Calibration of key parameters during the in-orbit phase for the Taiji-2 gravitational reference sensor

The Taiji mission, a pioneering Chinese space-borne gravitational wave observatory, requires ultra-precise calibration of its gravitational reference sensors (GRSs) to achieve its targeted sensitivity of $3\times10^{-15} \mathrm{\ m\ s^{-2}\ Hz^{-1/2}}$. Maintaining this precision is challenged by time-varying scale factors drifts and dynamic center-of-mass (c.m.) offsets between the test masses (TMs) and spacecraft, driven by factors such as propellant consumption, thermal effects and aging electronics. This paper develops an advanced in-orbit calibration framework that simultaneously estimates the GRS scale factors and c.m. offsets between TMs and spacecraft through a combination of spacecraft maneuvers and Kalman filter. By applying periodic torque signals to induce controlled spacecraft angular accelerations, we leverage star tracker and GRS readouts to disentangle coupled disturbances and achieve dual-parameter calibration with unprecedented precision, with scale factors errors below 0.2\% and c.m. offsets residuals within 100 $\mathrm{\mu}$m, satisfies the Taiji-2 calibration requirements. This method is robust across different satellite configurations. The results not only ensure the feasibility of Taiji-2's scientific objectives but also establish a scalable calibration paradigm for future missions such as Taiji-3, where sub-micrometer c.m. stability and ultra-low noise gravitational reference will be essential.