Least-squares geopotential approximation by windowed fourier transform and wavelet transform

Driscoll J.R., Healy D.M.: Computing Fourier Transforms and Convolutions on the 2-Sphere. Adv. Appl. Math., 15, (1996), 202–250.Google Scholar

Freeden, W.: Über eine Klasse von Integralformeln der Mathematischen Geodäsie. Veröff. Geod. Inst. RWTH Aachen, Heft 27, 1979.Google Scholar

Freeden, W.: On the Approximation of External Gravitational Potential With Closed Systems of (Trial) Functions., Bull. Geod., 54, (1980), 1–20.Google Scholar

Freeden, W.: Least Squares Approximation by Linear Combinations of (Multi-) Poles. Dept. Geod. Sci., 344, The Ohio State University, Columbus, 1983Google Scholar

Freeden, W.: A Spline Interpolation Method for Solving Boundary-value Problems of Potential Theory from Discretely Given Data. Numer. Meth. Part. Diff. Eqs., 3, (1987), 375–398.Google Scholar

Freeden, W.: Multiscale Modelling of Spaceborne Geodata, Teubner-Verlag, Stuttgart Leipzig, 1999.Google Scholar

Freeden, W., Gervens, T., Schreiner, M.: Constructive Approximation on the Sphere (with Applications to Geomathematics), Oxford Science Publications, Clarendon Press, Oxford, 1998.Google Scholar

Freeden, W., Glockner, O., Schreiner, M.: Spherical Panel Clustering and Its Numerical Aspects. J. of Geod., 72, (1998), 586–599.Google Scholar

Freeden, W., Kersten, H.: A Constructive Approximation Theorem for the Oblique Derivative Problem in Potential Theory. Math. Meth. in the Appl. Sci., 3, (1981), 104–114.Google Scholar

Freeden, W., Michel, V.: Constructive Approximation and Numerical Methods in Geodetic Research Today — An Attempt at a Categorization Based on an Uncertainty Principle., J. of Geod. (accepted for publication).Google Scholar

Freeden, W., Schneider, F.: An Integrated Wavelet Concept of Physical Geodesy. J. of Geod., 72, (1998), 259–281.Google Scholar

Freeden, W., Schneider, F.: Wavelet Approximation on Closed Surfaces and Their Application to Bounday-value Problems of Potential Theory. Math. Meth. Appl. Sci., 21, (1998), 129–165.Google Scholar

Freeden, W., Windheuser, U.: Spherical Wavelet Transform and its Discretization. Adv. Comp. Math., 5, (1996), 51–94.Google Scholar

Gabor, D.: Theory of Communications. J. Inst. Elec. Eng. (London), 93, (1946), 429–457.Google Scholar

Heil, C.E., Walnut, D.F.: Continuous and Discrete Wavelet Transforms. SIAM Review, 31, (1989), 628–666.Google Scholar

Kaiser, G.: A Friendly Guide to Wavelets. Birkhäuser-Verlag, Boston, 1994.Google Scholar

Kellogg, O.D.: Foundations of Potential Theory. Frederick Ungar Publishing Company, 1929.Google Scholar

Lemoine, F.G., Smith, D.E., Kunz, L., Smith, R., Pavlis, E.C., Pavlis, N.K., Klosko, S.M., Chinn, D.S., Torrence, M.H., Williamson, R.G., Cox, C.M., Rachlin, K.E., Wang, Y.M., Kenyon, S.C., Salman, R., Trimmer, R., Rapp, R.H., Nerem, R.S.: The Development of the NASA, GSFC, and NIMA Joint Geopotential Model. International Symposium on Gravity, Geoid, and Marine Geodesy, The University of Tokyo, Japan, Springer, IAG Symposia, 117, 1996, 461–469.Google Scholar

Michel, V.: A Multiscale Method for the Gravimetry Problem — Theoretical and Numerical Aspects of Harmonic and Anharmonic Modelling, PhD University of Kaiserslautern, Geomathematics Group, Shaker-Verlag, Aachen, 1999.Google Scholar

Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. W.H. Freeman and Company, New York, 1970.Google Scholar

Müller, C.: Spherical Harmonics, Lecture Notes in Mathematics, no. 17, Springer-Verlag, Heidelberg, 1966.Google Scholar

Rapp, R.H., Wang, M., Pavlis, N.: The Ohio State 1991 Geopotential and Sea Surface Topography Harmonic Coefficient Model. Dept. Geod. Sci., 410, The Ohio State University, Columbus, 1991.Google Scholar

Schwintzer, P., Reigber, C., Bode, A., Kang, Z., Zhu, S.Y., Massmann, F.H., Raimondo, J.C., Biancale, R., Balmino, G., Lemoine, J.M., Moynot, B., Marty, J.C., Barlier, F., Boudon, Y.: Long Wavelength Global Gravity Field Models: GRIM4-S4, GRIM4-C4. J. of Geod., 71, (1997), 189–208.Google Scholar