Page - 130 - 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

For each iteration in this estimation, the updated orientation is used to recompute 1. the design matrix for the APC vectors, as in eq. (6.4.30); 2. an updated antenna offset correction, as in eq. (4.3.6); 3. updated AOC covariance matricesΣs∆ρ˙AOC, linearised at the new estimated orien- tation as in eq. (8.1.22); 4. and an updated correction term for the ll-SST observation, as in eq. (9.1.30). These additional steps lengthen the computation time per iteration significantly. The stochastic model estimated in section 8.2 is used as a priori information to speed up convergence. The estimated stochastic model and the estimated orientations are then used in the computation of the full high degree and order gravity field solution. 9.3 Results The GRACE time series was again reprocessed, using the updated stochastic model as first introduced in chapter 8 and co-estimating improved satellite orientations as described in section 9.2. The following sections will give analysis of this time series, focusing on the estimated stochastic model, the estimated orientations, and the estimated monthly gravity fields. In addition to again highlighting some specific months representing several levels of data quality, the complete time series will also be analysed and contrasted to the previously computed solutions. 9.3.1 Stochastic Model and Residuals The initial inclusion of the stochastic information on the non-stationary AOC in the form of AOC covariance matrices had a large impact on the estimated stochastic model. The impact was noticeable both in terms of PSD and in terms of arc-wise variance factors. The same disentanglement of stationary and non-stationary noise sources is also present and unchanged in the TLS approach. The estimated stochastic models are consequently largely identical. The additional co-estimation of the satellite orientation isofcourseexpectedtohaveaneffectonthe ll-SSTresiduals,as in totala largernumber of parameters is estimated. Figure 9.1 gives an indication that this effect can not be very large, as the PSD estimated from the new residuals (pink) is largely identical to that computed only under consideration of the AOC covariances (blue). Figure 9.1 shows the PSD for a month of sub-par data quality, the PSDs for months of good data quality are similarly identical to those computed with AOC covariances only. A small improvement can however be observed when studying the correlation between the arc-wise variance factors and the mean opening angles for the respective arcs, as displayed in fig. 9.2. For the TLS solution, the mean of the correlation coefficients is reduced from 0.03 to 0.01. This is a much smaller improvement than what was previously achieved by introducing the AOC covariance matrices. Nevertheless, it is important to note that the co-estimation of the satellite orientation does not have a negative impact on either component of the stochastic model. Chapter9 Co-Estimation of Orientation Parameters130