## 4 Experimental Results and Discussion
### Real Experimentation
In the original scene F, when the integer ambiguity solution of all of the satellites needs to be resolved again, the advantage of the TC-RTK/INS (1) method putting the floating ambiguity into the filter state will no longer exist. As shown in Figure 16c, if the ambiguity estimation is biased, this error will continue until the corresponding satellite becomes invisible. As for the TC-RTK/INS (2) method, it is clear that the algorithm has poor performance when the number of available satellites is small. The reason is that obtaining a fixed solution in this case is highly dependent on the satellite geometry and the quality of pseudorange observations. If the AR process fails, the TC-RTK/INS \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{3}{c}{**Large Noise Scene H**} & \multicolumn{3}{c}{**Insufficient Satellite Scene I**} \\ \cline{2-7}  & **Max Error** & **RMSE** & **Fix Rate** & **Max Error** & **RMSE** & **Fix Rate** \\ \hline TC-RTK/INS (1) & 0.665 & 0.343 & 86.57\% & 1.548 & 0.597 & 81.59\% \\ TC-RTK/INS (2) & 1.253 & 0.239 & 72.14\% & 1.344 & 0.311 & 59.20\% \\ ARPD-RTK/INS & 0.320 & 0.082 & - & 0.458 & 0.124 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Trajectory error and fix rate for different RTK algorithms on the real dataset (unit: m). Figure 18: **(a)** Error distribution in the ECEF-X axis for Scene H; **(b)** Error distribution in the ECEF-Y axis for Scene H; **(c)** Error distribution in the ECEF-Z axis for Scene H; **(d)** Error distribution in the ECEF-X axis for Scene I; **(e)** Error distribution in the ECEF-Y axis for Scene I; **(f)** Error distribution in the ECEF-Z axis for Scene I. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{3}{c}{**Original Scene F**} & \multicolumn{3}{c}{**Frequent Cycle Slips Scene G**} \\ \cline{2-7}  & **Max Error** & **RMSE** & **Fix Rate** & **Max Error** & **RMSE** & **Fix Rate** \\ \hline TC-RTK/INS (1) & 0.351 & 0.244 & 90.05\% & 0.396 & 0.133 & 83.58\% \\ TC-RTK/INS (2) & 0.818 & 0.128 & 85.07\% & 0.821 & 0.126 & 85.07\% \\ ARPD-RTK/INS & 0.330 & 0.079 & - & 0.376 & 0.101 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Trajectory error and fix rate for different RTK algorithms on the real dataset (unit: m). (2) algorithm can only degenerate to the accuracy of pseudorange. Our ARPD-RTK/INS algorithm uses a weighted average instead of a fixed solution, so it can always provide a more precise ranging measurement than the pseudorange. This advantage is reflected in Tables 5 and 6. When the pseudorange noise is added to the real dataset, the ARPD-RTK/INS algorithm can still maintain submeter-level accuracy. The maximum difference between the position results of the proposed algorithm and Inertial Explorer is less than 0.5 m in GNSS-challenged environments. This demonstrates the practicability of the new algorithm in the real environment. However, the fix rate of the other two tightly coupled algorithms decreases with the increasing pseudorange noise. The blue lines in Figure 18a-c show the negative effect of biased ambiguity estimation in the filtering process. It can be concluded that the ARPD-RTK/INS algorithm performs better than the traditional RTK/INS integrated algorithms in terms of accuracy and stability, especially in environments with large pseudorange errors.