Page - 57 - 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

the linearised observation equation system for one short arc can be set up symbolically, giving      ∆lpod,A ∆lpod,B ∆lsst lgpm      =        A grav,d pod,A A sat pod,A 0 0 A grav,d pod,B 0 A sat pod,B 0 A grav,d sst A sat sst,A A sat sst,B A sst sst A grav,d gpm 0 0 0 · · · · · · Astatepod,A 0 A grav,m pod,A 0 Astatepod,B A grav,m pod,B Astatesst,A A state sst,B A grav,m sst 0 0 0                    ∆pgrav,d ∆psat,A ∆psat,B ∆psst ∆y0,A ∆y0,B ∆pgrav,m              , (6.4.32) or l=Ax in short. The indices for the arc m and day k have been omitted here for clarity. In eq. (6.4.32), empty matrix segments appear where the observations do not depend on the sought parameters. The POD observations for GRACE-A, for example, depend neither on the accelerometer calibration parameters for GRACE-B nor on that spacecraft’s initial state. When accumulating the observation equations, care has to be taken to not mix up parameters referring to only a specific day with other parameters of the same type referring to another day. An ordering for the parameter vector, and accordingly the blocks in the normal equation system, has to be chosen that ensures that the correct observation equations are accumulated together. Table 6.2 gives a summary of all P=46842 parameters estimated for a typical 31 day ITSG-Grace2016 monthly solution. Table 6.2: Estimated parameters for a month of K=31 days Type Parameter Parametrization Intervals Per Interval Total Potential cnm,snm D/O 2 to 40 Daily 957 29967 Potential cnm,snm D/O 2 to 120 Monthly 14637 14637 ACC bias b UCBS Daily 21 / sat 1302 ACC scale S Constant Daily 9 / sat 558 APC vector c Constant Monthly 3 / sat 6 Initial State y0 - Daily 6 / sat 372 Total 46842 6.4 Functional Models 57