Print Email Facebook Twitter How to deal with the high condition number of the noise covariance matrix of gravity field functionals synthesised from a satellite-only global gravity field model? Title How to deal with the high condition number of the noise covariance matrix of gravity field functionals synthesised from a satellite-only global gravity field model? Author Klees, R. (TU Delft Physical and Space Geodesy) Slobbe, D.C. (TU Delft Physical and Space Geodesy) Farahani, H. (TU Delft Novel Aerospace Materials) Date 2018-03-23 Abstract The posed question arises for instance in regional gravity field modelling using weighted least-squares techniques if the gravity field functionals are synthesised from the spherical harmonic coefficients of a satellite-only global gravity model (GGM), and are used as one of the noisy datasets. The associated noise covariance matrix, appeared to be extremely ill-conditioned with a singular value spectrum that decayed gradually to zero without any noticeable gap. We analysed three methods to deal with the ill-conditioned noise covariance matrix: Tihonov regularisation of the noise covariance matrix in combination with the standard formula for the weighted least-squares estimator, a formula of the weighted least-squares estimator, which does not involve the inverse noise covariance matrix, and an estimator based on Rao’s unified theory of least-squares. Our analysis was based on a numerical experiment involving a set of height anomalies synthesised from the GGM GOCO05s, which is provided with a full noise covariance matrix. We showed that the three estimators perform similar, provided that the two regularisation parameters each method knows were chosen properly. As standard regularisation parameter choice rules do not apply here, we suggested a new parameter choice rule, and demonstrated its performance. Using this rule, we found that the differences between the three least-squares estimates were within noise. For the standard formulation of the weighted least-squares estimator with regularised noise covariance matrix, this required an exceptionally strong regularisation, much larger than one expected from the condition number of the noise covariance matrix. The preferred method is the inversion-free formulation of the weighted least-squares estimator, because of its simplicity with respect to the choice of the two regularisation parameters. Subject Global gravity field modelLeast-squaresLocal quasi-geoidNoise covariance matrixRegularisationSpherical radial basis functionsUnified theory of least-squares To reference this document use: http://resolver.tudelft.nl/uuid:306ae6ce-65e0-487f-8f84-231d87e56f7d DOI https://doi.org/10.1007/s00190-018-1136-0 ISSN 0949-7714 Source Journal of Geodesy, 93 (2019), 29-44 Part of collection Institutional Repository Document type journal article Rights © 2018 R. Klees, D.C. Slobbe, H. Farahani Files PDF 10.1007_s00190_018_1136_0.pdf 2.43 MB Close viewer /islandora/object/uuid:306ae6ce-65e0-487f-8f84-231d87e56f7d/datastream/OBJ/view