# Performance Assessment of Multi-GNSS PPP Ambiguity Resolution with LEO-Augmentation
## 5 Conclusions and Discussion  
This paper focused on the positioning performance of single-system and four-system combined PPP-AR enhanced with the LEO ambiguity-float solution, to determine if the float solution could realize PPP-AR in a shorter TTFF. We designed two LEO constellations, L and M. L was a typical polar orbit constellation, with a larger number of visible satellites at high latitudes than at low and middle latitudes. M compensated for the shortage of visible satellites in L at low and middle latitudes, but it had no coverage in the polar regions. The ground observation data of the LEO satellites at the MGEX stations were simulated. Because GNSSs were fully operational, the GNSS data were real observation data from the MGEX stations. This study evaluated the positioning performance of LEO ambiguity-float solution-enhanced PPP-AR and compared it with LEO-enhanced PPP, based on the daily observation dataset collected at 258 stations in the global MGEX observation network over three days, from 1 January to 3 January 2022, in addition to LEO simulation data. In our estimated global GCE FCBs products, the NL FCBs of most GPS and Galileo satellites changed within 0.1 cycles in a day. For BDS-3, the stability was relatively poor. Satellites C34 and C46 had the largest changes, up to 0.6 cycles, while other satellites had changes within 0.4 cycles. The average STD of the NL FCBs for G, C, and E were 0.016, 0.054, and 0.014 cycles, respectively. By introducing L, M, and L+M constellations, the convergence time of single-system PPP was shortened from 29.1 to 9.7, 5.7, and 2.3 min, and the TTFF was shortened from 14.7 to 10.4, 9.4, and 7.9 min, respectively. The convergence time of the four-system combination PPP was shortened from 11.4 to 6.1, 3.0, and 1.8 min, and the TTFF was shortened from 8.6 to 6.8, 4.8, and 4.5 min. The L+M mixed constellation was the best solution for shortening convergence time of PPP and TTFF, followed by the M, and then the L constellation. Considering that the enhancement performance of the stations at different locations may vary, the 258 stations were divided into low-, middle-, and high-latitude zones for analysis. For ambiguity-float solutions, the convergence time of the L constellation-enhanced PPP in low, middle, and high latitudes was 14.1, 7.8, and 3.3 min, respectively. The higher the latitude, the faster the convergence speed. The convergence time of the M constellation-enhanced PPP in low, middle, and high latitudes was 5.4, 4.6, and 7.0 min, respectively. The convergence time of the L+M mixed constellations in low, middle, and high latitudes was within 3 min, and the latitude difference was not significant. Unlike ambiguity-float solutions, for the TTFF, the ambiguity-fixed solution PPP enhanced using the three LEO constellations showed the same latitude difference as that of the non-LEO constellation-enhanced PPP-AR. To further study the relationship between both PPP and PPP-AR enhanced with the LEO constellation and the number of LEO satellites, we controlled the number of LEO satellites in the L+M mixed constellation. For ambiguity-float solutions, the convergence speed increased nonlinearly with an increase in the number of LEO satellites, and gradually reached saturation. Meanwhile, the latitude difference in the convergence time almost disappeared with the control of the number of LEO satellites. For fixed-solution PPP, the TTFF decreased with an increase in the number of LEO satellites (which was not significant) and was close to saturation for four LEO satellites. We recommend the use of a mixed low-orbit constellation that integrates both inclined orbit satellites and polar orbit satellites, which have good enhancement performance not only in high latitudes but, more importantly, in low and middle latitudes as well. Since the world population is mostly distributed in the middle and low latitudes, the shorter convergence time in this region is more meaningful than that it would be in the high latitudes.