Page - 106 - 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

1 10 100 Stationary GRACE-A GRACE-B 14:00 15:00 16:00 0 5 10 Steering deadband Figure 8.4: Square root of main diagonal elements of covariance matrices in fig. 8.3,σ, and opening angle β for both spacecraft. In the top panel, the blue line shows the zero time-lag variance factor of the estimated stationary covariance function. The main diagonal of the AOC covariance matrix due to GRACE-A is shown in green, and that of the covariance matrix due to GRACE-B in orange. The bottom panel shows the opening angle β for the two satellites in the same colours. The darker shaded area indicates the nominal active steering deadband. 8.2 Updated Stochastic Model Having obtained detailed knowledge of the structure of the AOC covariance ma- trix, this information can be taken into consideration in defining and estimating the stochastic model for the ll-SST observation equations, as outlined in eq. (8.1.5). The stochastic model defined in eq. (6.5.18) is extended with the AOC covariance matrices for GRACE-A and GRACE-B to give Σmll=σ 2 m · Nm−1 ∑ n=0 Cnxx ·Vn+σ2AOC,AΣA∆ρ˙AOC+σ2AOC,BΣB∆ρ˙AOC (8.2.1) The variance propagation from the orientation uncertainty to the AOC was performed independently for each spacecraft, and for each short arc. The covariance matrices are then introduced into the stochastic model as cofactor matrices. This extends the model defined by the purely stationary process described by eq. (6.5.18) with information on the non-stationary behaviour of the AOC noise. To allow for imperfections in the result of the SCA/ACC sensor fusion algorithm, one additional variance factorσ2AOC,s was estimated per spacecraft s∈ [A,B], per month. As the propagation of variances Chapter8 Star Camera Observations and Uncertainties106