Optimal Formation Flying for Single-Pass, Multi-Baseline, Across-Track Synthetic Aperture Radar Interferometry

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Kurzfassung

Spaceborne Synthetic Aperture Radar (SAR) is at the cutting edge of space technology, providing high-resolution images for applications ranging from Earth observation to planetary exploration, independently of weather and daylight conditions. Among these techniques, SAR Interferometry enables the accurate quantification of a variety of geophysical parameters, such as ground deformation and elevation, fostering the generation of highly accurate Digital Elevation Models (DEMs). The combination of SAR with distributed concepts has opened a new frontier in Earth remote sensing, with the TanDEM-X mission by the German Aerospace Center having generated the most complete and accurate global DEM to date. This mission features a pair of satellites flying in a passively safe helix configuration, thereby reducing the control effort required to maintain the formation in the presence of external disturbances. However, despite the outstanding achievements, there are intrinsic limitations to this type of concept. Indeed, a formation of only two satellites adopting a non-fixed baseline forces trade-offs between accuracy and robustness to height ambiguities. Conversely, a time-invariant baseline would allow for a neat improvement in the accuracy at the price of a higher control demand. In the case of TanDEM-X, these issues are partially solved by performing repeated acquisitions of the same area with a different baseline after one year. Nevertheless, this solution presents additional problematic aspects, as it loses the benefits of single-pass interferometry in monitoring fast-changing phenomena. This thesis investigates whether it is possible to overcome such limitations in the context of single-pass, across-track interferometry by employing a multi-baseline approach. More precisely, the purpose is to determine the optimal set of orbital parameters to produce a high-quality DEM robust to height ambiguities while at the same time ensuring the passive safety of the formation. The proposed approach combines semi-analytical and numerical methods to solve sub-problems with increasing numbers of degrees of freedom. After having determined an analytical solution to the case with two satellites, genetic algorithms are employed to find configurations of three and four satellites compliant with both interferometric and safety-related requirements. Additionally, a comparative study of the necessary delta-velocity budget leveraging impulsive control strategies is conducted. The findings suggest that configurations based on nested helix relative trajectories could be designed to meet all the mentioned requirements, thereby providing a starting point for the design of future cost-effective and highly-accurate Earth observation missions.

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