Adaptive Gaussian Mixture Model for Uncertainty Propagation Using Virtual Sample Generation

Orbit uncertainty propagation plays an important role in the analysis of a space mission. The accuracy and computation expense are two critical essences of uncertainty propagation. Repeated evaluations of the objective model are required to improve the preciseness of prediction, especially for long-term propagation. To balance the computational complexity and accuracy, an adaptive Gaussian mixture model using virtual sample generation (AGMM-VSG) is proposed. First, an unscented transformation and Cubature rule (UT-CR) based splitting method is employed to adaptive update the weights of Gaussian components for nonlinear dynamics. The Gaussian mixture model (GMM) approximation is applied to better approximate the original probability density function. Second, instead of the pure expensive evaluations by conventional GMM methods, virtual samples are generated using a new active-sampling-based Kriging (AS-KRG) method to improve the propagation efficiency. Three cases of uncertain orbital dynamical systems are used to verify the accuracy and efficiency of the proposed manuscript. The likelihood agreement measure (LAM) criterion and the number of expense evaluations prove the performance.