Page - 152 - 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

improved satellite orientations. Importantly, it was shown that the TLS approach described by Reinking, 2008 is equivalent to the widely used practice of parameter elimination in a classical Gauß-Markov model, given correct linearisation at every iteration step and uncorrelated observation groups. Theestimationof thesatelliteorientationswas integratedinto theprocessingstrategyat the same stage where the stochastic model for GRACE SST observations is determined. In this context, the full SCA/ACC sensor fusion and AOC covariance matrices derived in chapter 8 formed important building blocks. Without these prerequisites, using ll-SST observations in the determination of the improved orientations would not be possible. The estimated stochastic model was not strongly affected by use of the TLS algorithm. The estimated orientations are plausible, and the variations in orientation estimated by the algorithm follow the constraints introduced through the a priori covariance information. Over the complete analysed time span, the estimates differ more from the orientation provided through SCA/ACC sensor fusion for periods where only one SCA head is active on the respective spacecraft. One major result is the improvement in the estimate of the antenna phase centre vectors through this approach. Where the estimate contained a large bias in the previous scenarios, using the TLS algorithm almost completely eliminates the bias. A large standard deviation remains, however. Crucially, this standard deviation is larger than that obtained through the formal errors of the least squares adjustment. This leads to the conclusion that further investigation is needed to either locate and model the remaining factors leading to this biased estimate, or to conclusively show the limits of co-estimation of the GRACE APC vectors in normal science operations. One promising avenue could be to follow the approach laid out by Horwath et al., 2011 and only estimate the deviations of the pitch and yaw components of the APC. The length of the APC vector would then be held constant at the value obtained from dedicated in-orbit KBR calibration manoeuvres. This approach could be combined with the TLS orientation estimate, which was shown to provide a more stable estimate of exactly these two angles. At the level of monthly gravity field solutions, the TLS estimate showed improve- ments especially for months containing non-nominal observations, such as periods of increased opening angles due to operational constraints on the GRACE satellites. The influence of the TLS estimate can be studied most clearly not at the level of individual monthly solutions, but when analysing their temporal variability. In the spatial domain, the variability is decreased more over the oceans than over land, which in first approximation indicates a reduction of noise, and not a damping of signal. Analysis in the spectral domain clearly showed that the variability of the Stokes coefficients corresponding to the GRACE pitch angle variations in geographical extent and frequency were amongst those most improved. However, some clear processing artefacts were visible for Stokes coefficients of degrees higher than 60, indicating that there is a need to further refine the processing chain incorporating a TLS estimate of the satellite orientations. Chapter9 Co-Estimation of Orientation Parameters152