Reduced-order uncertainty propagation for heliocentric gravitational wave observatories using semi-analytical sensitive directions

Orbit insertion uncertainties can significantly affect the configuration stability of heliocentric gravitational wave (GW) observatories, necessitating valid configuration uncertainty propagation techniques. Current configuration uncertainty propagation methods suffer from drawbacks related to their high computational complexity. To this end, this study proposes a novel configuration uncertainty propagation method for heliocentric GW observatories to reduce the computational complexity. First, the angular momentum and phase angle were found to be the two core variables for the orbit propagation of heliocentric GW observatories, the analytical solutions of which were derived using a perturbation-averaging technique. Subsequently, a first-order sensitivity matrix of the configuration stability index with respect to the initial states was derived based on the analytical solutions of the angular momentum and phase angle. Semi-analytically sensitive directions were obtained based on the derived sensitivity matrix, which was further employed to reduce the terms of configuration uncertainty propagation. The performance of the proposed method was validated using the example of a Laser Interferometer Space Antenna (LISA) project by comparing it with several competitive methods. The numerical results show that the proposed reduced-order method has a relative error close to that of the conventional full-state method and reduces the computational complexity by more than 46.