# GNSS RTK Positioning Augmented with Large LEO Constellation
## 3 Situation and Strategy
### Data Processing Strategy  
According to the Table 4, the estimated parameters, observation models and index settings of DD observables are showed to describe the data processing strategy for LEO augmented GNSS RTK in details. Then, based on above-mentioned simulated GPS and LEO observations, we can comprehensively analyze the RTK performances of different constellation schemes including the GPS-only scheme, as well as the combined constellation schemes of GPS with 60, 96, 192, and 288 LEO satellites, respectively. Especially for the different length baselines, the appropriate processing strategy must be adopted for the atmospheric residuals, otherwise it will hinder successful ambiguity resolution. Meanwhile, this study will only consider observation models of the single-baseline type, using two stationary receivers separated by different distances. This means that the ionospheric and tropospheric delay can be significantly reduced by forming DD observation equations for the short-range RTK solutions, but not for that of medium- and long-range baselines. However, the DD ionospheric and tropospheric delay can be set to zero initially and estimate them as a random walk in each processing session for medium-to-long baselines. Especially for the subsequent epoch, the atmospheric parameters and variances can employ the estimated results of last epoch as prior estimation values, where the atmospheric variances usually need to add a process noise. As for the vertical ionospheric delay, its process noise is set as \(10^{-3}m/\sqrt{s}\). So the empirical model can be expressed as follow:  
\[\left\{ \begin{array}{c}\sigma_{ion}^{2}=\ k\ q_{ion}^{2}\ \Delta t\\ q_{ion}=\ 10^{-3}\big{(}bl/10^{4}\ \cos(el)\big{)}\ m/\sqrt{s}\end{array} \right. \tag{10}\]  
where \(\sigma_{ion}\) is the ionospheric process noise; \(q_{ion}\) denotes the spectrum densities of random process for ionospheric parameter; \(bl\) is the length of baseline; \(el\) is the satellite elevation angle; \(\Delta t\) is the sampling interval; \(k\) is the coefficient to distinguish GPS and LEO satellite, which is set 1 for GPS satellite. Considering the fact that the different motion speed of GPS and LEO satellite leads to a ionospheric \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Short Baselines** & **Medium Baselines** & **Long Baselines** & **Long Baselines** \\ \hline P696-P695 & 1.1 km & P169-TRND & 33.0 km & P170-P339 & 138.2 km \\ P698-P696 & 2.8 km & SBCC-P474 & 44.2 km & P698-P372 & 390.5 km \\ P700-P695 & 4.7 km & P446-P698 & 57.0 km & P698-P663 & 514.7 km \\ P700-P696 & 5.5 km & P339-P341 & 68.7 km & P698-P349 & 604.7 km \\ P700-P701 & 6.8 km & P164-P339 & 88.0 km & P023-P343 & 739.2 km \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Length information of the short, medium and long baselines at mid latitudes. Figure 2: Distribution of stations at the mid latitudes. The small map shows the stations constituting short baselines and the larger one is for medium-to-long baselines. variation between adjacent epochs, the ionospheric process noise need to be adjusted for LEO-satellite observation. For the 30 s low sampling-interval data, the slant ionospheric delay varies a lot due to the fast motion of LEO satellite, thus the ionospheric process noise should be enlarged compared to that for GPS satellite. But for the high sampling-interval data, i.e., 1 s observation, it is usually insensitive to ionospheric variation. So in this study, the coefficient \(k\) for LEO satellite is also set 1 for the data with sampling interval. Meanwhile, it is noted that some cycle slip detection algorithms also need to be adjusted for LEO-satellite observation based on the above-mentioned consideration, such as the geometry-free combination method. The cycle-detection threshold can adopt a similar adjustment principle to that for the ionospheric process noise.