## 1 Introduction  
The long convergence time of precise point positioning [1] is a troublesome factor limiting its wider adoption, especially in real-time applications [2]. Thus, many efforts have been made to improve the PPP performance, such as improving the GNSS orbit and clock products [3], speeding up the ambiguity resolution (AR) [4; 5; 6; 7; 8], using multi-frequency GNSS signals [9; 10; 11], and combining multi-constellation GNSS systems [12; 13; 14]. With the rapid development of multi-GNSS constellations, multi-GNSS PPP has been of interest because of its potential to significantly improve the positioning performance in terms of accuracy and convergence time. The multi-GNSS PPP can be traced back to 2007 [12] when only GPS and the GLONASS systems were available. Since then the positioning accuracy and convergence time have been confirmed to be improved [13; 15; 16]. China's BeiDou Navigation Satellite System (BDS) has been providing the positioning, navigation, and timing (PNT) service to the whole Asia-Pacific region with the constellation of five geostationary Earth orbit (GEO) satellites, five inclined geosynchronous satellite orbit (IGSO) satellites, and four medium Earth orbit (MEO) satellites since the end of 2012 [17]. The European Galileo satellite navigation constellation has announced the start of initial service [18], which will consist of thirty satellites in three orbital planes. With this progress, multi-GNSS PPP has attracted increasing interest in the GNSS community, and many types of research have been conducted to show the performance of multi-GNSS [19; 20; 21; 22]. Though the convergence time can be indeed improved compared to single-system PPP, it still takes several tens of minutes for multi-GNSS PPP initialization since the satellite geometry change with respect to a ground station is slow, taking satellites hours to pass overhead. Recently, some commercial companies, such as SpaceX and OneWeb, have proposed to build global LEO constellations, which would consist of hundreds of LEO satellites to provide access to the Internet worldwide [23]. This sheer number of LEO satellites gives rise to great opportunities not only for broadband communication, but also as a platform for navigation services. Compared to the GNSS satellites, the LEO satellites have the advantage of being closer to the Earth, thus delivering potentially stronger signals. Moreover, LEO satellites move faster relative to ground stations, passing them in minutes instead of hours for MEO satellites. This brings great geometry changes and, consequently, results in a shorter convergence time for precise positioning. However, many LEO satellites are needed to cover the Earth because of their small footprint compared to GPS satellites. Scientists from Stanford University [24] made a thorough investigation of the user geometry, signal-in-space ranging error (SISRE), and how these LEO constellations can be piggybacked to deliver navigation services. In this study, we propose an extended GNSS system with a LEO constellation transmitting navigation signals, which is called a LEO-enhanced Global Navigation Satellite System (LeGNSS), for precise positioning service. Since there is no LEO GNSS-like data at ground stations so far, we developed simulation software to simulate all the observations, including GNSS observations and LEO observations for ground stations. Even though we can simulate all the GNSS observations, it is not necessary since the convergence time of multi-PPP still needs about 10 min. We employ 24 GPS satellites as initially designed, 14 BDS satellites serving the Asia-Pacific region currently, and the Iridium satellite constellation consisting of 66 LEO satellites for our LeGNSS system. The reasons we chose these three systems are as follows: Firstly, the products of GPS have the best consistency and the performance of GPS can be used as the reference in our data simulation. Secondly, BDS, as the regional navigation satellite system, has its own characteristics with three different types of orbits.