# GNSS RTK Positioning Augmented with Large LEO Constellation
## 6 Conclusions  
Aiming at investigating the performance of LEO constellations augmented GNSS RTK positioning, four kinds of LEO constellations with different satellite numbers and the nominal GPS constellation were adopted for analysis in this study. Based on the simulated GPS+LEO pseudorange and carrier-phase observations at the ground tracking stations, the augmentation performances of the single-baseline RTK solutions were comprehensively evaluated from the aspects of average convergence time, TTFF, fixing ratio, visible satellite number, PDOP value, and baseline solution precision. As for the different scales of LEO constellations augmented GPS RTK solutions, it was found that the improvement performances are closely related to the number of LEO satellites. The more LEO  
Figure 8: Average convergence time and TTFF of different LEO constellations augmented GPS RTK positioning for ten medium-to-long baselines. Figure 9: The solid lines describe the average convergence time and TTFF of five medium-baseline solutions with the augmentations of different LEO constellations, and the similar indexes of five long-baseline solutions are shown in dashed line. satellites are available, the less convergence time and TTFF can be achieved in RTK positioning, as well as the higher fixing ratio. The corresponding statistical results from a 68.7-km scheme show that when introducing 60-, 96-, 192-, and 288-LEO constellations, the convergence time can be shortened from 4.94 to 2.73, 1.47, 0.92, and 0.73 min, respectively. Furthermore, the TTFF can be decreased to 3.33, 2.38, 1.22, and 0.87 min, respectively, compared with that of 7.28 min for GPS-only scheme. Meanwhile, the fixing ratio can be also increased by 11.85, 16.33, 19.38, and 20.16%, respectively. Particularly, for 192- and 288-satellite LEO constellations, the improvement on RTK convergence and fixing is more obvious in contrast to that of the GPS-only scheme, where the convergence time and TTFF can be shortened to about 1 min and the average fixing ratio can reach above 95%. Owing to that more visible LEO satellites can move faster and streak longer tracks than GPS satellites during the same period, which contributes to the better geometric diversity at stations. Furthermore, the baseline solution precision is further analyzed to see whether or not similar RTK positioning precision can be obtained with the augmentations of different scales of LEO constellations after fixing DD ambiguities. It is found that adopting larger LEO constellations are conducive to achieve more stable and better positioning accuracy. Considering that the improved performance may be associated with different length baselines, 15 sample baselines in mid-latitude regions were selected for analysis. For short-baseline schemes, the average convergence time and TTFF can easily reach to within a few seconds, whether or not to introduce LEO satellites. For the medium and long baseline schemes, the statistical results of all baselines confirm that more LEO satellites can achieve faster convergence and fixing, but we have also noticed that it is still difficult to achieve instantaneous ambiguity-fixing. Besides, the improvement of long-baseline scheme is more obvious than that of the medium-baseline scheme, and the average TTFF for the long baselines can be shortened by about 90% from about 12 to within 2 min while introducing the larger LEO constellation of 192 or 288 satellites. As similar improvement can be observed from the convergence time. Overall, we made an initial assessment of GNSS RTK positioning augmented with LEO satellites and proved that the LEO satellites can helpfully improve convergence and ambiguity-fixed performance, which provides an important insight into the DD ambiguity resolution for the medium- and long-range RTK solutions. In future researches, further studies are therefore necessary to evaluate the LEO constellation-augmentation performance for multi-baseline RTK and PPP-RTK solutions.