Page - 79 - 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

Numerical Optimization in Orbit Integration 7 Attribution This chapter, as well as chapter 5 of this thesis focusing on the variational equations and dynamic orbit integration, are an extended version of a previous publication by the author: Ellmer and Mayer-Gu¨rr, 2017. Specifically, this chapter reproduces and expands on sections 3.6 to 5 of Ellmer and Mayer-Gu¨rr, 2017. The content of this chapter is the result of original research carried out by the author of this thesis. Section 7.2.3 does not appear in Ellmer and Mayer-Gu¨rr, 2017, and is first published in this work. Dynamic orbits are an integral part of determining a gravitational field using the variational equations. All forces that are known a priori, both from reference models andfromdirectobservations,areencapsulatedinthe integratedpositionsandvelocities of the GRACE satellites along their respective orbit arcs. The use of dynamic orbit positions to determine the accelerations due to conservative forces however means that dynamic orbit integration for GRACE must be an iterative procedure. Only when positions, velocities, and accelerations derived from an integrated dynamic orbit equal those used in its computation can one say that an equilibrium state has been reached. The dynamic orbit can then be described as self-consistent. Using a dynamic orbit as input for the orbit integration routine must then result in the same dynamic orbit as output. Any difference in the positions from the input orbit to the result can be regarded as either a defect in the orbit integration algorithm, a defect in its implementation, or as a manifestation of insufficient convergence. This chapter details an approach to characterize the quality and analyse the conver- gence of the dynamic orbit integration described in chapter 5. Building on this result, the improved algorithm used in ITSG-Grace2016 will be presented. The improved algorithm ensures self-consistency of the dynamic orbits at a level that allows for consistent processing of data from the GRACE-FO laser ranging interferometer (LRI), which is expected to surpass the accuracy provided by the GRACE KBR instrument (Sheard et al., 2012). 7.1 Quality of Convergence For real data processing, such as in the context of GRACE, the true position of the spacecraft is unknown. The obvious path for a quality check on orbit determination, the computationofpositiondifferences tosomeabsolutegroundtruth, is thusnotavailable. 79