# Performance Assessment of Multi-GNSS PPP Ambiguity Resolution with LEO-Augmentation
## 4 Analysis
### LEO-Enhanced PPP and PPP-AR  
#### 4.2.1 PPP and PPP-AR Enhanced with Different LEO Constellations  
The positioning performance of both PPP and PPP-AR (enhanced using the L, M, and L+M constellations) was evaluated using ground observation simulation data of different LEO constellations. MGEX station ASCG (7.92\({}^{\circ}\)S, 14.33\({}^{\circ}\)W) was selected as a typical example. The results of the single-system and four-system combined float solution, in addition to the fixed-solution PPP enhanced using different LEO constellations, for this station on 3 January 2022, are shown in Figure 4a,b. It can be seen that the addition of the LEO satellite could significantly accelerate the convergence of PPP, and effectively accelerated the first fix of PPP-AR. The convergence speeds in the east (E), north (N), and up (U) directions were clearly improved, and the fixed solutions exhibited similar results. Compared with single-system PPP, four-system combined PPP converges faster, leaving less room for improvement of LEO satellites. Similarly, the improvement of the fixed  
Figure 3: Time series of the NL GCE FCBs on 1 January 2022: (**a**) GPS; (**b**) BDS-3; and (**c**) Galileo. solution was not as significant as that of the float solution. The L+M mixed constellation was the best, followed by the M constellation, and then the L constellation. Figure 4: _Cont._  
Figure 5 shows the average convergence time of PPP enhanced using different LEO constellations. In this study, the convergence time was set as the time when the positioning error in the E, N, and U directions was less than 0.1 m and lasted for 10 min. By introducing the 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 convergence time of the four-system combined PPP could be shortened from 11.4 to 6.1, 3.0, and 1.8 min. The L+M constellation showed the shortest times, followed by the M constellation, and then the L constellation. This was because the L constellation had few visible satellites in almost the entire mid-low latitudes, and the M constellation had only a blank coverage in the polar region. The hybrid constellation combined the advantages of the L constellation in high latitudes and the M constellation in middle and low latitudes, with an abundance of visible satellites on a global scale, as shown in Figure 1. For the positioning scheme with only the BDS-3 system, the convergence speed of PPP improved significantly. After the introduction of the L, M, and L+M constellations, the convergence time was reduced from 45 min to 2 min, which is a 96% reduction. Figure 6 shows the average TTFF of the PPP-AR enhanced with different LEO constellations. In this study, TTFF was defined as the time required for at least five epochs to successfully achieve a fixed ambiguity solution. By introducing the L, M, and L+M constellations, the TTFF of single-system PPP could be shortened from 14.7 to 10.4, 9.4, and 7.9 min, respectively, and the time to first fix of the four-system combination PPP could be shortened from 8.6 to 6.8, 4.8, and 4.5 min, respectively. Similar to the float solution, the L+M constellation was the best, followed by the M constellation, and then the L constellation. The fixed solution showed only a 46% improvement, compared with a 92% improvement for the single-system float solution. Table 2 shows the average positioning accuracy of different LEO constellation-augmented PPP and PPP-AR in the east, north, and up directions, respectively. Again, the reference coordinate of this study was the coordinate value in the SNX weekly solution file provided by the IGS, and the positioning accuracy was represented by the positioning error of the last epoch. The positioning accuracy of ambiguity-float solution PPP in E, N, and U  
Figure 4: Comparison of positioning performances of different LEO constellations augmented PPP and PPP-AR in east, north, and up directions, respectively, at station ASCG on 3 January 2022: (**a**) PPP; (**b**) PPP-AR.