Time-Reversed Optimal Control-Based Metric for Maneuvering Targets Correlation

Correlation plays a crucial role in maintaining a space object catalog, serving the purpose of determining if a known target produced a particular measurement. Statistical distance-based approaches are not always enough when dealing with controlled objects, leading to alternative correlation metrics that exploit the effort linking the track to candidate orbits. This work describes a novel optical measurement correlation assistance tool, exploiting optimal control theory to backpropagate an admissible region of observables to catalog epochs through a patchwork of Taylor polynomial expansions. The resulting minimum expense distributions are combined with a standard statistical distance to support the correlation of maneuvering objects. A sensitivity analysis on the defined metrics is performed on a set of synthetic scenarios involving impulsive maneuvers, chosen to easily connect the detected expense and effect on the orbit to the features of the control action.