# Sampling Rate Impact on Precise Point Positioning with a Low-Cost GNSS Receiver
## 3 Results  
As was mentioned earlier, the calculation of the multipath effect (Figure 4) and signal-to-noise ratio (Figure 5) were made using the TEQC software for the low-cost GNSS and geodetic receivers at 0.1 and 0.2 s, respectively. In [40], it is mentioned that the multipath effect is inversely proportional to the signal-to-noise ratio, this is found in Figures 4 and 5. The low-cost GNSS receiver registered a high value of the multipath effect in both frequencies compared to the IGS recommended value of 0.3 m, this was despite the fact that the low-cost GNSS receiver does not have a polarized antenna to reduce the multipath effect. Nevertheless, a normal value of the multipath effect was registered in general terms compared to the mean global value of the multipath effect in IGS stations [41,42]. Despite the good behavior presented in the signal-to-noise ratio for the low-cost GNSS receiver, the multipath effect obtains high values in contrast to the value recommended by IGS and the geodetic receiver. The difference between the estimated and precise coordinates' position was calculated for each receiver in both modes at different sampling intervals (0.1, 0.2, 1, 5, 15 and 30 s). The values obtained for the low-cost GNSS receiver were small in high frequencies (0.1 and 1 s) for the PPP-static mode, where the height and longitude values presented the greatest difference in the solution. Nonetheless, the obtained values, in comparison with the geodetic receiver, are high (Figure 6). For the low-cost GNSS receiver, the longitude and height obtained solution was constant with the major difference. Regarding the best solution, the low-cost GNSS obtained the best solution in 0.1 and 0.2 s due to the data loss found at low frequencies. In the same way, for the low-cost and geodetic receivers, the difference of the precise and estimated coordinates was constant in all cases. Likewise, the geodetic receiver had the best estimation. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{**Processing Mode**} & \multicolumn{3}{c}{**Static and Kinematic**} \\ \hline Number of satellites tracked & Low-cost & GPS & 10 & 09 \\ Geodetic & GPS & 17 & GLONAS & 13 \\ \hline Reference frame & & ITRF in consideration to the epoch of GNSS data \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 4: Multipath effect for the low-cost and geodetic GNSS receivers. Yellow line: IGS recommended value (MP < 0.3 m). The standard deviation of the estimated positions for each receiver is presented in Figure 7. As was found in Figure 6, the solutions obtained by the geodetic receiver were small and constant. It is found that there is a clear correspondence between the sampling rate and the standard deviation obtained for the low-cost GNSS receiver. In this sense, the standard deviation obtained from the low-cost GNSS receiver is higher compared to the standard deviation from the geodetic receiver, this is clear for all sampling rates. However, the obtained deviation for 1 and 15 s showed the best results, the worst case being at 5 and 30 s. This is because the RINEX file corresponding to the sampling frequency of 5 s had a lower percentage of observations, affecting the processing with the PPP method and the final precision. On the other hand, according to [43] these differences in precision can also be caused by the multipath effect and atmospheric errors (tropospheric and ionospheric). It is also related to the fact that the low-cost GNSS antenna (Figure 3b) does not have an IGS antenna calibration, this affects the obtained solution making it impossible at this point to achieve a mm solution as a relative static method [44]. Figure 5: Signal-to-Noise ratio for the low-cost and geodetic GNSS receivers. Yellow line: IGS recommended value (SNR \(\geq\) 36 dBHz). Figure 6: Difference between estimated and precise coordinates of the low-cost and geodetic receiver by processing with PPP-static mode. The low-cost and geodetic receivers were set up to the maximum sampling rate they allow, 0.1 and 0.2 s, respectively.