Page - 53 - 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

Low degree daily coefficients Low degree monthly coefficients High degree monthly coefficients Am Ad1 AdK ... ... Figure 6.6: Schematic of daily and monthly Stokes coefficients design matrix blocks. Identical colours indicate that the low degree daily coefficient blocks are identical to the low degree monthly coefficient blocks for the same day. They are then inserted into eq. (5.3.9) for integration. With the K-day vector of daily Stokes coefficients pgrav,d=     xd1 ... xdK     (6.4.10) and the vector of monthly Stokes coefficients pgrav,m=x m (6.4.11) the complete vector of gravity field parameters is pgrav= [ pgrav,d pgrav,m ] . (6.4.12) More compactly, eq. (6.4.5) can then be written as l= [ Ad Am ][pgrav,d pgrav,m ] (6.4.13) With this parametrization, the equation system is not solvable directly, as the columns ofAm with the low degree monthly Stokes coefficients are a linear combination of the daily coefficient blocks, inducing a rank defect in the normal equation system. In ITSG-Grace2016 this problem is treated by requiring the daily solutions to have zero 6.4 Functional Models 53