Arbitrary Polynomial Chaos for Short-Arc Orbital Uncertainty Propagation

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Space object uncertainty propagation is critical to space situational awareness. However, due to a large number of space objects and limited available sensors, observations of a certain space object are sparse. As a result, short-arc orbit uncertainty propagation is common. By using various constraints, the admissible region for space objects can be identified using short-arc observations. The initial uncertainty of the space object can then be described by samples of the admissible region. The challenge is that the resultant initial uncertainty has no analytical form. Hence, the conventional generalized polynomial chaos method cannot be directly used. In this paper, an arbitrary polynomial chaos (aPC) is proposed to better represent the initial uncertainty, which requires only a finite number of moments of the initial uncertainty distribution, and does not require the complete knowledge or even existence of the probability density function. The moments can be easily calculated using sampling points in the admissible region. In addition, the multi-element aPC is utilized to improve the accuracy and computation efficiency of aPC for the long-term propagation. Simulation results demonstrate the superb performance of the proposed method to address both the short-term and long-term short-arc orbit uncertainty propagation problems.