# Assessment of Quad-Frequency Long-Baseline Positioning with BeiDou-3 and Galileo Observations
## 5 Conclusions  
In this study, founded on the principles of a small noise amplitude factor and a small ionospheric scalar factor, we selected the optimal triple-frequency EWL/WL signals (B1I,B3I,B2a) of BDS-3 and (E1,E5a,E6) of Galileo in the four frequencies. A long-baseline AR method based on optimal triple-frequency EWL/WL combinations was proposed. In order to test the positioning performance and AR of the optimal triple-frequency EWL/WL combinations, two configurations of typical triple-frequency EWL/WL signals and quad-frequency EWL/Second EWL/WL signals were added.  
From all the discussion above, we can draw the following conclusions:  
1. From the experimental results of the 104 km and 126 km baselines, it was shown that the ambiguities of EWL signals mentioned in this paper can be fixed reliably in single-epoch, whether it is BDS-3 or Galileo.  
Figure 10: The success rate of theoretical EWL AR under different total errors.  
2. The optimal triple-frequency EWL/WL combinations with (B1I,B3I,B2a) and (E1,E5a,E6) signals can achieve the same precision as that with quad-frequency signals, which can be applied to most long-baselines with a success rate of more than 99.4%.
3. This method can achieve instantaneous precision at the decimeter level and can be applied to large-range network RTK positioning, long-distance navigation, and positioning in open environments. In the application of relative positioning, filtering and smoothing methods can also be used to achieve higher precision positioning results.
4. With the increase in available satellites and satellite frequencies in the future, the dimension of matrix will be greater. It is necessary to eliminate redundant frequencies when calculate the multi-dimensional matrix. Selecting the optimal frequencies can greatly reduce the dimension of matrix and is an effective method.  
[PERSON] conceived the idea and designed the experiments with [PERSON] and [PERSON], [PERSON] wrote the main manuscript. [PERSON], [PERSON], and [PERSON] reviewed the paper. All components of this research were carried out under the supervision of [PERSON]. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (grant No. 41904022 and 41774027) and by the National Key Technologies R&D Program (grant No. 2016 YFB0502101).  
Not applicable.  
The data presented in this study are available upon request from the corresponding author. The data are not publicly available due to security issues.  
We thank all the scientists and principal researchers who prepared and provided the research data. We would also like to thank our colleagues from the School of Instrument Science and Engineering who provided profound insights and expertise to our research.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} EWL & extra-wide-lane \\ WL & wide-lane \\ DD & double-differenced \\ RTK & real-time kinematic \\ GB & geometry-based \\ GNSS & Global Navigation Satellite System \\ BDS & BeiDou Navigation Satellite System \\ IOV & In-orbit verification \\ FOC & operational capability \\ AR & ambiguity resolution \\ PPP & precise point positioning \\ MHz & Mega Hertz \\ OMC & observed minus computed \\ LAMBDA & Least-squares AMBiguity Decorrelation Adjustment \\
3D & three-dimensional \\ DOP & dilution of precision \\ DOY & day of year \\ GPT2w & Global Pressure and Temperature 2w \\ STD & standard deviation \\ \end{tabular}