Calibration of the in-orbit center-of-mass of Taiji-1

The Taiji program is a space mission aiming to detect gravitational waves in the low-frequency band. Taiji-1 is the first technology demonstration satellite of the Taiji Program in Space, with the gravitational reference sensor (GRS) serving as one of its key scientific payloads. For accurate accelerometer measurements, the test-mass center of the GRS must be positioned precisely at the center of gravity of the satellite to avoid measurement disturbances caused by angular acceleration and gradients. Due to installation and measurement errors, fuel consumption during the in-flight phase, and other factors, the offset between the test-mass center and the center of mass (c.m.) of the satellite can be significant, degrading the measurement accuracy of the accelerometer. Therefore, the offset needs to be estimated and controlled within the required range by the c.m. adjustment mechanism during the satellite's lifetime. In this paper, we present a novel method-the extended Kalman filter combined with the Rauch-Tung-Striebel smoother-to estimate the offset while utilizing the chi-square test to eliminate outliers. Additionally, the nonlinear least squares estimation algorithm is employed as a cross-check to estimate the offset of the c.m. The two methods are shown to give consistent results, with the offset estimated to be dx -0.19 mm, dy 0.64 mm, and dz -0.82 mm. The results indicate a significant improvement on the noise level of GRS after the c.m. calibration, which will be of great help for the future Taiji program.