NONLINEAR MAPPING OF GAUSSIAN STATE UNCERTAINTIES: THEORY AND APPLICATIONS TO SPACECRAFT CONTROL AND NAVIGATION

摘要

This paper discusses the nonlinear propagation of spacecraft trajectory uncertainties via solutions of the Fokker-Planck equation. We first discuss the solutions of the Fokker-PIanck equation for a deterministic system with a Gaussian boundary condition. Next we derive an analytic expression of a nonlinear trajectory solution using a higher-order Taylor series approach, discuss the region of convergence for the solutions, and apply the result to spacecraft applications. Such applications consist of nonlinear propagation of the mean and covariance matrix, design of statistically correct trajectories, and nonlinear statistical targeting. The two-body and Hill three-body problems are chosen as examples and realistic initial uncertainty models are considered.