Verified Interval Orbit Propagation in Satellite Collision Avoidance

Verified interval integration methods enclose a solution set corresponding to interval initial values and parameters, and bound integration and rounding errors. Verified methods suffer from overestimation of the solution, i.e., non-solutions are also included in the solution enclosure. Two verified integration methods, interval Taylor-series and Taylor-model based methods and their implementation in VNODE-LP and VSPODE, are used to reduce overestimation in verified satellite orbit propagation. Furthermore, two orbital state models based on integration constants, the modified equinoctial elements (MEE) and unified state model (USM), are used to reduce overestimation. Earth-satellite trajectories propagated using VSPODE have 2-3 times less overestimation than those propagated using VNODE-LP. Using the USM and MEE state models, overestimation is further reduced by a factor 4 to 10, depending on initial and parameter uncertainties. It is demonstrated that verified collision detection is feasible and may contribute to prevent satellite collisions to reduce future space debris