Insertion error correction and configuration maintenance optimization for geocentric gravitational wave detectors

Abstract

Space-based gravitational wave detectors have attracted considerable attention for their ability to detect low frequency gravitational waves generated by the universe’s most various sources. However, the high-precision detection requires extremely strict orbital insertion to maintain the configuration throughout the mission period. This paper presents an optimization method to correct orbital insertion errors using a low-frequency control strategy for long-duration, large-baseline spacecraft constellations. With active control, space-based gravitational wave detectors can mitigate initial orbit uncertainties. By presenting an evaluation algorithm and an estimating equation for fuel consumption and geometric indices, the segmented optimization method offers high computational efficiency. To adapt the control strategy to high-fidelity dynamics, an initial solution selection skill is proposed, and local refinements are employed. The application to the TianQin mission demonstrates the efficiency of the proposed method. The active control not only corrects the orbital insertion error but also reduces the geometric changes of the configuration by nearly 30% compared to an ideal deployment. The configuration maintenance strategy balances fuel efficiency and geometric stability, with a fuel consumption of only 421.57 m/s over the five-year mission period.