Comparison of Sensitivity Metrics for Orbit Uncertainty Propagation in Cislunar Space

Orbit state uncertainty quantification for objects in cislunar space, i.e., the regions between the Earth and the Moon, is required for space situational awareness as both nation-states and commercial entities seek to develop a permanent presence in the region. Unlike the near-Earth case, the stronger n-body dynamics produces orbits that may be non-Keplerian. In some cases, they may be chaotic. This creates new uncertainty propagation challenges to enable object tracking, sensor management, traffic management, and other elements that are required as the number of man-made objects in the region increases. The work in this paper presents the use of dynamics and uncertainty sensitivity indices to inform particle generation for uncertainty quantification. Specifically, this work presents two importance sampling distributions derived from (i) sensitivity indices and directions of fastest growth extracted from the state transition matrix, and (ii) Sobol’ indices in the random input space. The weighted particles drawn from the sampling distribution are then used to generate a Gaussian mixture model. The propagated probability density is then compared to a Monte Carlo-based solution to assess accuracy in the density prediction and its implications for follow-up data association in a target tracking algorithm. The indices based on the state transition matrix may be easily generated, but lack the accuracy of the predicted density produced via the Sobol’ indices. Both approaches do produce densities that will yield fewer missed detections than simple random sampling of the prior distribution.