Configuration uncertainty propagation of gravitational-wave observatory using a directional state transition tensor

Configuration stability is essential for a space-based Gravitational-Wave (GW) observatory, which can be impacted by orbit insertion uncertainties. Configuration uncertainty propagation is vital for investigating the influences of uncertainties on configuration stability and can be potentially useful in the navigation and control of GW observatories. Current methods suffer from drawbacks related to high computational burden. To this end, a Radial-Tangential-Ddirectional State Transition Tensor (RT-DSTT)-based configuration uncertainty propagation method is proposed. First, two sensitive directions are found by capturing the dominant secular terms. Considering the orbit insertion errors along the two sensitive directions only, a reduced-order RT-DSTT model is developed for orbital uncertainty propagation. Then, the relationship between the uncertainties in the orbital states and the uncertainties in the configuration stability indexes is mapped using high-order derivatives. The result is a semi-analytical solution that can predict the deviations in the configuration stability indexes given orbit insertion errors. The potential application of the proposed RT-DSTT-based method in calculating the feasible domain is presented. The performance of the proposed method is validated on the Laser Interferometer Space Antenna (LISA) project. Simulations show that the proposed method can provide similar results to the STT-based method but requires only half of the computational time.