Monte Carlo Pc Calculation from TCA (in equinoctial elements)(GSC-18072-1)

Calculates the probability of collision (Pc) between two conjuncting satellites using a Monte Carlo technique, executing the draws from the propagated states and covariances at the time of closest approach (TCA) between the two satellites. The algorithm begins with the primary and secondary objects states and covariances at TCA, converts the two covariances from Cartesian to equinoctial element representation, samples perturbations from each covariance in element space (presuming Gaussian behavior in this framework), converts each of these perturbations to a Cartesian representation, perturbs the primary and secondary states with these converted perturbations, propagates pair of perturbed states forward until a new TCA is reached, notes the miss distance at TCA, and then determines the Pc empirically from these miss distance data. This technique follows the findings of Sabol (2010) regarding the efficacy of post-propagation transformation to element space to preserve Gaussian error behavior. The algorithm set also includes design-of-experiment aids to determine the number of Monte Carlo trials necessary to achieve a Pc of a desired confidence level.