# An Efficient BDS-3 Long-Range Undifferenced Network RTK Positioning Algorithm
## 5 Conclusions  
This paper proposes a BDS-3 multi-frequency URTK method for a long-range reference station network. First, the double-difference multi-frequency phase integer AR model of a reference station network is constructed considering the atmospheric error. The double-difference integer ambiguity sum of the closed reference stations of zero is set as a constraint condition to realize accurate determination of the double-difference integer ambiguity of a reference station. Then, the double-difference integer ambiguity is converted into undifferenced integer ambiguity using a linear relationship of double-difference integer ambiguity between reference stations, and it is substituted into the observation equation of a reference station in order to calculate the comprehensive undifferenced error correction value. Considering different characteristics of the observation error, dispersion error (ionospheric delay error), and non-dispersion error based on the tropospheric delay error are calculated. The undifferenced error correction value of a rover station is calculated using inverse distance weighted interpolation; finally, the error correction and high-precision positioning of the rover station are realized.  
Using the CORS network data, the positioning process and accuracy analysis of B1I/B1C/B2a/B3I, BIC/B2a/B3I, B1I/B2a/B3I, BIC/B2a, B1I/B3I, and GPS are performed. The experimental results show that the B1I/B1C/B2a/B3I, BIC/B2a/B3I, and B1I/B2a/B3I are better than B1C/B2a, B1I/B3I, and GPS in terms of their AR success rate, stability, convergence time, and positioning accuracy; also, the positioning performance of the BDS-3 is generally better than that of the GPS system. Comparing the positioning results of each combined observation with the known values of coordinates, the deviations in the E, N, and U directions of coordinate components are calculated to be at the centimeter level; thus, centimeter-level positioning can be achieved using the proposed method. The proposed method has good application prospects in various fields, including agricultural production, location service, and deformation monitoring.  
The results have indicated that multi-frequency data can significantly improve the positioning performance of the URTK. However, in future work, it is necessary to study long-range URTK positioning performance for the gathering of further multi-system multi-frequency observation data.  
[PERSON] conceived the idea and designed the experiments with [PERSON], [PERSON], [PERSON] and [PERSON] and wrote the main manuscript. [PERSON], [PERSON] and [PERSON] reviewed the paper. All components of this research were carried out under the supervision of [PERSON] and [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 (Nos. 42030109, 42074012) and the open fund of the State Key Laboratory of Satellite Navigation System and Equipment Technology (No. CEPNT-2018 KF-13), and it was supported by the LiaoNing Revitalization Talents Program (Nos. XLYC2002101, XLYC2008034, XLYC2002098).  
The authors gratefully acknowledge Kepler for providing the multi-GNSS data. The other datasets are available from the corresponding author on reasonable request.  
The data in this paper were provided and allowed to be used by Kepler Satellite Technology Co Ltd., Wuhan, China. The authors gratefully acknowledge Kepler for providing the multi-GNSS data.  
The authors declare no conflict of interest.