Probabilistic Validation of Simplified Models of Spacecraft Formations near Libration Points

This paper introduces a method to probabilistically evaluate the validity of dynamics model approximations, and applies this method to simplified models of satellite formation dynamics near the Sun-Earth/Moon L2 libration point. The method uses a Monte Carlo scheme similar to a sampling importance resampling (SIR) filter to evolve state probability densities through several satellite dynamics models of differing complexity. The evolved densities are fit with a Gaussian mixture model and compared probabilistically to evaluate the validity of the simplified dynamics models over time. With this method, analysis of a formation flying mission on a halo orbit near the Sun/Earth-Moon L2 point reveals a 2 hr window of validity in which the relative satellite dynamics are indistinguishable from a double integrator (DI) and initial relative velocities drive model uncertainty.