## 3 Experiment and Result Analysis
### Performance Analysis of RZTD-Constrained Medium-Long Baseline RTK
The improvement of the height component was 25.8% for GPS, which was less than that for BDS and GPS/BDS. As shown in Figure 8, the effect of the external troposphere correction on the horizontal accuracy of RTK positioning was not apparent; thus, only the height component is shown in the following analysis. Figures 9 and 10 illustrate the statistical results of TTFF, fixed rate, STD, and RMS errors in the vertical direction for all 15 baselines on DOY016. As introduced in Section 3.1, for each baseline, the TTFF was calculated using the results of 41 sessions; the remaining three indicators were calculated using six independent sessions, in order to avoid duplication of statistics. The reference coordinates were determined by the post-processing GAMIT software [40]. It can be seen that TTFF was accelerated when the GPT2-constrained model was used. Generally, BDS showed longer TTFF, and the TTFF of two baselines was even more than 50 epochs (30 s interval) for the traditional model; this may be due to the heterogeneous satellite distribution and long convergence time of the ambiguity parameter for GEO satellites. Compared to GPS and BDS, GPS/BDS showed great improvement in TTFF; the TTFF of 11 baselines was less than three epochs in the GPT2-constrained model. In terms of ambiguity fixed rate, all 15 baselines improved using the GPT2-constrained model. For BDS, Baselines 7, 10, and 12 exhibited an improvement of 14.1%, 15.0%, and 9.3%, respectively; the average improvement was approximately 7.5%. However, only a slight improvement was observed for the GPS/BDS-constrained RTK model. Meanwhile, the fixing rate decreased as the baseline length became longer. A large residual atmospheric error--particularly for ionosphere delay--may account for such a result. In addition, the STD of the height component was reduced considerably. The height STDs of 11 baselines were reduced by over 50% for BDS, whereas the STDs of 10 baselines were reduced by over 40% for GPS/BDS. The STDs of the fixed results for three exceptional baselines were over 0.1 m. Incorrectly-fixed ambiguities for certain epochs were responsible for this situation. The correct integer ambiguities were judged by comparing the ambiguities derived from RTK mode with post-processing mode. The lengths of the two baselines were 138.9 km and 166.9 km, respectively. A long baseline  
Figure 8: Fixed RTK positioning results solved using the (**a**) traditional and (**b**) GPT2-constrained models. The letters e/n/u represent the standard deviation (STD) of position results in the east/north/up directions, respectively. will have a high probability of being incorrectly fixed, particularly for weak geometric structure conditions such as the BDS-only situation. In addition, the STD of Baseline 5 for BDS traditional RTK was also more than 0.1 m, which was similarly caused by incorrectly-fixed ambiguities for certain epochs. However, the STD became normal when the GPT2-constrained RTK model was used, indicating that external troposphere corrections were helpful in improving model strength and float ambiguity accuracy. The RMS error of the positioning results for the GPT2-constrained RTK model also decreased considerably compared with that for the traditional RTK model. The average performance improvement of height RMS error was 44.2% and 33.1% for BDS and GPS/BDS situations, respectively. Figure 10: (**a**) Vertical STD and (**b**) root mean square (RMS) error of the fixed solution using traditional and GPT2-constrained RTK. Figure 9: (**a**) Time to first fix (TTFF) and (**b**) fixed rate of the fixed solution using traditional and GPT2-constrained RTK. To analyze the effect of the GPT2-constrainted RTK model in different troposphere conditions, the data from the other three days (DOY092, 190, 289) in spring, summer, and autumn were processed, and the \(\sigma\) for the a priori RZTD in Equation (5) was set as 4 cm.