Analytical Nonlinear Propagation of Uncertainty in the Two-Body Problem
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One topic of recent interest in the field of space situational awareness is the accurate and consistent representation of an observed object's uncertainty under nonlinear dynamics. This paper presents a method of analytical nonlinear propagation of uncertainty under two-body dynamics. In particular, the probability density function over state space and its mean and covariance matrix are expressed analytically for all time via a special solution of the Fokker-Planck equations for deterministic Hamiltonian systems. The state transition tensor concept is used to express the solution flow of the dynamics. Some numerical examples, where a second-order state transition tensor is found to sufficiently capture the nonlinear effects, are also discussed. Copyright © 2011 by K. Fujimoto, D. J. Scheeres, and K. T. Alfriend.
author list (cited authors)
Fujimoto, K., Scheeres, D. J., & Alfriend, K. T.