## 3 Experiment and Result Analysis
### Performance Analysis of Traditional Medium-Long Baseline RTK  
Prior to evaluating the RZTD-constrained model, GPS, BDS, and GPS/BDS-combined data were processed with the traditional RTK model. Thus, the factors affecting the precision of BDS medium-long baseline RTK positioning were analyzed and compared with the GPS performance. A precise float ambiguity is a prerequisite for a reliable AR. To a certain extent, the float RTK positioning solution can reflect the precision of float ambiguity and other correlated parameters. Figure 2 illustrates the traditional float RTK positioning results from six independent sessions on DOY016 solved with BDS, GPS, and GPS/BDS data. Due to space limitations, only the result of one baseline (here Baseline 6) is presented. As shown in the figure, the standard deviations (STDs) of the three baseline components for BDS RTK positioning were 0.116, 0.068, and 0.325 m, which are apparently higher than those for GPS (0.043, 0.038, and 0.131 m) and GPS/BDS (0.048, 0.034, and 0.117 m), particularly for the height direction. The height error of BDS for traditional RTK was over 0.5 m, even after 1 h of initialization in the first session. Figure 3 shows the satellite number and geometric dilution of precision (GDOP) values of the three situations for the first 2 h. Notably, the number of satellites for BDS is one or two more than that for GPS. However, the GDOP values of GPS are lower than those of BDS in most cases. As shown in Figure 4, the weak satellite geometric structure of BDS may be responsible for this result. The BDS satellites are more unevenly distributed than the GPS satellites. These two items are indicators of satellite geometric structure in a single epoch. The filter estimator captures the changes in satellite geometry and mapping functions over a certain period. This capability of the filter estimator enables us to distinguish the troposphere zenith delay from the height component. The condition numbers of BDS, GPS, and GPS/BDS scenarios were computed in the Kalman filter process. The condition number is defined by the ratio of maximal and minimal eigenvalues of the normal matrix for the estimates. This is a measure of how numerically well-conditioned or ill-conditioned a problem is [18; 19]. As shown in Figure 5, with changes in satellite geometry, the condition number decreased over time and tended to become stable after a certain period. Simultaneously, the condition number of BDS was significantly higher than those of GPS and GPS/BDS-combined. The condition number of BDS was over \(10^{2.5}\), even after convergence, which is higher than the value of GPS for the first epoch. A high condition number means a serious ill-conditioned problem, and thus the height component is difficult to distinguish from the troposphere parameter. Consequently, the low precision of the height component for BDS appears reasonable due to the poor satellite geometric distribution and the ill-conditioned problem. In addition, it can be seen that the GPS condition numbers went below the GPS/BDS model in Figure 5 after a longer time-span filtering. Compared with condition number of GPS/BDS without GEO satellites, we can conclude that this is mainly attributable to the BDS GEO satellites. With GEO satellites, the ill-condition number can be alleviated in the initial period; however, the geometry of GEO satellites remains almost unchanged--they may even hinder the reduction of condition number as time goes by. Figure 4: Sky plots (azimuth vs. elevation) for the rover station of Baseline 6 from 00:00:00 to 02:00:00 (red: BDS, green: GPS). Figure 3: (**top**) Satellite numbers and (**bottom**) geometric dilution of precision (GDOP) values of BDS, GPS, and GPS/BDS-combined situations. Figure 2: Float positioning results using the traditional real-time kinematic (RTK) model for Baseline 6. In principle, the geometric structure of GPS/BDS is considerably better than that of single GPS.