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Open AccessArticle

Determination of the Regularization Parameter to Combine Heterogeneous Observations in Regional Gravity Field Modeling

1
Deutsches Geodätisches Forschungsinstitut der Technischen Universität München (DGFI-TUM), Arcisstr. 21, 80333 Munich, Germany
2
Institute for Astronomical and Physical Geodesy, Technical University of Munich, Arcisstr. 21, 80333 Munich, Germany
*
Author to whom correspondence should be addressed.
Remote Sens. 2020, 12(10), 1617; https://doi.org/10.3390/rs12101617
Received: 16 April 2020 / Revised: 14 May 2020 / Accepted: 17 May 2020 / Published: 19 May 2020
(This article belongs to the Special Issue Geodesy for Gravity and Height Systems)
Various types of heterogeneous observations can be combined within a parameter estimation process using spherical radial basis functions (SRBFs) for regional gravity field refinement. In this process, regularization is in most cases inevitable, and choosing an appropriate value for the regularization parameter is a crucial issue. This study discusses the drawbacks of two frequently used methods for choosing the regularization parameter, which are the L-curve method and the variance component estimation (VCE). To overcome their drawbacks, two approaches for the regularization parameter determination are proposed, which combine the L-curve method and VCE. The first approach, denoted as “VCE-Lc”, starts with the calculation of the relative weights between the observation techniques by means of VCE. Based on these weights, the L-curve method is applied to determine the regularization parameter. In the second approach, called “Lc-VCE”, the L-curve method determines first the regularization parameter, and it is set to be fixed during the calculation of the relative weights between the observation techniques from VCE. To evaluate and compare the performance of the two proposed methods with the L-curve method and VCE, all these four methods are applied in six study cases using four types of simulated observations in Europe, and their modeling results are compared with the validation data. The RMS errors (w.r.t the validation data) obtained by VCE-Lc and Lc-VCE are smaller than those obtained from the L-curve method and VCE in all the six cases. VCE-Lc performs the best among these four tested methods, no matter if using SRBFs with smoothing or non-smoothing features. These results prove the benefits of the two proposed methods for regularization parameter determination when different data sets are to be combined. View Full-Text
Keywords: regional gravity field modeling; spherical radial basis functions; combination of heterogeneous observations; regularization parameter; VCE; the L-curve method regional gravity field modeling; spherical radial basis functions; combination of heterogeneous observations; regularization parameter; VCE; the L-curve method
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MDPI and ACS Style

Liu, Q.; Schmidt, M.; Pail, R.; Willberg, M. Determination of the Regularization Parameter to Combine Heterogeneous Observations in Regional Gravity Field Modeling. Remote Sens. 2020, 12, 1617.

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