Mission Planning for Earth Observation: a Tree Tensor Network approach

The mission planning (MP) is a crucial aspect of Earth Observation (EO) that targets the optimal scheduling of satellites’ orbits for the data collection of Earth information upon end-users' requests. This task is a complex combinatorial problem that involves the optimization of a set of variables, describing both the acquisition of target images of the Earth's surface and the subsequent downloading of the acquired information to ground stations. The MP problem can be formulated as a knapsack problem (NP-hard problem), where the cost function consists of binary variables, whose optimal configuration provides the time-ordered shortlist of the possible observations and downlinks - the planned mission - according to some selected constraints. This Thesis represents the output of a six-month internship within the research division of Thales Alenia Space Italia (TASI). Starting from a mathematical formulation of the MP problem provided by TASI, we first map the original classical problem into a ground-state search for the corresponding quantum many-body Hamiltonian, reminiscent of spin glass models. We then explore the feasibility of reaching the optimal solution for a representative set of small problem instances using quantum-inspired algorithms based on Tree Tensor Networks (TTN), which allow for an efficient representation of the ground state of many body systems. This study concludes with a comparison to a Quadratic Program (QP) classical solver.