In-Orbit Calibration of the Gravitationa Reference Sensor’s stiffness for the Taiji Mission

In space-based gravitational wave detection missions, various internal physical effects within the spacecraft—such as circuit noise, magnetic noise, and self-gravity—introduce non-negligible equivalent stiffness. This stiffness couples with the test mass motion to generate acceleration noise,which directly constrains the precision of gravitational reference sensor and the achievement of scientific detection goals; therefore, stiffness estimation is of paramount importance. To address this issue, based on the installation layout of the gravitational reference sensor on the satellite for the Taiji mission, this paper proposes an in-orbit stiffness calibration scheme along the sensitive axes. First, a dynamic model incorporating stiffness coupling terms is established. Specific displacement excitation signals are then designed and injected into the drag-free control system to excite the dynamic response of the system. Subsequently, the relationship between the excitation input and the system response is analyzed, and a Kalman filter algorithm is applied to estimate the stiffness within a multi-source noise environment. Numerical simulation results demonstrate that after a 20,000 s in-orbit calibration experiment, the final relative errors of the stiffness estimation for test mass 1 and test mass 2 are 0.489% and 0.454%, respectively, thereby validating the feasibility of the proposed scheme under simulated realistic noise conditions.