Reachable domain for satellite relative motion along elliptic orbit with uncertainty and process noise

For satellite close-range relative motion under uncertainty and process noise, the relative reachable domain is the confidence region, upon providing a user-defined probability level, of the occurrence of a flying trajectory. The relative reachable domain is a risk-assessing tool used to prevent inadvertent collisions. This study conducted a follow-up relative reachable domain investigation with two improvements: (1) the reference orbit of the close-range relative motion is generalized to an arbitrary elliptic orbit and (2) the process noise during the relative motion is incorporated. The equation of the relative reachable domain envelope, the boundary of the relative reachable domain, is derived. An algorithm is proposed to solve for the relative reachable domain envelope. By comparing the solved relative reachable domain envelopes with the results of a direct Monte Carlo simulation, the accuracy of the proposed algorithm is verified. Moreover, a relative reachable domain-based collision detection method is presented to screen out encounters that have a low chance of collision. The proposed collision detection method exhibits efficiency and reliability in deciding whether a passive flyby mission is safe or not.