Page - 44 - 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

6.2 Sensor Fusion Klinger and Mayer-Gu¨rr (2016) have shown that the quality of GRACE-derived gravity field solutions can be enhanced by using an improved orientation product. This orien- tation product is the result of a sensor fusion algorithm merging information from the star camera sensors, which is stable at longer wavelengths, with angular accelerations observed by the on-board accelerometers, which have lower noise than the star cam- era observations at higher frequencies. These observations are combined through a weighted least squares adjustment which yields the fused orientation parameters. This sensor fusion is performed independently for each GRACE spacecraft. The star camera orientation product gives the rotation from the CRF to the SRF of the respective spacecraft. This rotation is given per epoch as a quaternion q= [ qw qx qy qz ]T , (6.2.1) with qw the scalar part and qx to qz the vectorial part of the quaternion. The angular accelerations of the spacecraft ω˙= [ ω˙x ω˙y ω˙z ]T (6.2.2) are given in the SRF. The angular accelerations are the first derivative of the angular velocitiesω, which are in turn the first derivatives of the orientation of the spacecraftα. These anglesαdeserve some further discussion, as their value is not immediately intuitive. They describe the divergence of the actual orientation of the spacecraft from its nominal orientation with the K-Frame x-axis towards the other satellite, as described in section 4.3. This divergence is given as a set of three Euler angles roll, pitch, and yaw, as illustrated in fig. 6.2. The nominal orientation of the spacecraft as described in section 4.3 is RNOMCRF =R SRF KFR KF LOSFR LOSF CRF , (6.2.3) where the rotation from the LOSF to the CRF can be determined from the satellite positions, e.g. from dynamic orbits. The rotation from the KF to the SRF is computed zSRF xSRF LOS roll pitch yaw Figure 6.2: GRACE attitude in roll, pitch, and yaw angles. ySRF is orthogonal to image plane. Chapter6 ITSG-Grace201644