Page - 136 - 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

Figure 9.5 shows that the change in AOC is smallest when all SCA heads are active (black, 57.8% of epochs), and largest when both spacecraft operate on one head only (red, 33.7% of epochs). Not conforming with the results from section 9.3.2, the change is almost identical when one SCA head is inactive on GRACE-B only (orange, 5.27% of epochs), as when GRACE-A is the sole spacecraft operating with one SCA head (green, 3.2% of epochs). 9.3.4 Estimated Antenna Phase Centre Vectors In the least squares adjustment for the Stokes coefficients, the KBR antenna phase centre vectors for GRACE-A and GRACE-B were co-estimated (compare section 6.4.2). The following results are based on the APC estimates obtained from within the determination of the stochastic model. The estimated APC vector for one satellite s is cˆs=cs+∆cˆs , (9.3.2) wherecs is the a priori calibrated KBR APC for the satellite, which was used as a Taylor point in the estimation. The in-orbit calibrated APC coordinates obtained from the GRACE sequence of events file are given in table 9.1. Alongside the calibrated values, the formal errors from the adjustment for∆cˆare given for an example month of good data quality. The formal errors are given for the adjustment using the old stochastic model, the model including AOC covariance matrices, and the TLS solution. Note that the formal errors do not vary much between months, and that they are small, on the orderofsomemicrometres.Theestimatedimprovements∆cˆ to thepublishedcalibrated APCs for the processed time series are displayed in fig. 9.6. Results for the period after August 2016, which are very strongly affected by the disabled accelerometer on GRACE-B (Flechtner, 2016), are excluded from the analysis in this section. Table 9.1: Calibrated KBR APC coordinates and formal errors from their estimation for April 2008. Calibrated value σOld model σIncl. AOC σWith TLS GRACE-A xAPC 1.445m 5.241µm 5.308µm 5.437µm yAPC −0.423µm 0.018µm 0.018µm 0.018µm zAPC 2.278µm 0.021µm 0.021µm 0.020µm GRACE-B xAPC 1.444m 10.062µm 10.052µm 10.095µm yAPC 0.576µm 0.031µm 0.030µm 0.030µm zAPC 3.304µm 0.041µm 0.041µm 0.041µm Chapter9 Co-Estimation of Orientation Parameters136