Page - (000015) - 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

List of Figures 2.1 Evaluation of an interpolation polynomial . . . . . . . . . . . . . . . . 12 3.1 Illustration of signal and difference degree amplitudes . . . . . . . . . 19 3.2 Stokes coefficients displayed as coefficient triangles . . . . . . . . . . . 20 3.3 Gaussian filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.1 GRACE interior view . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.2 Antenna phase center . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.3 GRACE KBR observation geometry . . . . . . . . . . . . . . . . . . . . 26 4.4 In-orbit formation of GRACE . . . . . . . . . . . . . . . . . . . . . . . . 27 6.1 Processing scheme for ITSG-Grace2016 solutions . . . . . . . . . . . . . 42 6.2 GRACE attitude in roll, pitch, and yaw angles . . . . . . . . . . . . . . 44 6.3 Structure of sensor fusion normal equation system . . . . . . . . . . . 48 6.4 Data flow in ITSG-Grace2016 dynamic orbit integration . . . . . . . . . 50 6.5 Daily total potential as piecewise constant function . . . . . . . . . . . 52 6.6 Daily and monthly Stokes coefficients design matrix structure . . . . . 53 6.7 Summary of Covariance and arc-wise variance factor estimation . . . 73 6.8 Examples of estimated PSDs and arc-wise variance factors for June 2010 75 6.9 Normal equation structure of ITSG-Grace2016 monthly solutions . . . 77 6.10 Degree Amplitude plot for June 2010 . . . . . . . . . . . . . . . . . . . 77 7.1 Convergence of dynamic orbit integration . . . . . . . . . . . . . . . . . 80 7.2 Osculating ellipse and best-fit ellipse . . . . . . . . . . . . . . . . . . . . 85 7.3 Encke ratio over one orbit arc . . . . . . . . . . . . . . . . . . . . . . . . 89 7.4 RMS of 3D coordinate difference for several iterations . . . . . . . . . 90 7.5 In-Track coordinate differences in both the spatial and spectral domain 91 7.6 In-Track coordinate differences after convergence for real GRACE orbits 93 7.7 Propagation of orbit noise to range rate measurement . . . . . . . . . . 95 8.1 Opening angle for GRACE-A antenna phase centre vector . . . . . . . 101 8.2 Orientation of spacecraft in nominal attitude with APC vector . . . . . 103 8.3 Full stationary and non-stationary covariance matrices . . . . . . . . . 105 8.4 Main diagonal elements of covariance matrices . . . . . . . . . . . . . . 106 8.5 Distribution of estimated AOC variance factors . . . . . . . . . . . . . 108 8.6 Arc-wise variance factors for two months of deteriorated data . . . . . 109 8.7 Correlation between arc-wise variance factors and opening angle . . . 110 8.8 Estimated ll-SST PSD using AOC covariance matrices . . . . . . . . . . 112 8.9 Estimated mean ll-SST PSD using AOC covariance matrices . . . . . . 113 8.10 PSDs of disentangled residuals . . . . . . . . . . . . . . . . . . . . . . . 114 8.11 Time-frequency-power diagram of disentangled residuals . . . . . . . 115 8.12 Time-frequency-power diagram and opening angle for June 2010 . . . 117 ix