To improve target acquisition in laser ranging to space debris under large orbit prediction errors, this study proposes a framework combining Gaussian Mixture Models (GMMs) and Polynomial Chaos Expansion (PCE) for nonlinear orbital uncertainty propagation. The method combines Gaussian-mixture decomposition with local PCE surrogates to represent the non-Gaussian evolution of propagated uncertainty. Numerical experiments are carried out for two debris-propagation cases, including a low-altitude low-Earth-orbit (LEO) case at about 340 km and a higher-altitude comparison case at about 1450 km. The results show that the proposed framework reproduces the main distributional characteristics of the Monte Carlo reference in both the Radial, Transverse, and Normal (RTN) frame and the station-centered observation domain, including the curved terminal distribution, non-Gaussian marginal behavior, and narrow visible-arc structure in the angular domain. The higher-altitude case further shows that, when atmospheric drag is substantially reduced, the terminal uncertainty remains strongly anisotropic and non-Gaussian, while its evolution is more strongly affected by eccentric-orbit geometry, nonspherical gravity, and Keplerian shear. Compared with brute-force Monte Carlo propagation, the proposed method substantially reduces the computational burden: once the local PCE coefficients have been determined from a limited set of propagated collocation points, the prediction of large terminal ensembles is carried out through algebraic polynomial evaluation without any further reliance on the numerical propagator. The proposed framework therefore provides practical uncertainty information for range-gate setting, pointing-window design, and related acquisition analysis in space-debris laser ranging.
Zhang et al. (Wed,) studied this question.