Short-Arc Orbital Uncertainty Propagation with Arbitrary Polynomial Chaos and Admissible Region

Abstract

This paper addresses the short-arc orbit uncertainty propagation by combining the admissible region with a new arbitrary polynomial chaos (APC) method. With short-arc optical observations, the admissible region in the range and range rate plane can be identified from various physical constraints. The initial uncertainty of the space object can be depicted by samples of the admissible region. The challenge is that such an initial uncertainty distribution is hard to characterize analytically. Hence, the parametric representation, such as the conventional polynomial chaos based on a priori assumption of the distribution, cannot be directly used. The proposed APC does not need complete knowledge or even existence of the probability density function of the uncertainty. It requires only a finite number of moments, which are used to construct the orthogonal polynomial basis functions of APC and generate the stochastic collocation points/weights to determine the APC coefficients. The moments can be easily calculated using sampling data in the admissible region. Furthermore, the multielement APC is used to improve the accuracy and computation efficiency of APC for the long-term propagation. The APC is especially efficient when it is applied in the two-dimensional admissible region because it does not need to propagate a large number of collocation points.