Page - 27 - 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

this is the light-time correction∆ρTOF. Further, a correction for the delay in the KBR signal propagation due to the ionosphere ∆ρIono is applied. Also considering the unknown ambiguity n due to the interferometric nature of the KBR observation and some random error e, the complete ranging equation is (Kim and Tapley, 2002) ρCOM= ρKBR+∆ρAOC+∆ρTOF+∆ρIono+n+e . (4.3.7) GRACE data is often not processed using biased range observations, but using derived range rate or range acceleration observations (Wu, Kruizinga, and Bertiger, 2006). The basis vector of the LOSF is e= u ‖u‖ . (4.3.8) As a very good approximation, the range rate is the projection of the differential velocity u˙= r˙B− r˙A onto the basis vector ρ˙COM= 〈e,u˙〉 , (4.3.9) while the range acceleration is, with the projection of the differential acceleration u¨= r¨B− r¨A, ρ¨COM= 〈e,u¨〉+〈e˙,u˙〉 . (4.3.10) The appropriate corrections for range rate or range acceleration observations can be obtained by differentiating the corrections computed for ranges numerically. In science mode, the satellites are steered in such a way that the KBR antenna phase centres are aligned with the satellite baselineu, their line of sight (LOS), to within a few milliradians. This pointing mode avoids multipath effects in the KBR observa- tions (Kirschner, Montenbruck, and Bettadpur, 2001). In this mode, the x-axes of the respective K-frames are not parallel to the satellite velocity vector, instead the satellites orbit with a pitch angle θA/B of 0.4° to 2.2°, as illustrated in fig. 4.4. In case of perfect steering to this nominal orientation, the LOSF and the KF coincide. GRACE-A LOS GRACE-B Flight direction r˙A r˙B xKFxKF rBrA θA θB Figure 4.4: In-orbit formation of the GRACE satellites in science mode with pitch bias θA/B. Adapted from Kirschner, Montenbruck, and Bettadpur (2001). 4.3 Observation Geometry 27