Orbital Uncertainty Propagation Using Adaptive Gaussian Mixture Model and Polynomial Chaos Kriging

Orbital uncertainty propagation is a fundamental issue for space situational awareness in cases such as collision warning, anomaly detection, and debris cloud evolution. However, efficiently obtaining a high-precision orbital uncertainty distribution is challenging when confronted with a large initial uncertainty distribution or a prolonged flight time. To address the problem of long-duration multirevolution uncertainty propagation, this paper proposes an adaptive approach by combining Gaussian mixture model (GMM) and polynomial chaos kriging (PCK). The initial distributions are split in multiple dimensions based on Sobol sensitivity; the samples of each surrogate model are updated based on Mahalanobis distance. The sample size and number of Gaussian mixtures are determined adaptively, and the sample points are shared by different local surrogate models, so the total sample size is reduced and the accuracy is enhanced. Having established the local surrogate models, the output and output error variance are calculated via data fusion. Simulations show that a new global estimation error method is derived, and the proposed adaptive GMM/PCK exhibits superior performance to PCK, active sampling PCK, GMM and unscented transformation, and Monte Carlo methods.