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New Covariance Models for Local Applications of Collocation

  • R. Barzaghi
  • A. Borghi
  • G. Sona
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 122)

Abstract

The least-squares collocation method, used to predict or filter a signal, is based on the estimation of the empirical covariance function and the fitting of the empirical values with a proper model function. Generally, with the standard methods on the sphere, we reach a good fitting only up to the first zero of the empirical function. In this work we have investigated how much the collocation filtering is affected by a poor fitting of the empirical covariance.

Numerical tests have been done both on 1D observed and simulated data to quantify the combined impact on filtering of non stationarity and covariance fitting.

Furthermore, a new model function on the sphere has been developed which is able to fit in an optimal way the empirical values.

Simulations have been also carried out on the sphere to test the effectiveness of the collocation filtering using the new covariance model.

Keywords

Covariance Function Legendre Polynomial Empirical Covariance Geoid Undulation Stationarity Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Albertella, A., Brovelli, M.A., and Sansò, F. (1994). What is a local solution in physical geodesy? Atti XIII Congresso Nazionale GNGTS, Roma 1994.Google Scholar
  2. Knudsen, P. (1987). Estimation and Modelling of the Local Empirical Covariance Function using gravity and satellite altimeter data. Bulletin Geodesique, 61:145–160.CrossRefGoogle Scholar
  3. Tscherning, C.C. (1994). Geoid Determination by Least-square Collocation Using GRAVSOFT-International School for the Determination and Use of the Geoid. In Lectures Notes, DIIAR, pages 135-164. Politecnico di Milano, October 10-15 1994.Google Scholar
  4. Tscherning, C.C. and Rapp, R. H. (1974). Closed Covariance Expressions for Gravity Anomalies Geoid Undulations, and the Deflections of the Vertical Implied by Anomaly Degree-Variance Models. Reports of the Department of Geodetic Science no. 208, The Ohio State University, Columbus, Ohio.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • R. Barzaghi
    • 1
  • A. Borghi
    • 1
  • G. Sona
    • 1
  1. 1.DIIAR—Politecnico di MilanoMilanoItaly

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