Comparison and Numerical Evaluation of Navigation Algorithms for Spacecraft Proximity Operations

Space missions involving proximity operations among spacecraft have gained increasing importance over the years. Indeed, they enable complex objectives that would be impossible, or at least very difficult, to achieve with a single spacecraft. These kinds of missions require a very high level of precision in maintaining relative distances among satellites throughout their operational lifespan. The challenge is heightened by the need for fully autonomous operation, as communication with ground stations becomes impractical or impossible (e.g., deep space missions). For these reasons, a robust and reliable Guidance, Navigation, and Control (GNC) system is essential for the success of spacecraft proximity operations. In particular, the selection of suitable sensors and algorithms for the navigation function is critical to ensure that the mission's objectives are met with the required precision. This thesis aims to provide an overview of the sensors and estimation methods used in space, highlighting their advantages and disadvantages with a focus on their application in proximity operations. Numerical simulations are conducted to evaluate the performance of different Navigation algorithms while considering various maneuvers. In particular, two key observer-based approaches are implemented: the Luenberger observer and the Kalman Filter. Simulation analyses are conducted in MATLAB and Simulink to test the effectiveness of these observers under sensor uncertainties and dynamic constraints.