A Decoupled-and-Reduced Method for Configuration Uncertainty Propagation of Gravitational-Wave Observatory

A space-based gravitational-wave observatory usually contains three spacecraft, forming a triangle configuration in space for interferometry. Configuration stability is significant for a gravitational-wave observatory to ensure interferometry detection performance. Although a pre-designed configuration can satisfy the stability requirements, the stability can be impacted by uncertainties such as orbit insertion errors, which necessitates the investigation of configuration uncertainty propagation. Current configuration uncertainty propagation methods suffer from drawbacks related to high computational burden. To this end, this paper presents a decoupled-and-reduced method. First, a decoupled-and-reduced state transition tensor (DR-STT) is developed for orbital uncertainty propagation. The conventional STT is reduced by capturing high-order dominant secular terms. The secular and periodic terms are decoupled and integrated independently to reduce computational costs further. Then, high-order analytical derivatives are proposed to transform the uncertainties in orbital states into uncertainties in configuration stability indexes. The proposed method is successfully applied to solve the configuration uncertainty propagation problem of the Laser Interferometer Space Antenna project (LISA). Simulation results show that the proposed method can provide results comparable to the conventional STT-based method, but it requires only one-third of the computational time.