## 1 Introduction  
Although traditional global navigation satellite systems (GNSSs), as sophisticated and complex systems, are widely used in navigation, positioning, and timing, GNSSs still cannot overcome their own bottlenecks, such as their weak signal power (only 20 W power interference can cause denial of a cell's GNSS signal [1]), coupled with multiple paths, especially in challenging environments, such as lush forests, canyons, cities with tall buildings, indoor locations, and polar regions. GNSS signals are easily blocked, and the number of visible satellites decreases as the visible elevation angle increases, leading to unusable multisatellite positioning. There are also deficiencies in the accuracy, reliability, availability, and anti-interference. In recent years, a program to provide global internet access based on broadband low earth orbit (LEO) constellations has been reproposed. The purpose of this program is to provide truly global and robust broadband coverage and access, to expand the coverage of geosynchronous (GEO) satellites to polar regions, and to improve the user positioning accuracy [2]. Compared with traditional GNSSs, LEO constellations offer the advantages of a large number of satellites, high accuracy, and high availability and the LEO system can be used for communication, cm-level navigation enhancement, and positioning services. In addition, LEO satellites are closer to the earth, which means that less path loss and the stronger signal power undoubtedly enhance the anti-interference ability of the system, and they are considered to be an important direction for future development. Radio communication and navigation have many similar technical foundations, but they have different needs in terms of information transmission and signal measurement and have evolved along their own routes. With the rise of concepts such as the internet and autonomous driving, positioning and communication functions have become inseparable, and the necessity of communication and navigation integration has become a consensus. Therefore, the concept of integration of the technology of positioning, navigation, timing, remote sensing, and communication (PNTRC) has been proposed in recent years [3] PNTRC can be used as a space-based internet access station to solve global internet access problems, but also as a navigation and communication information source to achieve the rapid convergence of precise positioning, communication, and navigation realized by only one link. Therefore, the study of LEO constellation single-satellite positioning technology solutions based on PNTRC has the outstanding advantage of a high availability, thereby providing an opportunity to solve the problem of location services in the challenging environments mentioned above. To apply the LEO constellation to the field of navigation and realize the PNTRC, many scholars have made bold attempts and provided many creative solutions. Reference [4] studied the feasibility and performance of the LEO constellation as a potential navigation enhancement platform and evaluated and analyzed the comprehensive performance, coverage rate, and signal strength of the LEO constellation. The results show that the LEO system has a better performance than GNSSs and can be used as a navigation enhancement platform in challenging environments. Reference [5] Based on PNTRC, the LEO communication satellite signal and the E-911 ground cellular signal have been integrated to provide positioning services. Reference [6] The new ideas and functions of PNTRC have been integrated into the signal system, and the basic technology of PNTRC has been researched at the signal-design level. To realize the benefits of PNTRC to enhance the GNSS system and improve the usability of LEO constellations, reference [7] proposed a global navigation enhancement system based on the LEO constellation.