Hybrid Method of Uncertainty Propagation for Near-Earth Conjunction Analysis

Abstract

In this research, several existing semi-analytical dynamics and uncertainty propagation techniques are combined with conjunction models to achieve fast and accurate probability of collision results. Initial Gaussian uncertainty associated with two objects is split into smaller Gaussian distributions using Gaussian mixture models to achieve mixture components that will maintain linearity over longer propagation times. These mixture components are propagated forward using second-order state transition tensors that can capture the nonlinearity in the propagation accurately by taking into account the desired dynamics. The dynamic solution and these tensors are computed using the Deprit–Lie averaging approach, including transformations between mean and osculating states, which accounts for perturbations due to solar radiation pressure and J2. This simplified dynamic system allows fast and accurate propagation by combining the speed of propagation with averaged dynamics and the accuracy of short-period variation addition. Combined, these mathematical tools are used to propagate the object’s uncertainties forward. The final distributions are compared using analytical conjunction methods to compute the probability of collision, which is then compared to the Monte Carlo result to confirm the method’s validity.