Bulletin géodésique

, Volume 61, Issue 1, pp 21–40 | Cite as

Averaging two functions

  • Helmut Moritz


The paper treats the problem of averaging two independent determinations of the same function (curve, surface, etc.). Starting from the simple arithmetic mean, the problem is successively generalized to scalar and vector functions, arriving at an integral equation of Wiener-Hopf type. Aspects of least-squares collocation are also included. Finally the problem of determining transformation parameters and other systematic deviations is treated, furnishing a simple example of continuous least-squares adjustment.


Integral Formula True Error Simple Arithmetic Error Covariance Matrix Physical Geodesy 
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  1. J. EEG: Continuous methods in least squares theory. Proceedings of the VIII Symposium on Mathematical Geodesy (Como, Sept. 1981), Firenze, 1983.Google Scholar
  2. W.A. HEISKANEN and H. MORITZ: Physical Geodesy. W.H. Freeman, San Francisco, 1967. (Reprint available from Institute of Theoretical Geodesy, Technical University, Graz, Austria.)Google Scholar
  3. H. MORITZ: Fehlertheorie der graphisch-mechanischen Integration: Grundzüge einer allgemeinen Fehlertheorie im Funktionenraum. Sonderheft 22, Österr. Zeitschrift für Vermessungswesen, Wien, 1961.Google Scholar
  4. H. MORITZ Integral formulas and collocation. Report 234, Dept. of Geodet. Science, Ohio State Univ., Columbus, 1975.Google Scholar
  5. H. MORITZ: Advanced Physical Geodesy. Herbert Wichmann, Karlsruhe, and Abacus Press, Tunbridge Wells, Kent, 1980.Google Scholar
  6. Yu. M. NEYMAN: Probabilistic modification of Stokes' formula for the computation of height anomalies (in Russian). Geod. Aerofotosyemka, pp. 21–24, 1974.Google Scholar
  7. C.C. TSCHERNING, F. SANSÓ and D. ARABELOS: Merging regional geoids: preliminary considerations and experiences. Presented at Symposium on the Definition of the Geoid Firenze, Italy, May 1986.Google Scholar

Copyright information

© Bureau Central de L’Association Internationale de Géodésie 1987

Authors and Affiliations

  • Helmut Moritz
    • 1
  1. 1.Technical UniversityGraz(Austria)

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