# Performance Assessment of the Medium Frequency R-Mode Baltic Testbed at Sea near Rostock
## 4 Mf R-Mode System Accuracy: Results and Discussion
### Night-Time Results  
The night-time data presented in this section was recorded between 2:05 UTC and 6:00 UTC on 22 September. As for the daytime scenario, Table 3 contains the information on the usable signals. It appears clear that the stations far away from the receiver, Hoburg, Rozewie and Holmsjo, were set as unhealthy due to the large error introduced by the sky-wave interference. Moreover, the CW2 of Gross Mohrdorf was also set as unhealthy due to the observed signal instability. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Hoburg** & \multicolumn{2}{c}{**Rozewie**} & \multicolumn{2}{c}{**Holmsjo**} & \multicolumn{2}{c}{**Helgoland**} & \multicolumn{2}{c}{**Hammerodde**} & \multicolumn{2}{c}{**Gros \& Mohrdorf**} \\ \hline CW1 & CW2 & CW1 & CW2 & CW1 & CW2 & CW1 & CW2 & CW1 & CW2 & CW1 & CW2 \\ \hline \(\mathbf{h}\) & \(\mathbf{h}\) & \(\mathbf{h}\) & \(\mathbf{uh}\) & \(\mathbf{h}\) & \(\mathbf{h}\) & \(\mathbf{h}\) & \(\mathbf{uh}\) & \(\mathbf{h}\) & \(\mathbf{h}\) & \(\mathbf{h}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Daytime: signals used for the position and time estimation in green with the “h” flag. Signals in red with the “uh” flag were not used. Figure 7: Daytime results. (**a**) Reference RTK (red circles) and R-Mode (blue crosses) tracks. (**b**) Scatterplot of the R-Mode positioning error in east and north. (**c**) Histogram of the estimated receiver clock bias. The R-Mode position solution was compared with the GNSS RTK reference track, as shown in Figure 8a in a local east-north coordinate system. It can be noted that the ship kept its position almost stable overnight. Therefore, we can think of this test as a semi-static case with a very limited position variation of the ship, in the order of 20 m, and induced by the wind and waves. The scatter of the R-Mode solution is presented in Figure 8b, where it is clear that the DOP plays an important role in this case. In fact, as mentioned before, only three stations were used to solve the navigation equation, and this increased the overall DOP. The east DOP and north DOP increased to 1.3 and 4.9, respectively, whereas the HDOP reached a value of 5.0. Thus, a loss in the performance level is expected. The 95 th quantile accuracy for this data set is 55.3 m, which again satisfies the requirements for coastal navigation, as stated in the previous section. Last but not least, the accuracy of the time estimation is given in the histogram represented in Figure 8c. By comparing this histogram with the one in Figure 7c, we can clearly observe the decrease in the timing accuracy. In particular, the overall bias of 2.3 ns improves, but the standard deviation of 32.3 ns increases by a factor of 3, approximately. In order to see the sky-wave effect on the ranging performance, the unbiased normalized distribution of the range error for the CW1 of all the transmitters is shown in Figure 9, for daytime and night-time. Looking at the Gross Mohrdorf plot (Figure 9a), a small difference between the daytime and night-time distributions is visible. Surprisingly, the standard deviation for the daytime range error is slightly higher (3.0 m) than the night-time one (1.7 m). Our hypothesis to explain this unexpected result is that the daytime accuracy is somewhat degraded by the AGDF impact. Additionally, there might be a difference between daytime and night-time atmospheric noise, which can change the carrier to noise-density ratio and, therefore, the accuracy of the phase estimation. Unfortunately, the carrier to noise-density ratio estimation was not available at the time of the campaign. Nevertheless, no sky-wave was expected to be visible for that radio beacon due to the distance of only 62 km. For Hammerodde (Figure 9b), there is a difference between the daytime standard deviation, 5.9 m, and the night-time one of 8.3 m. In this case, a decrease in the accuracy was expected due to the greater distance of about 212 km between the receiver and transmitter. Figure 8: Night-time results.