## 5 Experiment Setup and Result Discussion
First, the results demonstrate the effectiveness of the combined-constellation method. Besides that, the results of either single GPS or BDS take some time to enter a fixed solution while the combined method demonstrates a fast convergence as shown in the last row in Table 3. At the same time, the standard deviation as shown in the first three rows in Table 3 for all epochs of the combined method is much smaller than either single constellation method. Actually, for all epochs within the experiment, the overall standard deviation of GPS/BDS combined approach reaches 73.47 mm for East, 42.38 mm for North and 35.76 mm for Up which demonstrates an improvement over the other two methods. If we limit the scope to the fixed solutions, it is notable that all the three methods have similar precision level and the combined method does not show obvious improvement. Moreover, the proportion of fixed solution (ratio \(>\) 3) of the combined method (83.42%) is much higher than either single constellation method (39.98% and 34.08% respectively). This improvement shows that the GPS/BDS combination provides the higher availability of satellites and enhance the ability to enter fixed solution and therefore increase the availability of the RTK algorithm and its overall precision. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Item** & **GPS** & **BDS** & **GPS + BDS** \\ \hline East standard deviation (fixed solution)/mm & 0.30 & 0.48 & 0.26 \\ North standard deviation (fixed solution)/mm & 0.41 & 0.80 & 0.32 \\ Up standard deviation (fixed solution)/mm & 0.95 & 1.77 & 0.70 \\ Proportion of fixed solution (ratio\(>\)3) & 100\% & 100\% & 100\% \\ First time to fix/s & 1 & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistics of zero baseline experiment. Figure 6: ENU baseline result of 5.9 km baseline experiment (all epochs). Figure 8: Number of available satellites and ratio _vs_ time of 5.9 km baseline experiment. \begin{table}
\begin{tabular}{l l l l} \hline
**Item** & **GPS** & **BDS** & **GPS + BDS** \\ \hline East standard deviation (fixed solution)/mm & 3.60 & 3.20 & 2.67 \\ North standard deviation (fixed solution)/mm & 7.63 & 6.78 & 7.34 \\ Up standard deviation (fixed solution)/mm & 17.58 & 16.84 & 19.76 \\ Proportion of fixed solution (ratio \(>\) 3) & 39.98\% & 34.08\% & 83.42\% \\ First time to fix/s & 2277 & 2159 & 1 \\ \hline \end{tabular}
\end{table} 
Table 3: Statistics of 5.9 km baseline experiment. Figure 7: ENU baseline result of 5.9 km baseline experiment (fixed epochs, ratio \(>\) 3). The \"jumps\" of ENU baseline solution in Figure 6 are transitions between the float and the fixed solutions for which we only use a hard decision by the ratio threshold to determine if the solution is fixed or not. The ratio values for the three methods shown in the lower part of Figure 8 sometimes fall below the threshold in a sharp manner, and it can be observed from the upper part of Figure 8 that the sharp falls of ratio below the threshold are coincident with new satellite rising. This indicates that the falls are caused by the new rising satellite because, in general, the new rising satellite has a low elevation angle which brings a high risk with relatively low signal-to-noise ratio or/and severe multipath effect. This fact makes the new coming measurements introduce inconsistency into the Kalman filter's VC matrix \(\mathbf{P}_{\text{SD}}\), and causes the sharp falls of ratio. The third experiment has a longer baseline (9 km) and a longer testing time (6000 epochs) than the 5.9 km baseline test. Baseline positioning results are shown in Figures 9-11 (the variation of the number of satellites with time is shown in the upper part of Figure 11) and Table 4 which show some similarities to that of the 5.9 km baseline experiment. First, the fixed solution proportion of the combined method is higher than either using GPS or BDS.