Page - 54 - in Contributions to GRACE Gravity Field Recovery - Improvements in Dynamic Orbit Integration, Stochastic Modelling of the Antenna Offset Correction, and Co-Estimation of Satellite Orientations

mean. This is sensible, as the mean of the monthly gravity field is parametrized in the monthly mean coefficients. Further, the temporal and spatial correlations of the daily gravity fields are loosely constrained to conform to a process model derived from geophysical models. This is implementedasasetofpseudo-observationsfor thegeophysicalmodel lgpm=0 for the daily gravity field parameters, with an associated design matrixAgpm and cofactor matrixQgpm:[ l lgpm ] = [ Ad Am Agpm 0 ][ pgrav,d pgrav,m ] (6.4.14) A more in-depth description of this procedure is out of scope for this thesis. The approach is based on the GRACE Kalman filter introduced by Kurtenbach, 2011. A complete description of the implementation details of this approach with the refine- ments and further development made for ITSG-Grace2016 will be able to be found in the upcoming dissertation of Andreas Kvas, expected to be released in 2019. Satellite Parameters The observation of the GRACE accelerometers are not only subject to random noise, but also to systematic effects due to miscalibration and instrument imperfections. In ITSG-Grace2016, calibration parameters are estimated for each accelerometer using the calibration equation r¨cal=Sr¨obs+b . (6.4.15) Here,S is a fully populated 3×3 matrix describing the accelerometer scale factors, cross-talk between the observation axes, and the misalignment of the accelerometer with the SRF. The vectorbparametrizes one bias per accelerometer axis. In ITSG-Grace2016, the entries inS are estimated as constants per day. The biasesb are estimated daily as uniform cubic basis splines (UCBS) with a knot interval of 6h. Klinger (2018) gives a comprehensive analysis of this parametrization. This results in 30 calibration parametersxcal being estimated per day and satellite. The parameter vector is psat= [ xcal,A,1 . . .xcal,A,K xcal,B,1 . . .xcal,B,K ]T (6.4.16) with the Jacobians Jsat,A(τ)= [ ∂ r¨ACC,A(τ) ∂xcal,A,1 · · · ∂ r¨ACC,A(τ) ∂xcal,A,K ] , (6.4.17) Jsat,B(τ)= [ ∂ r¨ACC,B(τ) ∂xcal,B,1 · · · ∂ r¨ACC,B(τ) ∂xcal,B,K ] . (6.4.18) Chapter6 ITSG-Grace201654