Page - 101 - 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

cA e zSRF ySRF xSRF COMA βA COMB KBR antenna phase centre AOC A Figure 8.1: Opening angle for GRACE-A antenna phase centre vector. In theory, all quantities involved in the computation of the AOC are subject to some uncertainty. The uncertainty of the spacecraft orientation is known to some extent from the SCA/ACC sensor fusion, but as this fusion is based on a priori assumptions on the noise of the SCA and ACC observables, it can only be regarded as an approximation of the true uncertainties. The APC vectorscA andcB are determined through in-orbit calibration manoeuvres, and as such can not be expected to be error-free. Similarly, the baselinee is determined from the integrated dynamic orbits, and is certain to not represent the true relative positions of the satellites. The remainder of this chapter will focus on the uncertainty in the satellite orientation and its consideration in the gravity field adjustment, based on the formulation given in eq. (8.1.6). 8.1.2 AOC Covariance From Sensor Fusion The AOC as described in eq. (8.1.6) is a sum of two identical component summands, with only the rotation and APC vector specific to each satellite. It is thus sufficient to investigate variance propagation for only one summand, as the result for the other is then trivially obtained through substitution of these two quantities. To make this derivation easier to follow, the APC vector c and the satellite baseline ewill be subscripted with the coordinate system they are given in. The contribution to the AOC for one satellite is ∆ρsAOC= 〈 R˜SRFCRFcSRF,eCRF 〉 = ( R˜SRFCRFcSRF )T eCRF =cTSRF ( R˜SRFCRF )T eCRF . (8.1.8) The SCA/ACC sensor fusion gives uncertainties for small angle rotations in the SRF, but the rotaryR˜SRFCRF is a large rotation. So for variance propagation purposes, a suitable transformation is needed. To this end, a similar decomposition of the rotation as used in eq. (6.2.5) is employed, with R˜SRFCRF=R NOM CRF R˜ SRF NOM . (8.1.9) 8.1 The Antenna Offset Correction in the ll-SST Observation Equation 101