# Improved PPP Ambiguity Resolution with the Assistance of Multiple LEO Constellations and Signals
## 1 Introduction  
Traditional precise point positioning (PPP) [1; 2] still suffers from the problem of a long initialization time to achieve a centimeter-level positioning accuracy, which also limits the wider application of PPP in some time-critical applications, such as precision agriculture, tsunami and earthquake warning, etc. To shorten the initialization time and improve the positioning accuracy, PPP ambiguity resolution (AR) has been proposed in recent years [3; 4; 5; 6; 7]. After the employment of AR, the positioning error of GPS PPP can converge to 5 cm in the three components within 30 min [8]. With the rapid development of multiple Global Navigation Satellite Systems (multi-GNSS), it is anticipated that more than 120 navigation satellites will offer a precise positioning service to all ranges of users by 2020 [9]. To assess the precise positioning performance with current multi-constellation GNSS, observation data of Multi-GNSS Experiment (MGEX) and BeiDou Experimental Tracking Network (BETN) networks were employed by [PERSON] et al. [9; 10]. It has been confirmed that the performance of PPP in terms of convergence, accuracy, continuity, and reliability can be significantly improved by the fusion of multi-GNSS [9; 11; 12]. The convergence time of GPS-only PPP can be shortened by 70% when GLONASS, BDS, and Galileo observations are added, while the positioning accuracy is improved by about 25% [9]. For PPPAR, the time to first fix (TTFF) and positioning accuracy can also be improved by the fusion of multi-GNSS. The positioning accuracy of the GCRE fixed solution within 10 min is (1.84, 1.11, 1.53) cm, while the GPS-only result is (2.25, 1.29, 9.73) cm for the east, north, and vertical components [13]. Under a multi-frequency environment, the joint of the extra frequencies brings more combinations of signals, which could potentially further improve the performance of PPP AR. [PERSON] et al. [14] demonstrated that triple-frequency PPP can achieve a successful ambiguity resolution within a few minutes based on the simulated data. [PERSON] et al. [15] and [PERSON] et al. [16; 17] performed triple-frequency PPP AR based on raw observations of GPS, BDS, and Galileo, respectively. Their results indicated that the third frequency could lead to an improvement in the PPP accuracy during the initialization phase. Currently, the era of low earth orbit (LEO) constellation is coming. Some famous international enterprises, such as American OneWeb, SpaceX, and Boeing, have announced that they will launch and develop their commercial LEO constellations consisting of hundreds or thousands of satellites [18; 19; 20]. These LEO satellites can not only provide broadband Internet and communication services on the world scale, but also serve as navigation constellations, broadcasting navigation signals and providing a positioning, navigation, and timing (PNT) service. The navigation function has also been confirmed in the 66-satellite Iridium system, the only current LEO network with constant global coverage. Compared to the GNSS satellites located at medium or high orbit, LEO satellites take advantage of a lower orbit altitude and stronger signal strength, which is expected to achieve high-precision positioning in severely occluded areas [21]. At the same time, the LEO satellite has a fast motion and thus the spatial observation geometry changes rapidly, which provides an opportunity to solve the problem of a too long convergence time of PPP. In addition, the LEO satellite usually employs a polar orbit or near-polar orbit, and thus many visible satellites in high-latitude areas can be observed, which can improve the navigation and positioning accuracy in these regions. To demonstrate the contribution of LEO to GNSS, many researchers conducted numerous experiments about LEO-augmented high-precision positioning based on the simulated LEO observations. [PERSON] et al. [22] found that with the inclusion of the LEO satellites, the convergence time of the GPS-only PPP decreased by 51.31%. The results of [PERSON] et al.