Page - 2 - 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

Chapter 3 outlines the fundamentals of gravity signals in the Earth system and how they relate to the goals of GRACE. Some of the most fundamental disturbing factors for GRACE observations are presented, followed by a short introduction on the representation of gravitational potentials and their analysis. Chapter 4 mainly serves to give comprehensive background on the GRACE satellites, their construction, and instrumentation. Some of the most relevant reference frames are introduced, and the reader is referred to the authoritative sources for complete information on the satellites. Special consideration is made to give a thorough intro- duction to the observation geometry of the GRACE constellation, as this specific aspect of the mission is of primary importance to later parts of this thesis. Chapter 5 gives details on the technique of dynamic orbit integration through varia- tional equations, with a specific focus on their implementation at IfG. The variational equations form the basis of both the ITSG-Grace2016 and the ITSG-Grace2018 series of gravity field solutions. Chapter 6 aims to give a detailed description of the state of the art of gravity field processing at IfG, specifically the ITSG-Grace2016 time series of gravity fields. This series can be considered the basis of this thesis, although the contents of chapter 7 were already included in the final ITSG-Grace2016 processing chain. The functional model for all GRACE-based observables is derived, followed by a detailed description of the process used to estimate realistic stochastic models for GRACE observations, which is a feature unique to the ITSG-Grace series of gravity field solutions. Finally, the use of these stochastic models to determine a full monthly gravity field is outlined. The focus of chapter 7 is the improvement of the dynamic orbit integration based on variational equations, as outlined in chapter 5. First, a criteria is developed to quantify the quality of a dynamic orbit solution based on its convergence behaviour. This is followed by a description of the proposed improved algorithm, the heart of which is a generalization of the well-known orbit integration technique due to Encke. This approach is extended through rigorous optimization of the initial satellite state used for orbit integration. The improvements in dynamic orbit quality due to this new algorithm are analysed using the example of GRACE, and some observations are made on the applicability of the algorithm to GRACE-FO and other satellite missions. Chapter 8 gives a thorough analysis of the effects of uncertainty in the satellite orientation on the GRACE observables. This is followed by the development of a stochastic model for these effects, based on existing full covariance information on the satellite orientation as derived in chapter 6, and its application to the processing chain of ITSG-Grace2016. The impact on the estimated stochastic model as well as a time series of post-fit residuals is analysed, and the observed changes and improvements are discussed. Chapter 9 uses the orientation uncertainty information and updated stochastic model derived in chapter 8 to co-estimate improved satellite orientations together with the primary goal, the Stokes coefficients describing the monthly gravity fields. This estimation is prefaced by a comparison of two different formalisms used to consider Chapter1 Introduction2