Towards an optimal combination of satellite data and prior information

With the CHAMP and GRACE satellite gravity missions and the upcoming GOCE mission, millions of gravity-related observations are being released to the geodetic community. In order to provide an optimal gravity model in a statistical sense, it is common practice to combine satellite-only normal equations with prior information derived from terrestrial data or from previous satellite missions in the form of an existing gravity model. The weighting could be derived from formal error estimates, but more often these are adjusted based on heuristics like inspection of the residuals or of subset solutions. In recent years, rigorous approaches based on variance component estimation techniques have been developed and enjoy increasing popularity. At the same time, these techniques aim to provide more realistic error assessments of the combination solutions.

[1]  A. Eicker,et al.  ITG-CHAMP01: a CHAMP gravity field model from short kinematic arcs over a one-year observation period , 2005 .

[2]  Georgia Fotopoulos,et al.  Calibration of geoid error models via a combined adjustment of ellipsoidal, orthometric and gravimetric geoid height data , 2005 .

[3]  C. Jekeli.  The determination of gravitational potential differences from satellite-to-satellite tracking , 1999 .

[4]  J. Kusche,et al.  Continental hydrology retrieval from GPS time series and GRACE gravity solutions , 2007 .

[5]  N. K. Pavlis,et al.  The Development of the Joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) Geopotential Model EGM96 , 1998 .

[6]  M. Rothacher,et al.  Kinematic and reduced-dynamic precise orbit determination of low earth orbiters , 2003 .

[7]  N. Crocetto,et al.  Simplified formulae for the BIQUE estimation of variance components in disjunctive observation groups , 2000 .

[8]  Jürgen Kusche,et al.  Stochastic model validation of satellite gravity data: A test with CHAMP pseudo-observations , 2005 .

[9]  David E. Smith,et al.  The Development of the NASA GSFC and NIMA Joint Geopotential Model , 1997 .

[10]  M. Sideris.  Gravity, Geoid and Geodynamics 2000 , 2002 .

[11]  J. Kusche,et al.  A Monte-Carlo technique for weight estimation in satellite geodesy , 2003 .

[12]  E. C. Pavlis,et al.  An improved error assessment for the GEM-T1 gravitational model , 1989 .

[13]  Karl-Rudolf Koch,et al.  Maximum likelihood estimate of variance components , 1986 .

[14]  Nico Sneeuw,et al.  Energy integral method for gravity field determination from satellite orbit coordinates , 2003 .

[15]  Calyampudi R. Rao,et al.  Linear Statistical Inference and Its Applications. , 1975 .

[16]  C. Kotsakis.  A type of biased estimators for linear models with uniformly biased data , 2005 .

[17]  C. R. Rao,et al.  Estimation of variance and covariance components--MINQUE theory , 1971 .

[18]  Jean-Charles Marty,et al.  Long-wavelength global gravity field models: GRIM4-S4, GRIM4-C4 , 1997 .

[19]  B. Schaffrin,et al.  Integrating Heterogeneous Data Sets with Partial Inconsistencies , 2001 .