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• W1527031437 abstract "This paper evaluates the performance of traditional Monte Carlo (FMC) for the nonlinear propagation of initial uncertainty in the two-body problem: an essential task in space situational awareness. This is done in light of a newly developed Markov chain Monte Carlo (MCMC) based particle approach that combines the benefits of MCMC sampling with the method of characteristics (MOC) for solving first order partial differential equations — in this case, the stochastic Liouville equation (SLE). The resulting MCMC-MOC ensemble is by construction, equivalent in measure to the true state probability density. Our recent results on the MCMC-MOC approach indicate that for systems with divergence-free dynamics, the FMC and MCMC-MOC ensembles are statistically consistent. Unfortunately, the unperturbed two-body problem (Keplerian motion) is one such system. In this paper, we demonstrate through simulation that the traditional MC propagated ensemble is indeed equivalent in measure to MCMC-MOC ensemble, which in turn is the true system measure by construction. As a result, it is not possible to improve upon FMC and its slow convergence rate for this problem." @default.
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• W1527031437 date "2015-07-06" @default.
• W1527031437 modified "2023-09-24" @default.
• W1527031437 title "An evaluation of Monte Carlo for nonlinear initial uncertainty propagation in Keplerian mechanics" @default.
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