. (2002). “Development of Australia’s national GDA94 transformation grids.” Consultant’s report to the Intergovernmental Committee on Surveying and Mapping, Univ. of Melbourne, Australia.
De Smith, M. J., Goodchild, M. F., and Longley, P. A. (2007). Geospatial analysis: A comprehensive guide to principles, techniques and software tools, Troubador Publishing, Market Harborough, U.K.
Dermanis, A. (1984). “Kriging and collocation: A comparison.” Manuscripta Geod., 9(3), 159–167.
Dewhurst, W. T. (1990). “The application of minimum-curvature-derived surfaces in the transformation of positional data from the North American Datum of 1927 to the North American Datum of 1983.” NOAA Technical Memorandum NOS NGS-50, Rockville, MD.
Draper, N. R., and Smith, H. (1998). Applied regression analysis, 3rd Ed., Wiley, New York.
Fan, J., and Gijbels, I. (1996). Local polynomial modelling and its applications: Monographs on statistics and applied probability, Vol. 66, Chapman and Hall/CRC, London.
Forsberg, R., and Tscherning, C. C. T. (2008). An overview manual for the GRAVSOFT geodetic gravity field modelling programs, DTU Space, Kongens Lyngby, Denmark.
Grafarend, E. W., and Syffus, R. (1998). “Transformation of conformal coordinates of type Gauss-Krüger or UTM from local datum (regional, national, European) to global datum (WGS 84) part 1: The transformation equations.” Allgemeine Vermessungs-Nachrichten, 105(1998), 134–141.
Herzfeld, U. C. (1992). “Least-squares collocation, geophysical inverse theory and geostatistics: a bird’s eye view.” Geophys. J. Int., 111(2), 237–249.
Hirvonen, R. A., and Moritz, H. (1963). “Practical computation of gravity at high altitudes.” Rep. No. 27, Institute of Geodesy Photogrammetry and Cartography, Ohio State Univ. Research Foundation, Columbus, OH.
Hofmann-Wellenhof, B., Lichtenegger, H., and Wasle, E. (2007). GNSS–global navigation satellite systems: GPS, GLONASS, Galileo, and more, Springer, New York.
Imrek, E. (2005). “Homogenisation of the Austrian field of control points–preparatory work for a higher absolute accuracy in cadastre.” Report on the Symp. of the IAG Subcommission for Europe (EUREF). Reports of the EUREF Technical Working Group (TWG) (No. 15, p. 153), Bundesamt für Kartographie und Geodäsie, Frankfurt am Main, Germany.
Junkins, D. R., and Farley, S. A. (1995). National Transformation Version 2, user’s guide, Geodetic Survey Division-Geomatics, Ottawa, Canada.
Karunaratne, F. L. (2007). “Finding out transformation parameters and evaluation of new coordinate system in Sri Lanka.” M.S. thesis, International Institute for Geo-information Science and Earth Observation, Enschede, The Netherlands.
Kempe, C., Alfredsson, A., Engberg, L. E., and Lilje, M. (2006). “Correction model to rectify distorted co-ordinate systems.” FIG XXIII Conf. Congress, Munich, Germany.
Kutoglu, H. S., and Ayan, T. (2006). “The role of common point distribution in obtaining reliable parameters for coordinate transformation.” Appl. Math. Comput., 176(2), 751–758.
Lam, N. S. N. (1983). “Spatial interpolation methods: A review.” Am. Cartographer, 10(2), 129–149.
Lancaster, P., and Salkauskas, K. (1981). “Surfaces generated by moving least squares methods.” Math. Comput., 37(155), 141–158.
Lapaine, M., and Tutić, D. (2007). “O novoj službenoj kartografskoj projekciji Hrvatske-HTRS96/TM.” Kartografija i Geoinformacije, 6, 35–53.
Lee, D. T., and Schachter, B. J. (1980). “Two algorithms for constructing a Delaunay triangulation.” Int. J. Comput. Inf. Sci., 9(3), 219–242.
Lu, G. Y., and Wong, D. W. (2008). “An adaptive inverse-distance weighting spatial interpolation technique.” Comput. Geosci., 34(9), 1044–1055.
Łukaszyk, S. (2004). “A new concept of probability metric and its applications in approximation of scattered data sets.” Comput. Mech., 33(4), 299–304.
Mikhail, E. M. (1976). Observations and least squares, IEP-A Dun-Donnelly, New York.
Moritz, H. (1978). “Least‐squares collocation.” Rev. Geophys., 16(3), 421–430.
Myers, D. E. (1992). “Kriging, cokriging, radial basis functions and the role of positive definiteness.” Comput. Math. Appl., 24(12), 139–148.
Nadaraya, E. A. (1964). “On estimating regression.” Theor. Probab. Appl., 9(1), 141–142.
Ordnance Survey. (2013). “A guide to coordinate systems in Great Britain: An introduction to mapping coordinate systems and the use of GPS datasets with ordnance survey mapping.” Technical Rep. v2.2, Ordnance Survey, Southampton, U.K.
Petit, G., and Luzum, B. (2010). “IERS conventions (2010).” Rep. No. IERS-TN-36, Bureau International des Poids et Mesures Sevres, Sèvres, France.
Powell, M. J. (1987). “Radial basis functions for multivariable interpolation: a review.” Algorithms for approximation, Clarendon Press, Oxford, U.K., 143–167.
Shepard, D. (1968). “A two-dimensional interpolation function for irregularly-spaced data.” Proc., 1968 23rd ACM National Conf., Association for Computing Machinery, New York, 517–524.
Sibson, R. (1981). “A brief description of natural neighbour interpolation.” Interpreting multivariate data, V. Barnett, ed., John Wiley, Chichester, U.K., 21–36.
Smith, W. H. F., and Wessel, P. (1990). “Gridding with continuous curvature splines in tension.” Geophysics, 55(3), 293–305.
Su, P., and Drysdale, R. L. S. (1997). “A comparison of sequential Delaunay triangulation algorithms.” Comput. Geom., 7(5–6), 361–385.
Surfer [Computer software]. Golden Software, Golden, CO.
T7D [Computer software]. State Geodetic Administration, Zagreb, Croatia.
Vaníček, P., and Steeves, R. R. (1996). “Transformation of coordinates between two horizontal geodetic datums.” J. Geod., 70(11), 740–745.
Wolf, H. (1963). “Geometric connection and re-orientation of three-dimensional triangulation nets.” Bull. Géod. (1946–1975), 68(1), 165–169.

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Go to Journal of Surveying Engineering
Journal of Surveying Engineering
Volume 142Issue 2May 2016

History

Received: Jul 22, 2014
Accepted: Aug 17, 2015
Published online: Dec 30, 2015
Published in print: May 1, 2016
Discussion open until: May 30, 2016

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Authors

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Marijan Grgić [email protected]
Research Assistant, Ph.D. Student, Faculty of Geodesy, Univ. of Zagreb, Kačićeva 26, 10000 Zagreb, Croatia (corresponding author). E-mail: [email protected]
Matej Varga [email protected]
Research Assistant, Ph.D. Student, Faculty of Geodesy, Univ. of Zagreb, Kačićeva 26, 10000 Zagreb, Croatia. E-mail: [email protected]
Tomislav Bašić [email protected]
Full Professor, Faculty of Geodesy, Univ. of Zagreb, Kačićeva 26, 10000 Zagreb, Croatia. E-mail: [email protected]

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