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The Accuracy Analysis of Methods to solve the Geodetic Inverse Problem
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 Title & Authors
The Accuracy Analysis of Methods to solve the Geodetic Inverse Problem
Lee, Yong-Chang;
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 Abstract
The object of this paper is to compare the accuracy and the characteristic of various methods of solving the geodetic inverse problem for the geodesic lines which be in the standard case and special cases(antipodal, near antipodal, equatorial, and near equatorial situation) on the WGS84 reference ellipsoid. For this, the various algorithms (classical and recent solutions) to deal with the geodetic inverse problem are examined, and are programmed in order to evaluate the calculation ability of each method for the precise geodesic determination. The main factors of geodetic inverse problem, the distance and the forward azimuths between two points on the sphere(or ellipsoid) are determined by the 18 kinds of methods for the geodetic inverse solutions. After then, the results from the 17 kinds of methods in the both standard and special cases are compared with those from the Karney method as a reference. When judging these comparison, in case of the standard geodesics whose length do not exceed 100km, all of the methods show the almost same ability to Karney method. Whereas to the geodesics is longer than 4,000km, only two methods (Vincenty and Pittman) show the similar ability to the Karney method. In the cases of special geodesics, all methods except the Modified Vincenty method was not proper to solve the geodetic inverse problem through the comparison with Karney method. Therefore, it is needed to modify and compensate the algorithm of each methods by examining the various behaviors of geodesics on the special regions.
 Keywords
Geodetic inverse problem;geodesic;special cases;Karney method;
 Language
Korean
 Cited by
 References
1.
Bessel F.W. (1825), 'The calculation of longitude and latitude from geodesic measurements (1825)', Astron. Nachr. 331(8), pp. 852-861(2010); translated by C. F. F. Karney and R. E. Deakin. Preprint :arXiv : 0908.1824. crossref(new window)

2.
Bessel F.W. (1826), 'On the computation of geographical longitude and latitude from geodetic measurements', Astronomical Notes, Volume 4, Number 86, columns pp. 241-254.

3.
Bomford G. (1980), 'Geodesy', 4th Ed., Oxford University Press, Oxford, U.K.

4.
Borre Kai(2001), 'Ellipsoidal Geometry and Conformal Mapping', March 2001.

5.
Bowring B.R. (1981), 'The Direct and Inverse Problems for Short Geodesic Lines on the Ellipsoid', Surveying and Mapping, 41, 2, pp. 135-141.

6.
Bowring B.R. (1983), 'The Geodesic Inverse Problem', Bull. Geod. 57, pp. 109-120. crossref(new window)

7.
Bowring B.R. (1996), 'Total inverse solutions of the geodesic and great elliptic', Survey Review, 33 (261), pp. 461-476. crossref(new window)

8.
Deakin R.E. and Hunter M.N. (2007), 'Geodesics on an ellipsoid - Pittman's Method'. Presented at the Spatial Sciences Institute Biennial International Conference.

9.
Fichot M. and Gerson M. (1937), 'La Zone Geodesique Antipode, in Annales Hydrographiques, 3' sene', Tome Quinzieme, Service Hydrographique De Le Marine, Paris.

10.
Gupta R.M. (1972), 'A Comparative Study of Various direct and Inverse Foemulae for Lines up to 800km in Ellipsoidal Geodesy', M.S. thesis, The Ohio State University.

11.
Helmert F.R. (1964), 'Mathematical and Physical Theories of Higher Geodesy', Part 1, Aeronautical Chart and Information Center (St. Louis), Chaps. pp. 5-7.

12.
Hooijberg Maarten (1997), 'Practical Geodesy using computers', Sringer verlag Berlin Heidelberg.

13.
Jank W. and Kivioja L.A. (1980), 'Solution of the direct and inverse problems on reference ellipsoids by point-by-point integration using programmable pocket calculators', Surveying and Mapping, XL(3), pp. 325-337.

14.
Jekeli Christopher (2006), 'Geometric Reference Systems in Geodesy', OSU.

15.
Karney Charles F. F. (2010), 'GeographicLib, version 1.7', http://geographiclib.sf.net.

16.
Karney Charles F. F. (2011), 'Geodesics on an ellipsoid of revolution', arXiv:1102.1215v1, [physics.geo-ph].

17.
Kivioja L.A. (1971), 'Computation of geodetic direct and indirect problems by computers accumulating increments from geodetic line elements.', Bull.Geod., 99, pp. 55-63. crossref(new window)

18.
Krakiwsky E.J. and Thomson D.B. (1974), 'Geodetic position computations', Lecture notes, No.39, Dept. of Surveying and Engineering, Univ. of New Brunswick, Fredericton.

19.
Lambert W.D. (1942), 'The distance between two widely separated points on the surface of the earth', Journal of the Washington Academy of Sciences, Vol. 32, No. 5, pp. 125-130.

20.
Lewis E.A. (1963), 'Parametric Formulas for Geodesic Curves and Distances on a Slightly Oblate Earth', Air Force Cambridge Research Laboratories, Note No. 63-485, AD412501.

21.
Maxima (2009)', A computer algebra system', version 5.20.1.

22.
Pittman, M.E.(1986), 'Precision direct and inverse solutions of the geodesic', Surveying and Mapping, Vol.46, No.1, pp. 47-54.

23.
Rainsford H.F. (1955), 'Long geodesics on Ellipsoid', Bull. Geod., No.37, pp. 12-22.

24.
Rapp R.H. (1991), 'Geometric geodesy Part I', The Ohio State Univ. Rapp R.H. (1993), 'Geometric Geodesy Part II', OSU.

25.
Robbins A.R. (1962), 'Long lines on the spheroid.', Surv. Rev., XVI(125), pp. 301-309. crossref(new window)

26.
Saito T. (1970), 'The computation of long geodesics on the ellipsoid by non-series expanding procedure', Bulletin Geodesique, No. 98, pp. 341-374.

27.
Saito T. (1979), 'The computation of long geodesics on the ellipsoid through Gaussian quadrature', Bulletin Geodesique, Vol. 53, No. 2, pp. 165-177. crossref(new window)

28.
Sjoberg Lars E. (2006), 'New solutions to the direct and indirect geodetic problems on the ellipsoid', zfv, 2006(1):36 pp. 1-5.

29.
Sodano E.M. (1965), 'General non-iterative solution of the inverse and direct geodetic problem', Bull. Geod., No. 75.

30.
Thien G. (1967), 'A Solution to the Inverse Problem for Nearly-Antipodal Points on the Equator of the Ellipsoid of Revolution', M.S. thesis, The Ohio State University.

31.
Thomas C.M. and Featherstone W.E. (2005), 'Validation of Vincenty's Formulas for the Geodesic Using a New Fourth-Order Extension of Kivioja's Formula', Journal of Surveying Engineering, ASCE, pp. 20-26.

32.
Vermeille H. (2002), 'Direct transformation from geocentric coordinates to geodetic coordinates', J. Geod., 76(9), pp. 451-454. crossref(new window)

33.
Vincenty T. (1975a), 'Direct and Inverse Solutions of Geodesics on the Ellipsoid with Application of Nested Equations', Survey Review XXII, 176, pp. 88-93.

34.
Vincenty T. (1975b), 'Geodetic inverse solution between antipodal points', unpublished report, pp. 1-12.