# Inter-System Differencing between GPS and BDS for Medium-Baseline RTK Positioning
## 4 Experiments of Medium-Baseline RTK Positioning
### Positioning Results of the 22.4-km Baseline  
In the positioning tests, the initialization was carried out at the beginning of each day. Theoretically, real-time estimation of DISBs with characteristics of the slow time-variation is beneficial to both AR \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Baseline** & **Length/km** & **Duration** & **Sampling Interval** & **Receivers (Modules)** & **Location** \\ \hline CUT0-PERT & 22.4 km & 6 days (DOY 001–006, 2017) & 30 s & Trimble NETR9 & Perth, Australia \\ \hline TG00-TGT0 & 75.9 km & 20 h (UTC 4.00–2400, DOY 23, 2016) & 15 s & Trimble BD970 & Tianjin, China \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Information of the two medium baselines used in positioning experiments. Figure 5: L1-B1 and L2-B2 phase and code DISB time series for the baseline at Southeast University with receiver types of ComNav and Unicore. Figure 6: Number of GPS and BDS satellites for the two baselines with a cut-off elevation of \(10^{\circ}\). (a) CUT0-PERT. (b) TG00-TGT0. and positioning since additional redundancies are introduced. However, we find that the improvement for the AR in the RTK initialization period is very small. The average time to first fix (TTFF) of the two models with different visible satellites is shown in Figure 7. We can see that the TTFFs for the two models are very close, and just have small difference when a small number of satellites are visible. The reason is that in the initialization period, the DISB parameters with float ambiguities cannot achieve high precision, and thus only have small contribution to the convergence of ambiguities. However, once the ambiguities are correctly fixed for the first time, we can obtain the high-precision DISB estimators, and these will become useful information to strengthen the positioning model for the subsequent epochs. Figure 8 shows the positioning results with seven satellites for the 22.4-km baseline. The top three panels represent the results with the classical differencing model, while the bottom three represent the results with the inter-system differencing model. The positioning errors are obtained by comparing with the known coordinates. The initialization was carried out at the beginning of each day. On the whole, we can see that the ambiguity-fixed positioning results with the inter-system differencing model are more stable than those with the classical differencing model. The RMSs of positioning errors in North/East/Up directions are 1.07 cm/1.18 cm/6.96 cm for the classical differencing model. While for the inter-system differencing model, they are 0.81 cm/0.95 cm/4.59 cm, which represents an improvement of 23.9%/19.6%/34.1% in the three directions. Figure 9 depicts the theoretical positioning precisions with ambiguity-fixed solutions for the two models, which are derived from the corresponding diagonal elements of the variance-covariance matrix at each epoch. Regardless of the actual observations, the theoretical positioning precisions can directly reflect the strength of the positioning model. We can see that at most  
Figure 8: Positioning errors with seven satellites for the 22.4-km baseline with the classical differencing model and the inter-system differencing model. The vertical dot lines are the separation between consecutive initializations. Figure 7: The average time to first fix (TTFF) of the classical differencing model and the inter-system differencing model with different visible satellites. positioning precisions with the inter-system differencing model are obviously higher than those with the classical differencing model. This can also certify that the inter-system differencing model can strengthen the positioning model. The RMSs of positioning errors with different number of visible satellites are listed in Table 5. These values are derived from the positioning errors by comparing with the known coordinates. We can see that as the number of visible satellites increases, the positioning performances become generally closer for the two models.