## 4 Test and Result
### Ambiguity Resolution Analysis  
In the triangle network formed by BONE-STNY-NEWH, all baselines shared the common pivot satellite, and the closure residual of DD ambiguities should meet the following constraint: \(\
abla\Delta N_{\text{closure}}=\
abla\Delta N_{\text{BONE-STNY}}+\
abla \Delta N_{\text{STNY-NEWH}}+\
abla\Delta N_{\text{NEWH-BONE}}=0\). Thus, \(\
abla\Delta N_{\text{closure}}\) could be used to verify the proposed DF data-aided AR method. It should be noted that only DF data from GPS is used for a long baseline test since only GPS signal is stably received. To illustrate the reasonability for setting the window width of the moving average to be five epochs, Figure 9 gives the differential residuals of adjacent \(\
abla\Delta N_{w}\) on each baseline. The statics of results are shown in Table 3 and the results within \(\pm 1\) cycle are shown for easy observation. The threshold of \(\pm 0.1\) cycles, \(\pm 0.15\) cycles, and \(\pm 0.5\) cycles are also illustrated as limitations bounds. Figure 8: RMS improvement on each baseline. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Baseline** & **(\(-\)0.1, 0.1)** & **(\(-\)0.15, 0.15)** & **(0.5, 0.5)** & **Others** \\ \hline BONE\_STNY & 98.6679\% & 98.7700\% & 99.0339\% & 0.9661\% \\ NEWH\_BONE & 98.3097\% & 98.5279\% & 98.9901\% & 1.0099\% \\ STNY\_NEWH & 98.8000\% & 98.8726\% & 99.1373\% & 0.8627\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: \(\
abla\Delta N_{w}\) statistics of the triangle closure network. In Table 3, the proportion of residuals suppressed within \(\pm\)0.1 cycles is 98.6679% for BONE-STNY, 98.3097% for NEWH-BONE, and 98.8000% for STNY-NEWH, respectively. Meanwhile, the results increase slightly when the threshold bounds increase. Thus, set  
Figure 9: The \(\
abla\Delta N_{\text{w}}\) for each baseline of the triangle closure network. (**a**) BONE-STNY; (**b**) NEWH-BONE; (**c**) STNY-NEWH. ting the threshold to 0.1 cycles is reasonable and conservative, as most validated epochs are included. abla\Delta N_{\text{closure}}\) of all available satellites is shown in Figure 10. It could be found that, for most satellites, the \(\
abla\Delta N_{\text{closure}}\) converges to 0 once they are used and \(\
abla\Delta N_{\text{closure}}=0\) accounts for the majority. This means that \(\
abla\Delta N_{\text{BONE-STNY}}\), \(\
abla\Delta N_{\text{STNY-NEWH}}\), \(\
abla\Delta N_{\text{NEWH-BONE}}\) are fixed correctly without initialization. The outliers usually appeared at discrete epochs contaminated by cycle slip and could be further eliminated by refined data synchronization and cycle-slip detection. Figure 11 shows the detailed results of \(\
abla\Delta N_{\text{closure}}\) with a total of 23377 effective epochs used. The minimum and maximum outliers accompanied by the cycle slip are (\(-283.56\) cycles, 365.86 cycles). According to Table 4, the \(\
abla\Delta N_{\text{closure}}\) < 0.5 cycles in most epochs, meaning that the \(\
abla\Delta N_{\text{w}}\) can be correctly fixed by integer rounding with a success rate of not less than 93%. The 1.7154% epochs fall into 0.5-1 cycles and 2.7848% fall into 1-5 cycles are treated as small residuals and could be improved by synchronization and cycle-slip repair. However, at least one of the three baselines fails to fix its ambiguity for the remaining 1.6041% of epochs that include residuals larger than 10 cycles. Once the \(\
abla\Delta N_{\text{w}}\) is fixed, the corrected \(\
abla\Delta\varphi\) is used for the float solution, which is expected to be with a small variance. Figure 11: Ambiguity closure residual in the network. The BONE-GSBN and BONE-GSBN with the distance of 106.877 km and 58.942 km, respectively, are used for the long baseline test. The improvements are both benefiting from the 'DF Data-aid AR stage' and the 'filter stage'. Figure 12 and Table 5 show the positioning error on ENU components. The AMC-KF maintains the positioning error around 0 and no obvious difference occurs in all directions.