# Evaluation of BDS/GPS Multi-Frequency RTK Positioning Performance under Different Baseline Lengths
## 4 Multi-Frequency RTK Positioning Accuracy Analysis
### Positioning Accuracy
In DOY218, due to the low number of BDS-3 satellites, the B1 CB2a positioning error is large in the instantaneous mode, but it can still achieve high accuracy positioning when the continuous mode is selected. Since single epoch RTK ambiguity fixing ignores the correlation of ambiguities among epochs, its ambiguity fixing rate is low, especially in the case of long baseline RTK position  
Figure 5: Number of available satellites and PDOP value of METG–MET3 (3 km) baseline in DOY218 for BDS-3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Frequency**} & \multirow{2}{*}{**Fixing Rate**} & \multicolumn{3}{c}{**RMS**} \\ \cline{3-5}  & & **N (m)** & **E (m)** & **U (m)** \\ \hline BIC/B2a & 97.68\% & 0.010 & 0.006 & 0.021 \\ B1I/B3I & 100.00\% & 0.007 & 0.003 & 0.011 \\ L1L2 & 99.60\% & 0.008 & 0.004 & 0.017 \\ B1I/B3I(BDS-3) & 98.18\% & 0.008 & 0.005 & 0.020 \\ BIC/B2a/B3I & 98.30\% & 0.007 & 0.003 & 0.013 \\ \hline BIC/B2a & 98.49\% & 0.005 & 0.003 & 0.010 \\ B1I/B3I & 100.00\% & 0.005 & 0.003 & 0.010 \\ L1L2 & 99.96\% & 0.005 & 0.004 & 0.011 \\ B1I/B3I(BDS-3) & 98.43\% & 0.006 & 0.004 & 0.011 \\ B1C/B2a/B3I & 98.49\% & 0.005 & 0.003 & 0.010 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: METG–MET3 (3 km) average of instantaneous short baseline RTK RMS and ambiguity fixing rate. The upper part of the table is the instantaneous ambiguity fixing strategy, and the bottom part of the table is the continuous ambiguity fixing strategy. ing, and it is difficult to get a better RTK performance. Therefore, in practical applications, continuous ambiguity fixing strategy is generally adopted. To analyze the effect of the increasing baseline length, three groups of baselines, TGCU-TGBU (30 km), TGCU-TGDA (96 km), and TGCU-TGD2 (128 km), were selected. The RMSs of the above five frequency sets (BDS-3 (B1C/B2a), BDS-2+BDS-3 (B1I/B3I), GPS (L1L2), BDS-3 (B1C/B2a/B3I), BDS-3 (B1I/B3I)) in the RTK positioning mode are shown in Figures 6-8, and the seven-day RMS and ambiguity fixing rates of the average values are shown in Tables 6-8. In the region where the three baselines are located, the ionosphere is more active on two days between DOY220 and DOY221, resulting in generally high RMS values and slightly poor positioning accuracy. Due to the fewer visible satellites and poorer geometry distribution of BDS-3, the ambiguity fixing rates of BDS-3 (B1C/B2a), BDS-3 (B1C/B2a/B3I), and BDS-3 (B1I/B3I) are lower than those of BDS-2+BDS-3 (B1I/B3I) and GPS (L1L2). When the baseline length increases, the atmosphere residual increases and the accuracy of the ambiguity floating-point solution decreases, which makes the ambiguity fixing rate decrease. On the other hand, the increase in atmosphere residual increases the probability of ambiguity being fixed incorrectly, which affects the RTK positioning accuracy. The positioning accuracy of the five frequency sets is comparable for the short baseline, and the positioning accuracy of the BDS-2+BDS-3 (B1I/B3I) and GPS (L1L2) is slightly better. From Figures 6-8, we can see that with the increase in baseline length, the advantages of BDS-3 (B1C/B2a) and BDS-3 (B1C/B2a/B3I) become obvious, with errors in the N, E, and U directions being within 0.015 m, 0.010 m, and 0.030 m or less. Under the condition that only the BDS-3 satellite is used, the triple-frequency BDS-3 (B1C/B2a/B3I) is superior to the BDS-3 (B1C/B2a) and BDS-3 (B1I/B3I) in both positioning accuracy and ambiguity fixing rate. However, the improvement relative to BDS-3 (B1C/B2a) is not significant. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Frequency**} & **Fixing** & \multicolumn{3}{c}{**RMS**} \\ \cline{2-5}  & **Rate** & **N (m)** & **E (m)** & **U (m)** \\ \hline B1C/B2a & 93.53\% & 0.014 & 0.013 & 0.024 \\ B1I/B3I & 99.44\% & 0.014 & 0.011 & 0.025 \\ L1L2 & 99.59\% & 0.012 & 0.008 & 0.024 \\ B1I/B3I(BDS-3) & 93.07\% & 0.014 & 0.012 & 0.027 \\ B1C/B2a/B3I & 93.65\% & 0.013 & 0.010 & 0.024 \\ \hline \hline \end{tabular}
\end{table}