Analytical Nonlinear Propagation of Uncertainty in the Two-Body Problem

作者：Fujimoto K^*; Scheeres D J; Alfriend K T

来源：Journal of Guidance, Control, and Dynamics, 2012, 35(2): 497-509.

DOI：10.2514/1.54385

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.

• 出版日期2012-4