Page - 132 - 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

9.3.2 Estimated Satellite Orientation The TLS algorithm gives a least squares estimate for improved orientation quaternions for the two GRACE spacecraft. Investigating noise in the orientation through numerical simulationshasshownthat twoprocessingstepsareparticularlysensitive toorientation uncertainties. These are the computation of the antenna offset correction, and the computation of the design matrix for parameters that directly depend on the satellite orientation such as the antenna phase centre vectors. The rotation of the accelerometer data into the CRF, as required for dynamic orbit integration, is for example not as sensitive to noise in the orientation. As shown by Harvey, 2016, the release 2.0 spacecraft orientations are subject to a bug in the on board star camera software, leading to defective data in the SCA1B data files. As of the time of this writing, no corrected data is generally available. This known deficiency in the source data, together with the sensitivity of certain parameters to the spacecraft orientation discussed above, serves as motivation for the co-estimation of the satellite orientations. Where the SCA/ACC sensor fusion only considers sensors on one GRACE spacecraft, theTLSestimateof theorientationalso includesobservationsbytheveryhighprecision ll-SST KBR link in the orientation estimate. The KBR range rate observations give an additional constraint on the relative motion of the satellites w.r.t. each other. Full covariance information on both the orientation parameters and on the KBR observable allows for the combination of these heterogeneous observation types. It must be expected that the additional KBR observations would have a negligible impact on the adjusted orientation parameters if their noise were too high with respect to the orientation observations from the SCA/ACC sensor fusion. Figure 9.3 shows the TLS estimate of the satellite orientation of both GRACE spacecraft for a 3hour segment of data on June 11, 2010. This particular segment was chosen as it shows rather unremarkable satellite orientations. No large excursions from the steering deadband occur during this time period. The SCA/ACC sensor fusion orientationα, used as a Taylor point in the estimation, is plotted in the background (brown), overlaid by the TLS result αˆ (in pink) and the difference between the two∆αˆ (in blue). The areas shaded with a darker background mark periods of time where only one SCA head was active on the respective spacecraft. During these times, the uncertainty of the satellite orientation resulting from the SCA/ACC sensor fusion is naturally higher (compare e.g. fig. 8.3). The top row of fig. 9.3 shows the roll angles of the two GRACE spacecraft. The TLS estimate for this angle is virtually unchanged from the SCA/ACC sensor fusion estimate. This result is reassuring as, due to the geometry of the observations, the inter-satellite link is comparatively insensitive to changes in satellite roll. The lower two rows of fig. 9.3 show the satellite pitch and yaw rotations, respectively. For these angles the difference between the a priori fusion orientation and the TLS estimate is consistently small for periods where both SCA heads are active. It is only when observations are based on only one SCA head that the TLS estimate significantly Chapter9 Co-Estimation of Orientation Parameters132