Page - (000013) - 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

8.3.3 Covariance Function . . . . . . . . . . . . . . . . . . . . . . . . . 111 8.3.4 Impact on Residuals . . . . . . . . . . . . . . . . . . . . . . . . . 113 8.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 9 Co-Estimation of Orientation Parameters 119 9.1 Uncertainties in Independent Variables . . . . . . . . . . . . . . . . . . 120 9.1.1 As Gauß-Markov Model with Derived Observations . . . . . . 121 9.1.2 As Gauß-Markov Model with Eliminated Observations . . . . 124 9.1.3 Equivalence of Approaches . . . . . . . . . . . . . . . . . . . . . 126 9.2 Application to GRACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 9.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 9.3.1 Stochastic Model and Residuals . . . . . . . . . . . . . . . . . . 130 9.3.2 Estimated Satellite Orientation . . . . . . . . . . . . . . . . . . . 132 9.3.3 Effect on Antenna Offset Correction . . . . . . . . . . . . . . . . 135 9.3.4 Estimated Antenna Phase Centre Vectors . . . . . . . . . . . . . 136 9.3.5 Gravity Field Solutions . . . . . . . . . . . . . . . . . . . . . . . 141 9.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 10 Conclusion and Outlook 153 List of Abbreviations 157 Bibliography 161 vii