## 2 Materials and Methods
### Data and Processing
The products used in this work are provided by Centre National d'Etudes Spatiales (CNES), in RINEX format. The products are ultra-rapid but provided in post-processing, meaning that the products would be the same as those used by a real-time engine. However, instead of doing the processing in real-time, it is done in post-processing with real-time products. Therefore, the performance in this work is expected to be same as the performance a real-time user would get. This fact is promising and increases the importance of the results in this manuscript, as it allows the assessment of the attainable performance for real-time applications, for example, autonomous vehicles, or any application interested in real-time use of PPP. As the model is based on uncombined processing of measurements, the float ambiguities are estimated in their uncombined state. These ambiguities, together with their corresponding covariance matrix, are fed into the mLAMBDA (modified Least-squares AMBERity Decorrelation Adjustment) method [31], which is a more computationally efficient version of the LAMBDA method introduced in [32]. The uncombined ambiguities are therefore fixed to their integer values based on the float ambiguities and their covariances on each epoch, and all the estimated states are updated based on the fixed integer ambiguities. For each dataset, the fixing of ambiguities is attempted from the first epoch of processing, with the fixing only being attempted on satellites with elevation angles above 15 degrees. The reason for eliminating satellites below that threshold is that such satellites would be expected to have more multipath, ionospheric refraction and measurement noise, which would affect the estimation of those satellites' ambiguities. The fixing of the ambiguities is validated using a standard ratio test. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Strategy** \\ \hline Receiver coordinates & Kinematic mode: estimated with process noise equivalent to 100 km/h \\  & Static mode: estimated as constants \\ Receiver reference coordinates & IGS SINEX positions \\ Receiver code and phase clocks & Estimated as white noise processes \\ Receiver L2 and L3 phase biases & Estimated as white noise processes \\ and IFB & Estimated as white noise processes \\ Tropospheric delay & Dry: GMF model and mapping function [29]. \\  & Wet: estimated as a random walk process with process noise of 0.05 mm/\(\sqrt{h}\) \\ Ionospheric delays & Estimated as white noise processes \\ Ambiguities & Estimated as constants on each continuous arc \\ Elevation angle cut-off & \(7^{\circ}\) \\ Satellite orbits and clocks & Corrected for using CNES ultra-rapid products [30] \\ Code and phase biases & Corrected for using CNES ultra-rapid observable-specific bias (OSB) products \\ Weighting strategy & Elevation dependent weighting: \(\sigma=\frac{\sigma_{\text{obs}}}{\pi+\text{bin}\,\text{d}}\) with \(\sigma_{\text{0}}\) equal to \\  & 0.3 m and 0.003 m for the pseudorange and carrier-phase measurements, \\  & respectively, and _el_ being the elevation angle. \(a\) and \(b\) were determined \\  & based on a residual and measurement quality analysis. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Processing strategies.