Height transformation models from ellipsoidal into the normal orthometric height system for the territory of the City of Zagreb
Tóm tắt
The paper presents the testing of the possibility of determining the heights of GPS points in the homogeneous field in the new Croatian Height Reference System (HVRS71) by using the method of height transformation. The testing was made in the area of Zagreb. As part of the field works, normal orthometric heights of 27 GPS points were determined according to the new height system, by transferring the benchmark heights using the geometric levelling method, thus obtaining GPS/levelling points of known ellipsoidal and normal orthometric heights. The GPS/levelling points served as the basis for determining the transformation models that enabled the computation of normal orthometric heights from ellipsoidal heights of any GPS point in the observed area. The empirical data used for modelling were reduced undulation dN values of GPS/levelling points. As part of the dN modelling with parametric functions, the approximation surfaces were obtained on the basis of three polynomials: FN310, FN312 and FN318. The transformation models were also tested using non-parametric Watson and Loess algorithms. The FN318 and Loess models yielded the best results.
Tài liệu tham khảo
Akima H., 1978. A method of bivariate interpolation and smooth surface fitting for irregularly distributed data points. ACM Trans. Math. Softw., 4, 144–159.
Akima H., 1996. Algorithm 761: scattered-data surface fitting that has the accuracy of a cubic polynomial. ACM Trans. Math. Softw., 22, 362–371.
Bašić T., Brkić M. and Sünkel H., 1999. A new, more accurate geoid for Croatia. Phys. Chem. Earth (A), 24, 67–72.
Bašić T., 2001. Detail model of geoid of Republic of Croatia HRG200. Almanac of State Geodetic Administration of Republic of Croatia, Reports of Scientific-Professional Projects of Year 2000, 11–2 (in Croatian).
Cleveland W.S., 1993. Visualizing Data. Hobart Press, Lafayette, IN, USA.
Čolić K., 1998. GPS Network of City of Zagreb, Book 1–4. State Geodetic Administration of Republic of Croatia, Faculty of Geodesy, Zagreb, Croatia (in Croatian).
Dinter G., Illner M. and Jäger R., 1997. A synergetic approach for the transformation of ellipsoidal heights into a standard height reference system (HRS). In: Gubler E. and Hornik H. (Eds.), EUREF Publ. No.6, Bayerische Kommission für die Internationale Erdmessung, No. 58, München, Germany, ISBN 3 7696 9621 2.
Draper N.R. and Smith H., 1998. Applied Regression Analysis. Third Edition. John Wiley & Sons Inc., New York.
Feil L., 1989. Theory of Errors and Adjustment Computations-First Part. University of Zagreb, Faculty of Geodesy, Zagreb, Croatia (in Croatian).
Feil L., Rožić N., Pavičić S. and Gucek M., 2003. Documentation Necessary for Putting Croatian Height Datum in Official Use. University of Zagreb, Faculty of Geodesy, Zagreb, Croatia (in Croatian).
Gucek M., 2005. Determination of Normal Orthometric Heights of GPS Heights Homogeneous Field by Transformation Method. Master Thesis, University of Zagreb, Faculty of Geodesy, Zagreb, Croatia.
Heiskanen A.W. and Moritz H., 1996. Physical Geodesy. Freeman and Co., San Francisco, London.
Kavouras M., 1982. On the detection of outliers and determination of reliability in geodetic networks. Technical Report No.87, Department of Surveying Engineering, University of New Brunswick, Canada.
Niemeier W., 2002. Ausgleichungsrechnung. Eine Einführung für Studierende und Praktiker des Vermessungs-und Geoinformationswesens. Walter de Gruyter, Berlin, New York (in German).
Official Gazette, 2001. Program of state survey and real estate cadastre for period 2001–2005. Official Newspaper of Republic of Croatia, No.64, 1948–1954.
Official Gazette, 2004. Resolution for establishing official geodetic datum and Cartography projection of Republic of Croatia. Official Newspaper of Republic of Croatia, 110/04, 117/04.
Renka R.J., 1996. Algorithm 751: TRIPACK: A constrained two-dimensional Delaunay triangulation package. ACM Trans. Math. Softw., 22, 1–8.
Sambridge M., Braun J. and McQueen H., 1995. Geophysical parameterisation and interpolation of irregular data using natural neighbours. Geophys. J. Int., 122, 837–857.
Soycan M. and Soycan, A. 2003. Surface modelling for GPS-levelling geoid determination. Newton’s Bulletin, No.1, 11–17.
Švehla D., 1997. Preliminary Determination of Astrogeodetic Geoid of City of Zagreb. Diploma Thesis, University of Zagreb, Faculty of Geodesy, Zagreb, Croatia (in Croatian).
Torge W., 1989. Gravimetry. Walter de Gruyter, Berlin, New York.
Torge W., 2001. Geodesy. Walter de Gruyter, Berlin, New York.
Zhong D., 1997. Robust estimation and optimal selection of polynomial parameters for the interpolation of GPS geoid heights. J. Geodesy, 71, 552–561.