# Sampling Rate Impact on Precise Point Positioning with a Low-Cost GNSS Receiver
## 3 Results
According to [21, 43] the convergence time represents the time to reach a stable accuracy level, which depends on many factors such as observation quality, noise level of code observations, user environment, the number and geometry of visible satellites, sampling rate and algorithms. As a result, for measurements obtained from CSRS-PPP for both of the PPP modes, the convergence and the difference of precise (from a previous campaign in static relative mode) and estimated coordinates are analyzed in Figures 14 and 15 with 3D coordinates. As stated by [45] the general rule for the time for the PPP-static solution to converge for a horizontal accuracy (cm) of 5 cm is reached is at 60 min. The PPP-static mode reaches the convergence at 15 min from the first observation (Figure 14), which is seen at each sampling rate for the horizontal and vertical components [46, 47]. For the PPP-static mode, the best accuracy and estimated position are achieved at 1, 15 and 0.2 s, compared to 5, 0.1 and 30 s. Notwithstanding, the obtained solution is accurate for all sampling rates. It is clear that for high frequencies, the low-cost GNSS receiver lost data. This affected the accuracy and positioning obtained. Nevertheless, for the high sampling rates, the solution was not affected due to the quantity of observation data. The PPP-kinematic mode was the most affected mode due to the data loss (Figure 15). This data loss generated an offset in the difference, between estimated and precise positions in the time series. In this sense, the kinematic mode was more affected than the static  
Figure 13: Standard deviation (95%) of estimated positions of low-cost and geodetic receivers at 0.1 and 0.2 s respectively, by processing with PPP-kinematic mode. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Receiver**} & **Sampling** & **DLAT** & **DLON** & **DHGT** & **SDLAT** & **SDLON** & **SDHGT** \\  & **Rate (s)** & **(m)** & **(m)** & **(m)** & **(m)** & **(m)** & **(m)** \\ \hline \multirow{8}{*}{Geodetic} & 0.2 & \(-\)0.006 & \(-\)0.006 & 0.041 & 0.017 & 0.018 & 0.042 \\  & 1 & \(-\)0.006 & \(-\)0.006 & 0.039 & 0.019 & 0.019 & 0.046 \\  & 5 & \(-\)0.006 & \(-\)0.006 & 0.041 & 0.019 & 0.020 & 0.048 \\  & 15 & \(-\)0.006 & \(-\)0.006 & 0.042 & 0.019 & 0.020 & 0.048 \\  & 30 & \(-\)0.006 & \(-\)0.006 & 0.042 & 0.019 & 0.020 & 0.048 \\ \hline \multirow{8}{*}{Low-cost} & 0.1 & 0.062 & \(-\)0.195 & \(-\)0.129 & 0.032 & 0.043 & 0.082 \\  & 0.2 & \(-\)0.021 & \(-\)0.432 & \(-\)0.100 & 0.035 & 0.052 & 0.093 \\ \cline{1-1}  & 1 & 0.017 & \(-\)0.145 & \(-\)0.278 & 0.046 & 0.086 & 0.116 \\ \cline{1-1} GNSS & 5 & 0.096 & \(-\)0.177 & \(-\)0.019 & 0.105 & 0.241 & 0.222 \\ \cline{1-1}  & 15 & 0.079 & \(-\)0.254 & \(-\)0.140 & 0.155 & 0.342 & 0.317 \\ \cline{1-1}  & 30 & \(-\)0.007 & \(-\)0.272 & \(-\)0.033 & 0.322 & 0.573 & 0.624 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Differences and Standard deviation obtained at different sampling rates for the PPP-kinematic mode. mode due to the data loss at low frequencies, being more affected at > 5 s sampling rates. The obtained solution at 0.1 s seemed to have linear behaviors as with the rest of the solutions obtained. Nevertheless, as the sampling rates diminished, an offset is seen at the same time in all cases. Apparently, at 30 s the solution obtained was not affected by the data loss due to the linear behavior of the time series. To evaluate the performance of the PPP-AR convergence time, the differences between the reference coordinates (which were taken as true) and the estimated coordinates obtained by kinematic and static PPP were used. It was considered convergent when the differences reached \(\pm\) 0.1 m and remained within that limit. The time of convergence was defined as the period from the first epoch to the epoch of convergence (indicated as a red line in Figures 16 and 17). It is observed that the convergence time was more stable in the PPP-static method, however, it was slower compared to PPP-kinematic method.