# An Efficient BDS-3 Long-Range Undifferenced Network RTK Positioning Algorithm
###### Abstract  
In 2020, the BeiDou-3 global navigation satellite system (BDS-3) was officially completed and put into service. Currently, network real-time kinematic (RTK) technology is considered the main means through which to improve the positioning accuracy of the BeiDou navigation satellite system (BDS). This paper proposes a long-range undifferenced network RTK (URTK) algorithm, based on multi-frequency observation data of the BDS. First, the multi-frequency phase integer ambiguity resolution (AR) model considering atmospheric error parameters is designed, and the multi-frequency phase integer ambiguity of the long-range BDS reference station is determined. Then, the undifferenced integer ambiguity of each reference station is obtained, using linear variation based on the accurately determined phase integer ambiguity between reference stations, and the undifferenced observation error of each reference station is calculated. Considering the weakening spatial correlation of the observation errors between long-range stations, undifferenced classification error corrections of a reference station network are separated, according to different error characteristics. Finally, the inverse distance weighting method is employed to calculate the classification undifferenced error correction of the rover station. The rover station corrects the observation error through applying the undifferenced error correction to achieve high-precision positioning. The measured data of a long-range continuous operation reference station (CORS) network are selected for an experiment. The results show that the proposed algorithm can quickly and accurately realize the resolution of the BDS integer ambiguity of a reference station network and establish an undifferenced area error correction model in order to achieve accurate classification of undifferenced error correction values for a rover station. In China, the BDS-3 is superior to the global positioning system (GPS) in terms of the satellite number, position dilution of precision (PDOP) value, AR success rate, stability, and convergence time. The results show that the AR success rate, stability, and convergence time increase with the operational frequency, and the BDS-3 can achieve centimeter-level positioning of single-system rover stations without relying on the GPS. BDS-3; multi-frequency data; long-range; network RTK; classification error; undifferenced error correction 2023  
[PERSON], [PERSON], [PERSON], A. An Efficient BDS-3 Long-Range Undifferenced Network RTK Positioning Algorithm R. R.  
orbit (IGSO) satellites. The BDS-3 and BDS-2 have two of the same frequencies, B1I and B3I, but the B1C, B2a, and B2b frequencies have been added to the BDS-3 for the broadcast of B1I (1561.098 MHz), B2b (1207.14 MHz), B3I (1268.52 MHz), B1C (1575.42 MHz), and B2a (1176.45 MHz) signals. The increase in observation frequency has addressed data redundancy and improved positioning performance. Moreover, additional frequencies have provided a guarantee for the ambiguity resolution (AR) of the carrier phase in the solution process, and the positioning accuracy can also be significantly increased. Particularly under poor observation conditions, more frequencies can provide better positioning results. Furthermore, a larger number of frequencies improves compatibility and interoperability with other global satellite navigation systems (GNSS). The B1I and B3I signals of the BDS-3 are compatible with those of the BDS-2, and the B1C and B2a signals are compatible with the global position system (GPS) L1/L5 and Galileo E1/E5a signals, which provides favorable conditions for combining the BDS-3 with other systems. In [2], the authors studied the PNT, satellite-based augmentation, precise point positioning, short message communication, and Cospas-Sarsat performances of the BDS-3. In [3], the signal-to-noise ratio, pseudo-range observation error, and multipath error of the BDS-3 test system were studied and compared with those of the BDS-2.