Page - 26 - 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

4.3 Observation Geometry The fundamental quantities when describing GRACE observations are the positions of the two satellites,rA andrB, given in the CRF, and their orientation in spaceRA and RB, giving a rotation from the CRF to the respective SRF. The vectorial difference of the satellites’ centres of mass is given by u=rB−rA . (4.3.1) The satellite range is then ρCOM=‖u‖ . (4.3.2) This is however not what is observed by the KBR system. The KBR observation is instead the range as observed from the K-band antenna phase centre on GRACE-A to the K-band antenna phase centre on GRACE-B, as illustrated in fig. 4.3. The range as observed by the KBR is in fact ρKBR=‖(rB+RBcB)−(rA+RAcA)‖ , (4.3.3) wherecA/B are the calibrated coordinates of the GRACE KBR antenna phase centres given in the respective SRF. More compactly, it is ρKBR=‖u+v‖ (4.3.4) with v=RBcB−RAcA . (4.3.5) The range observation as made by the KBR is thus too small, and must be corrected with the antenna offset correction (AOC) ∆ρAOC= ρCOM−ρKBR=‖u‖−‖u+v‖ . (4.3.6) In addition to this purely geometrical correction, the ranging observation must also be corrected for the distance the satellites travelled during the signal time-of-flight, cA rA rB cB ρKBR ρCOM zSRF xSRF xSRF zSRF GR AC E-A GRACE-B Figure 4.3: Observation geometry of the GRACE KBR measurement. Chapter4 The GRACE Satellites26