Advances in Geosciences www.adv-geosci.net 1680-7340 1680-7359 1 G1. The new gravity field mission (CHAMP, GRACE, GOCE): from measurements to geophysical interpretation 2003 10.5194/adgeo-1-87-2003 http://www.adv-geosci.net/1/87/2003/ http://www.adv-geosci.net/1/87/2003/adgeo-1-87-2003.html http://www.adv-geosci.net/1/87/2003/adgeo-1-87-2003.pdf 87 94 2003-06-30 On the joint inversion of SGG and SST data from the GOCE mission P. Ditmar P. Visser R. Klees Physical, Geometrical and Space Geodesy (FMR), Faculty of Civil Engineering and Geosciences (CiTG), Delft University of Technology (TUD), Thijsseweg 11, 2629 JA Delft, The Netherlands Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands The computation of spherical harmonic coefficients of the Earth’s gravity field from satellite-to-satellite tracking (SST) data and satellite gravity gradiometry (SGG) data is considered. As long as the functional model related to SST data contains nuisance parameters (e.g. unknown initial state vectors), assembling of the corresponding normal matrix must be supplied with the back-substitution operation, so that the nuisance parameters are excluded from consideration. The traditional back-substitution algorithm, however, may result in large round-off errors. Hence an alternative approach, back-substitution at the level of the design matrix, is implemented. Both a stand-alone inversion of either type of data and a joint inversion of both types are considered. The conclusion drawn is that the joint inversion results in a much better model of the Earth’s gravity field than a standalone inversion. Furthermore, two numerical techniques for solving the joint system of normal equations are compared: (i) the Cholesky method based on an explicit computation of the normal matrix, and (ii) the pre-conditioned conjugate gradient method (PCCG), for which an explicit computation of the entire normal matrix is not needed. The comparison shows that the PCCG method is much faster than the Cholesky method.<br><br><b>Key words.</b> Earth’s gravity field, GOCE, satellite-tosatellite tracking, satellite gravity gradiometry, backsubstitution