In-orbit calibration of the gravitational reference sensor’s stiffness for the Taiji mission

Abstract Accurate in-orbit calibration of gravitational reference sensor (GRS) stiffness is essential for achieving the ultra-high precision required by space-based gravitational wave detection. This paper proposes a dedicated calibration scheme for calibrating the stiffness along the sensitive axis according to the installation layout of the GRS of the Taiji mission. The core innovation lies in designing a displacement excitation signal applied to the drag-free control system. By analyzing the relationship between the excitation input and the control system response, the stiffness is estimated using a Kalman-filter algorithm. Simulation results demonstrate that after 20 000 s of calibration experiments, the stiffness estimation accuracy meets the requirements of the Taiji mission, with the final relative error of 4.0 % . Accurate stiffness calibration is crucial for the in-orbit operation of Taiji’s GRS, as the system relies on this parameter to compensate the stiffness coupling acceleration, thereby further improving the precision and stability of the GRS.