Seite - 50 - 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

Dynamic Orbit and Variational Equation Integration ACC KBR re, r˙eVcons r, r˙ Φ Fit of Dynamic Orbit to hl-SST and ll-SST Observations POD Dynamic Orbit and Variational Equation Integration r, r˙ Φ Φ Input Data Intermediate Results Final Results xcal r, r˙ Figure 6.4: Data flow in ITSG-Grace2016 dynamic orbit integration for one spacecraft. Vcons are the background models from which the accelerations due to conservative forces are derived, as given in table 6.1.Φ is the state transition matrix of the variational equations.xcal are the co-estimated calibration parameters for the accelerometer. An initial integration step using background models, the level 1B dynamic orbit, and the accelerometer observations as input is followed by an orbit fit to KBR and POD data, as described above. The resulting dynamic orbit and calibration parameters are used to re-integrate the orbit once more to ensure convergence. This results in the final dynamic orbit and state transition matrix, which are used in the set-up of GRACE hl-SST and ll-SST observation equations. It is important that all calibration and state parameters estimated here are also re-estimated when computing the final gravity field models, so as to not bias the solution towards the a priori models used in the orbit integration. 6.4 Functional Models All observation equations for GRACE in ITSG-Grace2016 are derived using variational equations.Afterdeterminingthedynamicorbit forbothGRACEspacecraftasdescribed in chapter 5 and section 6.3, the parameter sensitivity matrix for each spacecraft is computed from eq. (5.3.13). Here, the matrixZp from eq. (5.3.9) describing the dependence of the forces acting on the satellite on some parameters p is needed. At this point, recall that f(τ) is in fact a rather complex function, describing the Chapter6 ITSG-Grace201650