Page - 113 - 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

0.1 1 10 100 Frequency [mHz] 10−7 10−6 10−5 Oldmodel Incl. AOC Figure 8.9: Mean PSDs for the old processing model (in brown) and considering full AOC covariance matrices (in blue). The new model shows decreased power in the band strongly influenced by uncertainties in the spacecraft orientation. The shaded frequency band has the same bounds as in fig. 8.8. 8.3.4 Impact on Residuals As the estimated residuals eˆare a superposition of residuals due to a stationary noise process and due to the non-stationary AOC noise, they can be disentangled to give the residuals attributed to each of the individual sources with eˆsst=Σsst(Σsst+Σ∆ρ˙AOC) −1 eˆ (8.3.2) and eˆAOC=Σ∆ρ˙AOC (Σsst+Σ∆ρ˙AOC) −1 eˆ . (8.3.3) Figure 8.10 shows the PSDs of all three groups of residuals — combined, stationary, and non-stationary — for June 2010. It can be seen that the power in the non-stationary residuals (blue) is even larger than that of the stationary residuals (green) in the highlighted frequency-band, where a large impact of the orientation uncertainty is expected. It must be said, however, that a PSD is decidedly the wrong instrument to display this information, as stationarity of the signal is a fundamental assumption when computing the PSD. Figure 8.10 could lead one to assume that the AOC residuals have the same quite high power at a frequency of≈6mHz to≈10mHz throughout the complete month, with no discernible variability from one time segment to another. This is however not true, as will be illustrated in fig. 8.11. The non-stationary nature of 8.3 Results 113