Measures of Nonlinearity and non-Gaussianity in Orbital Uncertainty Propagation

Orbit uncertainty propagation (OUP) is an important tracking problem appearing in space situational awareness. The uncertainty, which is initially approximately Gaussian, is transformed by the time propagation and eventually becomes non-Gaussian. Gaussian representation of the uncertainty becomes gradually inaccurate, which is often addressed by splitting the Gaussian representation into a mixture of Gaussian densities (GM), which can describe the uncertainty with arbitrary accuracy. Measures of nonlinearity (MoNL) and non-Gaussianity (MoNG) assess the degree of the model nonlinearity around a working point and thus they pose a convenient means to indicate time instants suitable for the splitting. The paper provides an analysis of several MoNLs and MoNGs with a special focus on their behavior in the OUP from the numerical, theoretical, and practical points of view. Based on the analysis, measures eligible for governing the splitting in the OUP based on GM are recommended.