A Randomized Approach to Probabilistic Footprint Estimation of a Space Debris Uncontrolled Reentry

This paper studies the problem of characterizing the region of the airspace that will be occupied by a space debris during an uncontrolled reentry (footprint), with the final goal of supporting the air traffic controllers in their task of guiding aircraft safely from their origin to their destination. Given the various sources of uncertainty affecting the debris dynamics, the reentry process is characterized probabilistically and the problem of determining the footprint is formulated in terms of a chance-constrained optimization program, which is solved via a simulation-based method. When observations of the debris initial position and radar measurements of the aircraft prior to the reentry event are available, nonlinear filtering techniques can be adopted and the posterior probability distribution of the debris position as well as of the wind field affecting the reentry process can be integrated in the chance-constraint formulation so as to obtain an enhanced estimate of the footprint. Simulation results show the efficacy of the approach.