Global precision analysis of carrier phase relative positioning in BeiDou navigation satellite system and United States global positioning system

In this paper, we derived a high-efficiency formula for calculating the precision of carrier phase relative positioning, analyzed the various factors that affect the positioning accuracy using the carrier phase, and proposed the concept of using a frequency dilution of precision to describe the quantitative effect of different frequency combinations on the positioning precision. To this end, we computed and plotted the global spatial distribution map of the relative positioning dilution of precision for single-day solution, half-hour solution, and single-epoch solution of the global positioning system (GPS), regional Beidou navigation satellite system (BDS2), future global Beidou navigation satellite system (BDS3), and their fusion systems. Using processing software with autonomous intellectual property rights (GCN and VENUS/ARSNet), we solved the measurement data and examined the positioning precision of the single-day solution and single-epoch solution of GPS and BDS2. The analysis demonstrated that the B1/B2 frequency positioning precision of BDS2 was better than that of L1/L2 frequency positioning of GPS, but the positioning precision of the BDS2 is worse than that of GPS over most of the service region of the BDS2. Further, the positioning precision of BDS3 is better than that of GPS in the Asia-Pacific region, while it is the opposite in other regions. Based on these conclusions, we put forth some optimization recommendations regarding the signal frequency of the navigation system and GPS measurement standards to serve as references for optimizing the system performance and formulating standards.