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Hybrid Method for Uncertainty Propagation of Orbital Motion

Published Online:https://doi.org/10.2514/1.G001834

The efficient and accurate representation of uncertainty for orbiting objects under nonlinear dynamics is a topic of great interest for space situational awareness. This paper presents a hybrid method that enables an efficient propagation of uncertainty while maintaining accuracy. The method proposed in this research is defined by combining two ideas. First, the second-order semianalytic solutions are derived, based on a Deprit–Lie transformation, in order to describe a perturbed orbiting motion due to central-body oblateness and solar radiation pressure. From this theory, a simplified dynamical system is defined by eliminating the short-period variation. Next, this simplified dynamical system is expanded by using the state transition tensors, which can directly map uncertainty while capturing the nonlinearity of higher-order dynamics. In this paper, it is verified that the hybrid method propagates uncertainty accurately by comparing uncertainty from Monte Carlo methods through statistical approaches. It is also shown that the method reduces the computational burden of the Monte Carlo methods to less than 0.002%.

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