Page - 140 - 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 9.7 shows the Euler angles computed from the estimates cˆA and cˆB for the studied period. In this representation, some characteristics of the estimated APCs appear much clearer than in the Cartesian representation of fig. 9.6. The stabilizing effect of the TLS estimate can clearly be observed, especially in the roll and yaw angles for GRACE-A, and to a lesser extent in the same angles for GRACE-B. Compared to later data, the first months of 2003 show a noticeably more unstable estimate of the APC vectors. An attempt was made to correlate the large jumps in June 2003 with important events, such as COM or KBR calibration manoeuvres, but this was not successful. The jump could possibly be simply due to the inferior data quality at the beginning of the mission lifetime. The estimated pitch angle misalignments for both spacecraft show a striking symme- try, with the misalignment angle for GRACE-A decreasing when that for GRACE-B increases, and vice versa. Comparison with important events in the GRACE mission lifetime reveals that the large jumps in the estimated pitch angle misalignment occur at the same times as orbit swaps of the satellites. This strongly indicates that this effect depends on a systematic effect in the GRACE attitude determination, and not on a geophysical effect aliasing into the estimate. It also partly confirms previous results by Horwath et al., 2011, where a similar jump was observed in estimated daily pitch and yaw misalignment biases at the 2005 satellite swap manoeuvre. Horwath et al. however do not observe the mirrored behaviour in the pitch jump, rather both pitch angles decrease in their estimate. Further, the yaw angle misalignment has a much larger magnitude for Horwath et al., on the order of 2mrad. In the presented solution the estimate is, in first approximation, median-free. Where Horwath et al., 2011 did not make a statement on the temporal variability of the misalignment angles, apart from the jump at the December 2005 satellite swap, the longer time series estimated here allows for the identification of such behaviour. In general, the periodicity in the roll and yaw estimates are much more easily identifi- able in this representation, as opposed to the Cartesian plot in fig. 9.6. Spectral analysis revealed that the largest amplitude is found at one cycle per 322d, which corresponds to one full revolution of the longitude of the ascending node for the GRACE orbital plane. The observed period indicates an influence of the orientation of the spacecraft in inertial space on the APC estimate. The most obvious explanation would be an effect on the satellites due to the changing angles of incidence of solar radiation. This would also explain the jumps in the pitch angle at orbit swap manoeuvres, when the satellites quickly rotate by 180° in their orbit. The effect of such a rotation on the inertial orientation is the same as that of a rotation of the orbital plane by 180°. Other sources, like an origin in e.g. the field of view of the star camera assembly or the miscalibrated release 2.0 SCA1B data can however not be discounted outright. Due to the dependency on the leader-follower configuration, the pitch misalignment estimates for both GRACE-A and GRACE-B show a bimodal distribution. Both other misalignment angles are unimodally distributed. The spread of the TLS estimates of the misalignment angles over the time series is either comparable to or smaller than that of the other two approaches. Interestingly, the reduction of active thermal Chapter9 Co-Estimation of Orientation Parameters140