A two-stage approach to satellite constellation optimization: classical and QUBO formulations

Abstract

The design of satellite constellations for Earth observation requires balancing spatial coverage, revisit time, cost, and operational complexity. This paper considers the problem of designing the orbits of a given number of Low Earth Orbit (LEO) or Very Low Earth Orbit (VLEO) satellites to maximize the spatial and temporal resolution achieved over a prescribed set of ground targets. This kind of problem is inherently nonconvex and possibly combinatorial, making its solution computationally demanding for large constellations and target sets. To address this challenge, we propose a two-stage optimization strategy that separates spatial-coverage design from temporal-resolution optimization, thereby reducing the complexity of the overall problem. Two variants of the method are developed. The first employs continuous decision variables during the spatial-optimization stage, whereas the second discretizes these variables and reformulates the problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem. The latter formulation enables the use of efficient classical QUBO solvers and is directly compatible with quantum-annealing hardware. The proposed framework provides a scalable approach to the design of heterogeneous LEO and VLEO Earth-observation constellations and establishes a pathway for exploiting emerging quantum-optimization technologies in satellite mission design. Preliminary simulation results are presented to demonstrate the effectiveness of the strategy.