## 2 Scale Factor Calibrated Using Different AG Values  
Generally, calibration of SF was carried out in the baseline field before the gravity survey, and the AG values on the baseline are observed quasi-synchronously. However, AG measurements are usually completed only once a year, and owing to various uncontrollable reasons, the actual number of AG values might be less. Therefore, although relatively stable stations in a survey network can be selected as starting points for SF calibration, the different interval of AG values will affect the calibration results. In the following, taking the observation data of July 2020 in Yunnan as an example, the influences of different AG values on SF calibration are analyzed in combination with ABIC values. Based on Equation (7), the noise variance, drift variance, and SF are taken as hyperparameters, and the estimation of hyperparameters is optimized by calculating the ABIC minimum value. Table 2 lists the calibrated SFs of two CG-5 instruments in the YN Survey network obtained using AG values from different stations. Obviously, the ABIC values obtained using the MBGA method are all less than those derived using the BGA method. When SF calibration is performed using the AG values of all the 10 stations (Xiangcheng, Lijiang, Dali, Panzhihua, Kunming, Ruili, Gengma, Simao, Mengzi, Funing) in the survey network (Case 1), because the GD of the AG values can cover the maximum GD (approximately 305 mGal) of the entire network of YN and because there is a sufficient number of stations participating in the adjustment, the ABIC value is sufficiently small, which means that the calibrated SF is accurate. When taking only Lijiang, Kunming, Funing, Gengma, and Ruili into the adjustment to calibrate the SF (Case 2), because the number of AG values involved in the adjustment is reduced, the ABIC value is increased slightly; however, the calibrated SFs of two instruments remain almost the same as in Case 1 as the AG value can cover the maximum GD of the network. The influence on SF calibration of using only two AG values with different gravity intervals was tested. Case 3: When Lijiang and Funing are used as the control stations to optimize the SFs, the gravity interval of the two AG stations is approximately 302 mGal, which broadly covers the maximum GD. Although the ABIC value increased owing to the reduced number of AG stations, the SF deviation compared with Case 1 is only 25 ppm, and the deviation of the maximum GD is only 7.5 uGal, which is within the uncertainty of measurement error. Case 4: Further reduction of the difference between the two AG values to approximately half that of the maximum GD in the survey area, the deviation is approximately 60 ppm, the effect on the maximum GD reaches to 18 uGal, and the corresponding ABIC value keeps increasing. Therefore, we think that such calibration results are not reliable. Case 5: Finally, when the GD of the AG values is 56 mGal (Case 5), which is only one fifth that of the maximum GD, the ABIC value increases notably, and the deviation of the SF reaches 260 ppm, making the average error up to 16 uGal. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Relative**} & \multicolumn{6}{c}{**Scale Factors**} \\ \cline{2-7}  & **Original 1** & **Calibrated** & **Deviation** & **Original 2** & **Calibrated** & **Deviation** \\  & & **by CG-170** & **(ppm 3)** & **Original 2** & **by CG-170** & **(ppm)** \\ \hline CG-169 & 1.000253 & 1.000259 & 6 & 0.999956 & 0.999949 & 7 \\ CG-170 & 1.000066 & - & - & 0.999752 & - & - \\ \hline \hline \end{tabular} 1 calibrated using the long-baseline; 2 calibrated using the MBGA method; 3 ppm represents \(10^{-6}\).  
\end{table} 
Table 1: One gravimeter used to calibrate the scale factor of another. The above results lead to the following conclusions. (1) When under the same conditon, the ABIC values obtained using the MBGA method are all less than those derived using the BGA method, which means that the SFs calibrated by MBGA method are more appropriate.