Appl. Sci. 2023, 13, 1872 
40f£17 
1eight of the two points is zero. Further details on the least squares algorithm are given 
n [14]. 
3. Mf Signal Impairments 
The propagation of MF signals is characterized by a variety of impairments which 
need to be considered when these signals are used for positioning purposes. From this 
point of view, the main two challenges in obtaining an accurate positioning performance 
in the MF R-Mode system are the following: mitigating the sky-wave reflection arriving 
:rom the ionosphere at night, and predicting the wave-propagation delay induced by the 
variation of the electrical properties of the atmosphere and ground along the propagation 
path. In the following sections, the two issues will be briefly described. Furthermore, a 
third issue concerning the possible transmitter instability is also discussed. 
3.1. Atmospheric and Ground Delay Factor (AGDF) 
MF signals propagate along the earth’s surface as the ground-wave [18]. This is an es- 
sential characteristic, which allows the signal to travel over longer distances in comparison 
to the line-of-sight propagation limitation, which is typical for higher frequency signals. 
Above the ground, the atmospheric refractive index causes a propagation speed reduction 
which becomes visible as a delay of the signal in the time domain. Furthermore, at the 
earth’s surface, the signal encounters different types of land and water segments which 
are characterized by different materials with specific electrical properties. Each of these 
segments has a specific ground conductivity and electric permittivity, which produce a 
damping of the signal’s amplitude and a further change of propagation speed [19]. The 
overall delay experienced by the signal has been defined as AGDF [20]. 
It is possible to predict the AGDF for an arbitrary propagation path composed by 
several sections of different electrical properties by using the ITU World Atlas of Ground 
Conductivities [21]. For each section, the attenuation and delay of the signal is computed 
with the method introduced by Rotheram [22,23] and Wait [24]. Finally, the overall delay is 
obtained through the application of the Millington/Pressey method, as explained in [24,25]. 
As an example, Figure 2 shows the phase delay in radians with respect to the prop- 
agation in the vacuum for the signal transmitted by the radio beacon located in Groß 
Mohrdorf, Germany, over the southern Baltic Sea. It is caused by the refractive index of the 
atmosphere, here assumed to be constant, and the variation of the ground conductivity, as 
given in the ITU maps. 
Measurements in specific areas can be used to apply an enhanced correction technique 
on these AGDF maps to improve the R-Mode performance [20]. 
3.2. Sky-Wave Self-Interference 
MF radio waves can travel either as ground-waves, by following the earth’s surface, or 
as a sky-wave reflection between the earth and the ionosphere [18]. While the ground-wave 
is characterized by the propagation phenomena, which attenuate and delay the signal, as 
described in Section 3.1, the sky-wave can be observed as a multipath effect which generates 
self-interference on the receiver side, degrading the ranging accuracy. This effect depends 
on several factors, such as the frequency of the signal itself, the ionospheric reflection 
neight, the angle of the incidence, the geographical region of interest and solar activity [13] 
Radio waves in the 300 kHz frequency range are significantly absorbed by the D- 
ıayer of the ionosphere during the daytime. Therefore, the sky-wave interference effect is 
naegligible, since its field strength is far smaller than the ground-wave in the service areca 
of the radio beacon. In contrast, at night, the D-layer tends to disappear. The signal is 
therefore no longer attenuated and hits the upper ionospheric E-layer, which is capable of 
reflecting signals below 10 MHz.