## 5 Discussion and Outlook  
The results show that an ambiguity-fixed precise coordinate solution with PPP-RTK without regional atmospheric corrections can be reduced to just a few epochs when multi-frequency multi-GNSS observations with a temporal resolution of 30 s are used in ideal conditions at the user level. When only dual-frequency observations are available, the single epoch positioning accuracy decreases significantly as a result of no wide-lane ambiguities qualifying for instantaneous ambiguity resolution. Furthermore, the minimum number of epochs required to achieve an ambiguity-fixed solution increases significantly when only dual-frequency observations are considered by the user. These results have been achieved with a regional network based in Europe, where only forward-filtered network products have been considered and no regional atmospheric corrections have been used. In theory, the results should be similar when global networks are considered. The reason is that satellite and station coordinates were fixed at the network level, so the only remaining parameter that is affected by the network geometry, i.e., the spatial distribution of the reference receivers, is the wet tropospheric zenith delay. The relevant network products for the user, i.e., satellite clocks and biases, are non-geometric parameters. In cases where the spatial distribution of reference receivers is not large enough, a rank deficiency between the wet tropospheric zenith delay and the satellite clock occurs, as described in [2]. This is, however, not applicable to the network considered here, as the spatial distribution is sufficient. As a consequence, the quality of the user solution and the time to fix it should not significantly depend on the distance of the user receiver from the reference stations, as long as it can be assumed that satellite clocks and biases estimated by the reference stations are available for the satellites observed by the user. This, of course, cannot be the case if the rover is too far away from the reference network and observes a different set of satellites. In this study, final satellite orbits are used that are generally only available for post-processing applications. In the event that PPP-RTK corrections were to be made available in real time, the repeatability of these results using predicted satellite orbits needs to be investigated further. For 30 s observations, it was shown that ambiguity resolution can be achieved in just a few epochs in most cases. It needs to be further investigated how these findings translate to high-rate observations, as they are of higher relevance in kinematic applications. The methods presented here can also be used to process high-rate observations at the network and user levels. However, new problems may arise that were not present  
Figure 9: Single epoch positioning performance for dual-frequency observations. Reparameterized ambiguities could not be fixed with the introduced methods in a single epoch. in 30 s observations. One issue that becomes more prevalent when high-rate observations are considered is the temporal correlation of especially code observations, as shown by, e.g., [36], where significant correlation for up to 10 s was observed for all signals. This could influence the validity of the stochastic assumptions that were made for the 30 s observations. Furthermore, it may be unrealistic to expect high-rate observations to be processed at the network level and the satellite clocks made available to the user at, e.g., each second. In cases where the observation sampling rate of the user receiver exceeds that of the reference network, one must think about extrapolating satellite clocks and how their quality decreases as time passes. The first part could be solved by adding a satellite clock drift to the state vector. The latter part needs to be investigated for different satellite clocks as the time stability between satellite clocks varies.