Regularization of gravity field estimation from satellite gravity gradients |
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Authors: | J Kusche R Klees |
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Institution: | (1) Delft Institute for Earth-Oriented Space Research (DEOS), Delft University of Technology, Thijsseweg 11, 2629 JA Delft, The Netherlands; e-mail: j.kusche@citg.tudelft.nl; Tel.: +31-15-278-2562; Fax: 31-15-278-3711, NL |
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Abstract: | The performance of the L-curve criterion and of the generalized cross-validation (GCV) method for the Tikhonov regularization
of the ill-conditioned normal equations associated with the determination of the gravity field from satellite gravity gradiometry
is investigated. Special attention is devoted to the computation of the corner point of the L-curve, to the numerically efficient
computation of the trace term in the GCV target function, and to the choice of the norm of the residuals, which is important
for the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) in the presence of colored observation noise. The
trace term in the GCV target function is estimated using an unbiased minimum-variance stochastic estimator. The performance
analysis is based on a simulation of gravity gradients along a 60-day repeat circular orbit and a gravity field recovery complete
up to degree and order 300. Randomized GCV yields the optimal regularization parameter in all the simulations if the colored
noise is properly taken into account. Moreover, it seems to be quite robust against the choice of the norm of the residuals.
It performs much better than the L-curve criterion, which always yields over-smooth solutions. The numerical costs for randomized
GCV are limited provided that a reasonable first guess of the regularization parameter can be found.
Received: 17 May 2001 / Accepted: 17 January 2002 |
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Keywords: | : GOCE – Satellite gravity gradiometry – Regularization – Generalized cross-validation – L-curve criterion |
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