## 4 Experimental Results and Discussion
### Experiments on Simulation Datasets
The new scene is defined as Scene C and Scene D, where the standard deviation of carrier-phase noise is still 5 mm, and the standard deviation of pseudorange noise becomes 3 m. The differences between the corresponding positioning results and the true values are shown in Figure 9 and Table 3.  
In theory, except for the ARPD-RTK/INS algorithm, the positioning results of the remaining algorithms are all related to the quality of the pseudorange observations. When the pseudorange noise \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{3}{c}{**Conditional Control Group C**} & \multicolumn{3}{c}{**Experimental Group D**} \\ \cline{2-7}  & **Max Error** & **RMSE** & **Fix Rate** & **Max Error** & **RMSE** & **Fix Rate** \\ \hline Single Epoch RTK & 15.811 & 0.442 & 87.51\% & 33.887 & 2.576 & 72.85\% \\ TC-RTK/INS (1) & 0.026 & 0.009 & 100\% & 3.976 & 1.208 & 83.62\% \\ TC-RTK/INS (2) & 0.195 & 0.019 & 88.78\% & 1.482 & 0.073 & 75.68\% \\ ARPD-RTK/INS & 0.021 & 0.009 & - & 0.044 & 0.012 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Trajectory error and fix rate for different RTK algorithms with large pseudorange errors (Unit: m). Figure 9: (a) Error distribution in ECEF-XY axis under Scene C; (b) Error distribution in ECEF-XY axis under Scene D.  
is large, it can cause errors when searching in the ambiguity domain. If satellites can be observed continuously, TC-RTK/INS (1) can maintain good accuracy due to the constraints of the correct fixed solution at the initial time. However, the algorithms that need to search for fixed solutions at each epoch, such as single-epoch RTK and TC-RTK/INS (2), will show a significant drop in the fix rate. The advantages of the new ARPD-RTK/INS algorithm are reflected when some of the satellites need to be re-tracked. At this time, the TC-RTK/INS (1) algorithm will suffer from the biased estimation of new ambiguities due to the influence of pseudorange errors, and this estimation will be reserved during the subsequent filtering process. In addition, we also conducted experiments in an environment with insufficient satellites. From 0 s to 1800 s, there exist frequent satellite changes, and there is no guarantee that there are more than five visible satellites. The standard deviation of the carrier phase noise is 5 mm, and the standard deviation of the pseudorange noise is 30 cm. The visibility of the satellites is shown in Figure 10. In this condition, only the tightly coupled RTK/INS integrations can obtain the positioning results continuously. From the position errors shown in Table 4 and Figure 11, we can conclude that as long as the number of visible satellites is not less than three, the ARPD-RTK/INS algorithm can obtain the available integer ambiguity solutions near the position predicted by INS. When the number of satellites is only two or less, it can only rely on the short-term positioning results of dead reckoning. Therefore, the overall accuracy is lower than the above four scenes, but it can still maintain decimeter-level accuracy. For TC-RTK/INS (1), when the number of visible satellites is small, a biased ambiguity estimation may be obtained. If the corresponding satellite is still being tracked continuously, the biased ambiguity will remain in the filter and cause the positioning result to shift, as shown by the blue line in Figure 12. For TC-RTK/INS (2), although the float ambiguity solution can be obtained with the aid of INS when the number of satellites is small, the fix rate is lower than 70%. Thus, this algorithm can only maintain the precision of the pseudorange most of the time.