Active Sampling Based Polynomial-Chaos–Kriging Model for Orbital Uncertainty Propagation

Abstract

Propagating uncertainties usually requires repeated evaluation of the subject model for a large number of different input parameters. Surrogate models have been widely used to avoid this computationally intensive uncertainty propagation by replacing the original model by an easy-to-evaluate function model. In this Paper, the polynomial chaos based Kriging is used as such a surrogate model for orbital uncertainty propagation. The polynomial chaos represents the global trend of the uncertainty distribution, while the Kriging describes the local variations. Such a combination can provide a more precise surrogate model than individual polynomial chaos or ordinary Kriging representation. To further enhance the accuracy, a new active sampling strategy is proposed to incrementally build and improve the polynomial chaos based Kriging model. This new modeling scheme only requires a small number of sampling points while achieving close performance to the Monte Carlo based propagation. It is also more accurate than the random sampling based Kriging model. Three orbital uncertainty propagation examples are used to demonstrate the effectiveness of the proposed surrogate model.