# An Efficient BDS-3 Long-Range Undifferenced Network RTK Positioning Algorithm
###### Abstract
In [4; 5], the overall design, coordinate reference system, time reference system, and the basic performance of the BDS-3 were introduced. The aforementioned studies provide an important reference base for the study of the BDS-3. The distance between reference stations is generally tens or hundreds of kilometers. The correlation between the atmospheric delay and the satellite orbit error is low, so the residual error of observation equations is larger than half the wavelength of the phase observation. Even when a reference station's coordinates are known, it is difficult to separate the integer ambiguity from the error. Therefore, the issue of how to address the integer ambiguity of the reference station has been one of the main problems in the undifferenced network real-time kinematic (URTK) algorithms [6]. The URTK algorithms include the development of a regional error model and the calculation of the user phase integer ambiguity. The network real-time kinematic (RTK) has been widely used in many fields, including deformation monitoring, cadastral surveying, and automatic driving [7; 8; 9; 10]. In [11], the network RTK was used to correct errors in local areas in order to improve the positioning accuracy of the RTK. In recent years, extensive research has been conducted on the AR of the network RTK reference stations. In [12; 13], the ionospheric model constraint method was used to improve a reference station's AR speed. In [14], an improved AR method for long-range reference stations with double tropospheric parameter restrictions was proposed. In [15], the authors proposed an ionospheric-free (IF) three-carrier ambiguity resolution (TCAR) method through which to resolve the ambiguity problem between the reference stations over long baselines. Further, in [16], the correlation between the baselines, composed of reference stations, was considered, and an efficient method of determining the AR of reference stations was developed based on the network solution mode to improve the accuracy of float ambiguity and accelerate the convergence speed of ambiguity. In [17], the optimal ambiguity subset was obtained via the optimized partial ambiguity solution method, which improved the AR rate between reference stations. In [18], a long-range BDS triple-frequency phase integer AR method, which considered the actual atmospheric delay variation constraint and integer ambiguity constraint of GEO satellites, was developed. In [19], a single-epoch determination method of triple-frequency phase integer ambiguity for a BDS reference station was studied. Recently, there have been many studies on network RTK algorithms. In [20], an undifferenced algorithm was proposed for network RTK; this algorithm uses the regional undifferenced error correction to correct the error of a rover station and realize its positioning. In [21], the authors conducted a comparative analysis of the double-difference model and the undifferenced model of the network RTK using the observed data of the BDS-2. A long-range network RTK method for the BeiDou satellite navigation system was studied in [22]. Currently, the GPS is the most mature and widely used GNSS. In [23; 24; 25], the network RTK positioning algorithm for the hybrid BDS-2-GPS system was studied under atmospheric constraints. In addition, much research on the BDS-3 has been conducted in recent years. In [26; 27], the authors mainly studied the network RTK performance of the BDS-3 at the B1C and B2a frequencies, and the results showed that the overall performance of B1C/B2a was better than that of B1I/B3I. In [28], the long-range network RTK of the BDS-3 four-frequency ionospheric weighted model was studied in order to improve its AR rate. The aforementioned studies mainly considered the BDS-2 and GPS systems, along with the performance of the BDS-3. However, there have been fewer studies on the long-range URTK algorithm of the BDS-3. This paper studies a BDS-3 single-system multi-frequency long-range undifferenced network RTK method.