Nonlinear Mapping of Gaussian Statistics: Theory and Applications to Spacecraft Trajectory Design

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Asteroid close encounters characterization using differential algebra: the case of Apophis (2010, methodology): “An alternate way to analyze trajectory statistics by incorporating higher-order Taylor series terms that describe localized nonlinear motion is proposed by Park and Scheeres (2006).”
Gaussian Sum Filters for Space Surveillance: Theory and Simulations (2011, background): “For deterministic dynamics, it follows that the exact PDF at any future time t > t0 is given by [21]”
Nonlinear Propagation of Orbit Uncertainty Using Non-Intrusive Polynomial Chaos (2013, methodology): “Examples of research attempting to nonlinearly propagate the state uncertainty include Monte Carlo methods [3,4], Gaussian mixtures [5–7], and state transition tensors (STT) [8–10].”