  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 gradient. Due to installation and measurement
errors, fuel consumption during in-flight phase, and other factors, the offset
between the test-mass center and the center-of-mass (COM) 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 center-of-mass adjustment mechanism during the satellite's
lifetime. In this paper, we present a novel method, the Extended Kalman Filter
combined with 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 crosscheck to
estimate the offset of COM. The two methods are shown to give consistent
results, with the offset estimated to be $dx \approx $$-$$0.19$ mm, $dy \approx
0.64$ mm, and $dz \approx $$-$$0.82$ mm. The results indicate a significant
improvement on the noise level of GRS after the COM calibration, which will be
of great help for the future Taiji program.
