Orbital Uncertainty Propagation via Multi-Element Arbitrary Polynomial Chaos

Space object uncertainty propagation is critical to space situational awareness. One of uncertainty representations is the polynomial chaos (PC) or generalized PC (gPC) using a set of fixed orthogonal polynomials in a given propagation time. However, it is inconvenient to use the gPC for very long-term propagation since required terms increase dramatically as the order of the gPC increases. To reduce the computational complexity, we propose a new multi-element polynomial chaos strategy. Due to the irregular uncertainty distribution of each element, we propose to use the arbitrary polynomial chaos (aPC) to represent the initial uncertainty at the beginning of each element. The aPC is a data-driven approach to construct PC, which does not require the complete knowledge or even existence of the probability density function, but requires only a finite number of moments of the distribution, which can be readily computed from sampling data. The stochastic collocation with the sparse-grid technique is used to compute the coefficients of the aPC. Simulation results demonstrate the superb performance of the proposed method for the long-term orbit uncertainty propagation.