# Improved PPP Ambiguity Resolution with the Assistance of Multiple LEO Constellations and Signals
## 5 Conclusions  
This paper investigated the performance of PPP ambiguity resolution with the augmentation of different LEO constellations. The contribution of triple-frequency observation of LEO to ambiguity resolution was also analyzed. Based on the simulated observation data for ground stations, the UPD products of the GNSS and LEO satellites were estimated and the temporal characteristic, as well as residuals distribution, were analyzed. With the UPD products, the LEO-augmented PPP ambiguity resolution was achieved and the performance in terms of time to first fix and positioning accuracy was also evaluated. Observations of 29 global distributed MGEX stations were employed for UPD estimation. The resultant narrow-lane UPD products showed a high temporal stability during a whole day, with the average STD being less than 0.1 cycles. The residual distributions of five systems (GPS, GLONASS, Galileo, BDS, and LEO) were all close to a normal distribution, with the mean value of zero. With the fixing criteria of 0.15 cycles, the fixing percentage of wide-lane and narrow-lane ambiguity was greater than 90% and 80% for each system, respectively. With stable UPD products, a PPP ambiguity resolution using the LEO and GNSS observations can be achieved. The performance of multi-GNSS PPP AR can be significantly improved with the augmentation of LEO satellites and more LEO satellites contribute to a better performance. The TTFF of GREC PPP AR can be shortened from 7.1 to 4.8, 1.1, and 0.7 min by introducing observations from 60, 192, and 288 LEO satellites, respectively. The positioning accuracy of multi-GNSS fixed solutions is improved by about 60%, 80%, and 90% with the inclusion of 60, 192, and 288 LEO satellites, respectively. Moreover, a millimeter-level accuracy in the horizontal direction can be achieved within 5 min for GNSS PPP AR with the augmentation of 192 and 288 satellites. The improvement of the PPP performance benefits from the augmentation of the LEO constellation, which increases the number of visible satellites, optimizes the spatial geometry, and provides more candidate ambiguities to be resolved. The multiple signals of LEO satellites bring a variety of combinations applied for accelerating ambiguity resolution. With the inclusion of 288-LEO constellation, the triple-frequency LEO-augmented triple-frequency PPP AR was conducted. Compared to the dual-frequency fixed solutions, the triple-frequency AR achieved a faster convergence and higher positioning accuracy. The TTFF of the LEO-augmented GREC PPP AR was shortened from 42 s to 33 s. The multi-frequency LEO-only PPP AR was explored for the first time based on 288-satellite LEO constellation. The TTFF of the triple-frequency PPP AR was less than 80 s for all user stations and the average TTFF was 55.2 s,with an improvement of 23.1% compared to the dual-frequency solutions. The positioning error of triple-frequency PPP AR at 1 min was (1.69, 0.75, 4.16) cm in the east, north, and up components, respectively, with an improvement of 63.2%, 67.2%, and 20.7% compared to the PPP float solutions, and 50.2%, 56.8% and 17.2% compared to the dual-frequency PPP fixed solutions. We are glad to see that the inclusion of the LEO constellation will bring great improvement for the PPP AR and the multiple signals of LEO satellites will provide more possibilities for improving the efficiency of ambiguity resolution. [PERSON]. ([PERSON]), [PERSON] ([PERSON]), and [PERSON] conceived and designed the experiments; [PERSON]. ([PERSON]), [PERSON] ([PERSON]), and [PERSON] performed the experiments, analyzed the data, drew pictures, and wrote the paper; [PERSON], [PERSON], [PERSON], and [PERSON] reviewed the paper. This research was funded by the National Natural Science Foundation of China (Grant No. 41774030), National Science Fund for Distinguished Young Scholars (Grant No. 41825009), the Hubei Province Natural Science Foundation of China (Grant No. 2018 CFA081), and the National Youth Thousand Talents Program.