Appl. Sci. 2023, 13, 1872 
100f 17 
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. 
Hoburg Rozewie Holmsjö Helgoland Hammerodde Groß Mohrdorf 
CWI CW2 _ CWI1 CW2 CWI1 CW2 CWI CW2 CW1_  CW2 CW1 CW2 
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 5km 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 100m (95%) given by the IALA Recommendation R-129 [29]. 
[his result is also very close to the 12m 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 —6.5ns is observed with a standard deviation of 11.3 ns. 
5000 
4000 oh 
E3000 7 * 
= 4 
5 2000 
Ss 1005 T100 [200 ' 
1000} 
RTK 
R-Mode 
100 
— 50 
E 
£ 0 
t 
a 7ı] 
ve 
0: 
—100 
= | | 
0 1000 2000 3000 4000 5000 —100 -50 0 50 100 
Fast [m] Fast [m] 
(a 
bh) 
350: 
0 
2300 
5250 
v 
5 
5200 
° 
5150 
8 
E100 
59; 
| 2 rn] 
450-100 50 0 50 100 150 
Clock bias [ns] 
"C) 
Figure 7. Daytime results. (a) Reference RTK (red circles) and R-Mode (blue crosses) tracks. (b) Scat- 
terplot of the R-Mode positioning error in east and north. (c) Histogram of the estimated receiver 
clock bias. 
4.2. 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 Holmsjö, 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.