Page - 51 - 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

superposition of accelerations due to gravitational, tidal, and non-conservative forces f(τ)=g(τ)+ r¨ACC(τ) . (6.4.1) In ITSG-Grace2016, the parameters to be estimated are divided in groups along similar lines. The first parameter grouppgrav contains the parameters due to gravitational effects. These parameters are common to both satellites, as they move in the same conservative potential field. The second parameter grouppsat contains the parameters describing the dependence of the observations on non-conservative forces. These are specific to each satellite. These two sets of parameters pgrav and psat are force model parameters, and are computed through integrating the parameter sensitivity matrix in the variational equations. A third parameter grouppsst is neither specific to each satellite nor to the potential fields in which the satellite move, but rather describes effects due to the specific ll-SST observation system and geometry. The ll-SST parameterspsst are computed using the dynamic orbits resulting from the variational equations as a Taylor point. 6.4.1 Force Model Parameters To compute Zp(τ), the partials of the forcef(τ)w.r.t. the force model parameters are needed. The following paragraphs give a short description of how these are obtained and then integrated. Gravity Field Parameters In ITSG-Grace2016, both monthly mean and daily mean Stokes coefficients for each day of the month k∈ [1,K] are estimated. The total disturbing potential on the k-th day of the month Vtk is modelled as the sum of the monthly mean potential V m and the mean of the potential for that day Vdk Vtk=V m+Vdk . (6.4.2) The total potential for the month can be written as a piecewise constant function Vt(t)=Vm+ K ∑ k=1 δk(t)Vdk (6.4.3) as illustrated in fig. 6.5, and with δk(t)= { 1 if t is on the k-th day, 0 otherwise. (6.4.4) 6.4 Functional Models 51