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.
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References
Albertella, A., Brovelli, M.A., and Sansò, F. (1994). What is a local solution in physical geodesy? Atti XIII Congresso Nazionale GNGTS, Roma 1994.
Knudsen, P. (1987). Estimation and Modelling of the Local Empirical Covariance Function using gravity and satellite altimeter data. Bulletin Geodesique, 61:145–160.
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.
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.
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© 2001 Springer-Verlag Berlin Heidelberg
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Barzaghi, R., Borghi, A., Sona, G. (2001). New Covariance Models for Local Applications of Collocation. In: Benciolini, B. (eds) IV Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56677-6_15
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DOI: https://doi.org/10.1007/978-3-642-56677-6_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-62574-9
Online ISBN: 978-3-642-56677-6
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