Orbital Error Propagation for Geocentric Space-based Gravitational Wave Observatory Based on KRG-HDMR Method

The long-term configuration stability is essential for the space-based gravitational waves observatory (SGWO). The orbit insertion error immensely impact the configuration stability, whose propagation is essentially a high-dimensional problem and causes a heavy computational burden because of the long-term propagation requirement. This paper investigates the insertion state error propagation problem and comprehensively analyzes the effects of the error on configuration stability based on the Kriging-High Dimensional Model representation (KRG-HDMR) method. The high-dimensional error propagation problem is first divided into several low-dimensional sub-problems effectively according to the HDMR theory, which greatly reduces the computational burden. Then the KRG model is employed to ensure the efficiency and accuracy of the propagation. Finally, the influence of the insertion direction and magnitude is widely analyzed. Simulations show that the KRG-HDMR method is highly efficient and accurate with the relative errors smaller than 0.2% compared with Monte-Carlo simulation. The results show that the radial position and tangential velocity insertion errors have great effects on the configuration stability. The position and velocity insertion errors less than 16 m and 0.33 mm/s as well as 45 m and 0.88 mm/s for 2 and 5 yrs, respectively, can meet the stability requirement. The results provide comprehensive reference for the configuration design and mission implementation of geocentric SGWO.