# Performance Assessment of the Medium Frequency R-Mode Baltic Testbed at Sea near Rostock
## 4 Mf R-Mode System Accuracy: Results and Discussion
### Daytime Results  
The results presented in this section are related to data recorded during the day. Moreover, the impact of the AGDF for this data set was almost negligible, due to the limited area in which the vessel was operating. We therefore rate the scenario as \"optimal\" in the sense that the achievable accuracy depends mainly on the receiver noise and the signals' received power. The data set was recorded between \(7\):\(56\,\mathrm{UTC}\) and \(14\):\(00\,\mathrm{UTC}\), and at least one signal per radio beacon was usable during this time. This means that all the transmitters were used in the positioning solution. The signals used are visible in Table 2 with the \"h\" flag, which stands for healthy, whereas the unusable signals are indicated as unhealthy with the \"uh\" flag. The unhealthy flag was set for some of the signals due to the observed transmitter instabilities, as explained in Section 3.3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Station Name** & **Lat [deg]** & **Lon [deg]** & **Distance [km]** \\ \hline Hoburg & 56.9209 & 18.1520 & 486 \\ Rozewie & 54.8308 & 18.3347 & 414 \\ Holmsjo & 56.4440 & 15.6551 & 334 \\ Helgoland & 54.1859 & 7.9052 & 267 \\ Hammerodde & 55.2981 & 14.7738 & 211 \\ Gross Mohrdorf & 53.3740 & 12.9344 & 62 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Distance between the transmitters and the centre point of the test area.  
Figure 6: MF transmitters (yellow triangles) available during the campaign and test area (red rectangle).  
Figure 7a presents the R-Mode positioning solution, as blue crosses, in a local reference frame (east-north) along with the reference RTK trajectory visible as red circles. The test area, approximately, consists of 5 km in the east direction and 2 km in the north one. In general, it appears clear that the R-Mode solution consistently follows the reference, which is better visible in the inset presented in same plot.  
To better evaluate the horizontal error, the scatterplot given in Figure 7b is used. Here, we can observe that the error spreads more in the north direction than in the east, and this is explained by the difference between the Dilution Of Precision (DOP) for the two axes. The DOP value for the east is 0.7, while for the north it is roughly 2. The overall horizontal (H)DOP is 2.11, which is a good geometrical indicator of the transmitter distribution with respect to the receiver. In principle, the expected performance of the system increases with the decrease in the DOP values; therefore, the smaller the DOP is, the better the position solution will be. The 95% horizontal accuracy results in the value of 15.1 m. Such a level of accuracy is compliant with the accuracy requirements for backup navigation systems for the coastal navigation of 100 m (95%) given by the IALA Recommendation R-129 [29]. This result is also very close to the 12 m accuracy achieved in [14], where the HDOP was approximately 1.7.  
Figure 7c shows the histogram of the estimated receiver clock bias. As explained earlier, a stable and accurate clock was used in the setup. Consequently, no bias or drift was expected to be observed. As can be observed in the histogram, there is no clear large bias or drift. An small overall bias of \(-\)6.5 ns is observed with a standard deviation of 11.3 ns.