Appl. Sci. 2023, 13, 1872 
12 of 17 
The sky-wave impact is remarkably visible for Helgoland (Figure 9c), located at a distance 
of 267 km. It can be noted how the night-time distribution spreads much more than the 
daytime distribution. In detail, the standard deviation is 6.0 m for the day and 15.3 m for 
the night. 
In Figure 9, we can observe in the lower plots the distribution of the error for the 
stations which were not used in the navigation solution, i.e., Hoburg (Figure 9d), Holmsjö 
(Figure 9e) and Rozewie (Figure 9f). It is important to note that a different scale is used 
on the horizontal axis with respect to the upper plots. It appears clear that the error 
at night is significantly larger than during the day. We can deduce that the sky-wave 
also depends on the distance between the transmitter and the receiver. In general, at 
larger distances the ground-wave is more attenuated than the sky-wave, which introduces 
larger errors. Moreover, the attenuation of the ground-wave depends on the propagation 
path, as explained in Section 3.1. Therefore, a signal which travels mostly over land will 
be attenuated more than a signal travelling over water. This effect explains the larger 
difference in range accuracy between Hammerodde and Helgoland. Despite the fact that 
*he distance from each of them to the receiver is similar, the signal from Helgoland travels 
mostly over land, whereas the one from Hammerodde travels mostly over water, as is 
visible in Figure 6. 
Gross Mohrdorf 
1.0 
Hammerodde _ 
Night 
Day 
1.0} 
— Night 
Day 
3.8) 
0.8/ 
9.6) 
9.6 
9.4) 
A 
3.2 
g.2) 
0.0) *—— = — 
—75 -50 -25 0 25 50 75 
range error [m] 
0.0| — Sn z—— 
—75 -50 -25 0 25 50 75 
range error [m] 
(b) 
Holmsjö 
(a) 
Hoburg 
0. 
— Night x 
Da 
Y 0.8 
1,8. 
Night ' 
Day 
3:6! 
0.6\ 
na} 
0.4 
l 
D.2 
0.2 
0.0] HA nn Wera 0.0| a“ . 
—200 —=100 0 100 200 —200 —=100 0 100 200 
range error [m] range error [m] 
. N 
L 94 
(e) 
1.0 
Helgoland 
0.8 
— Night 
Day 
D.6 
0.4 
D.7 
0.0) — = Win 
—75 -50 -25 0 25 50 75 
range error [m] 
(c) 
Rozewie 
1.0 
—- Night 
Day 
D.£ 
D.€ 
D.4 
D.' 
D.0) — EC 
m 
—200 —100 0 100 200 
range error [m] 
(f) 
Figure 9. Normalized range error distribution for the CW1 signal. Solid blue line represents night- 
dime data, while orange dashed line represents daytime data. (a) Groß Mohrdorf. (b) Hammerodde. 
(c) Helgoland. (d) Hoburg. (e) Holmsjö. (f) Rozewie. 
5. Conclusions 
This paper presents a detailed description of the MF R-Mode system, as implemented 
in the Baltic Sea. Eight radio beacons around the southern Baltic Sea are able to provide 
(he R-Mode as an additional service for testing and development in order to support safe 
navigation at sea. 
The system presents three challenges which are addressed in the paper. The ground 
wave, which is the expected propagation path for the R-Mode signal, is affected by different 
propagation velocities depending on type of land and water (fresh, sea). The effect can be 
modeled or measured.