Nonlinear Uncertainty Propagation in Orbital Elements and Transformation to Cartesian Space Without Loss of Realism

A number of methods for nonlinear uncertainty propagation used for space situational awareness (SSA) exploit orbital-element-based representations of orbital-state uncertainty in order to mitigate the departure from Gaussianity and thereby improve performance. However, some downstream SSA functions require that orbital-state uncertainty be represented in a Cartesian space. This paper reconciles the two practices by describing a way in which uncertainty that has been propagated in orbital elements can be transformed to Cartesian space without loss of realism via Gaussian mixtures. The efficiency of this approach is compared to an alternative approach to uncertainty propagation wherein uncertainty is both represented and propagated in Cartesian space (using Gaussian mixtures). Metrics for assessing the realism of a Gaussian mixture are also presented.

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