## 3 Experiment and Result Analysis
### Performance Analysis of RZTD-Constrained Medium-Long Baseline RTK  
To alleviate the ill-conditioned problem and improve height precision in medium-long baseline RTK, the GPT2-constrained RTK model was used. The performance of RTK positioning were assessed based on this empirical model, and results are presented in this section. For fixed solutions, the TTFF,  
Figure 5: Condition numbers of the four situations in the Kalman filter process. GEO: geostationary Earth orbit. Figure 6: Bias of float ambiguities for satellites with a low elevation angle from 00:00:00 to 02:00:00.  
ambiguity fixed rate, and precision of the fixed solution were analyzed compared with the traditional RTK. In addition, the effect of the RZTD-constrained RTK model were analyzed with the data in different troposphere conditions. GPT2 is a global empirical model that provides troposphere delays. First, pressure, temperature and its lapse rate, water vapor pressure, and the hydrostatic and wet mapping function coefficients were determined for specific sites near the surface of the Earth. Thereafter, considering these meteorological parameters, the zenith hydrostatic delay (ZHD) and zenith wet delay (ZWD) were calculated using the equation in the Saastamoinen model [38]. Compared with ZTD provided by 341 IGS stations for one year, the mean bias and root mean square (RMS) errors of the GPT2 model were about 0.28 and 3.79 cm [39]. As a result, the \(\sigma\) for the a priori RZTD information in Equation (5) for every epoch was temporarily set as 4 cm here; the effects of different variances will also be discussed in next section. Figure 7 presents the float RTK positioning results of six independent sessions for the aforementioned baseline, where the GPT2-constrained RTK model was implemented. The STDs of the height component for BDS, GPS, and GPS/BDS were 0.135, 0.120, and 0.070 m, respectively, which were improved by 58.5%, 8.4%, and 40.2%, respectively, compared with the traditional RTK (Figure 2). Evidently, significant reductions in height deviation occurred in the initial period. The large fluctuations for the traditional BDS RTK shown in Figure 2 also disappeared. In terms of the eastern and northern components, nearly no improvement occurred compared with Figure 2. Although the positioning results from the two methods became comparable after convergence, the GPT2-constrained RTK solution tended to be more stable and exhibit fewer variations. The RTK fixed solution was determined for all 15 baselines on DOY016 given the AR strategies in Section 3.1. The ambiguity-fixed east/north/up coordinate solutions using the traditional and GPT2-constrained RTK model for six independent sessions of Baseline 6 are shown in Figure 8. The fixing rate of BDS was 82.7% for traditional RTK and 87.9% for GPT2-constrained RTK, an improvement of 6.3%. The fixing rate of GPS/BDS was 98.9% for the GPT2-constrained RTK, which was nearly unchanged compared with 97.9% for the traditional RTK. A possible reason for this is that the geometry of GPS/BDS is considerably better than that of single BDS. The contribution of external troposphere corrections to float ambiguity was not as apparent for GPS/BDS compared with single BDS. In terms of the accuracy of the fixed solution, the eastern/northern component was nearly unchanged, similar to that in the float solution. However, the height accuracy of the GPT2-constrained model improved considerably compared with the traditional RTK. The height STD of the GPT2-constrained RTK model was 0.021 m for BDS, which was improved by 61.1% over the 0.054 m in the traditional model. In addition, for the BDS of traditional RTK, the height error was over  
Figure 7: Float RTK positioning result using GPT2-constrained RTK model for Baseline 6. 0.1 m for a certain percentage of epochs, whereas the height error for all epochs was less than 0.1 m for GPT2-constrained RTK. In the GPS/BDS situation, the accuracy of the height component was improved by 51.5% and the abnormal values in the traditional RTK disappeared in the GPT2-constrained RTK.