Appl. Sci. 2023, 13, 1872 
13 0f 17 
Secondly, during the night, a reflection of the transmitted signal at the E-layer of the 
ionosphere comes into effect, which causes a degradation of the R-Mode performance due 
to the interference with the ground-wave at the receiver site. The sky-wave interference 
was modeled in the paper and analyzed with respect to the impact on the received signal 
amplitude phase and the phase error compared to the ground-wave. This model enabled 
the calculation of the maximum error that can be expected during sky-wave conditions. In 
‘he future, this model could also be used to calculate the expected sky-wave impact, taking 
into account the statistics of the expected sky-wave amplitudes and delays. 
The third challenge is some features of the R-Mode signals that can be observed in the 
transmissions from different stations, which seem to have a technical cause. They appear as 
jumps in the phase by several meters from one second to the next, which makes it possible 
to detect them. For now, the affected signals are not used. 
The performance of the MF R-Mode system in the testbed area close to Rostock was 
presented in terms of horizontal positioning and timing accuracy. We demonstrated that 
good accuracy can be achieved during the day, whereas the problem of the sky-wave 
multipath degrades system performance at night. In this contribution, we have been able 
to confirm that the R-Mode could be a suitable backup system for the maritime domain. 
In particular, the 95% horizontal accuracy achieved was 15.1m for 6h during the day 
and 55.3m for 4h at night. In both cases, the accuracy requirement of 100m for coastal 
navigation was met over the time slots considered. 
Furthermore, we found that at night, no sky-wave disturbance is visible for a distance 
of up to 62 km. For distances of 210 km to 270 km, the composition of the propagation 
path is important. On a nearly complete over-sea path, the sky wave has a low impact. 
Ihe R-Mode signal shows a low degradation. For propagation half over sea and half over 
‚and, the standard deviation error increased by a factor of 2.6. In the future, this knowledge 
could be used to design an adaptive filter for weighting the different measurements in 
the positioning algorithm at night to provide measurements with an expected higher 
probability of the sky-wave with less weight. 
In general, predicting the effect of the sky-wave can be very challenging due to its 
dependency on solar activity. Different performance levels might be experienced by the 
users on different days, during different seasons or at different times of the day. Therefore, 
the correct modelling of the sky-wave interference effect on phase estimation may be an 
interesting area of research, given the large number of parameters to be considered in the 
model itself. For the moment, a working solution is to detect the sky-wave by a stronger 
variation of the signal amplitude and reduce the service range at night. 
Finally, the study of interference mitigation strategies may be an important point of 
the investigation for the future in order to improve the MF R-Mode system performance 
at night. 
Author Contributions: Conceptualization, FG.R., L.G. and S5.G.; Methodology, F.G.R., L.G. and 
5.G.; Software, F.G.R., L.G. and S.G.; Validation, FG.R.; Formal analysis, F.G.R., L.G. and 5.G.; 
Investigation, F.G.R.; Data curation, F.G.R., L.G. and 5.G.; Writing—original draft, F.G.R., L.G., 
5.G. and T.E.; Writing—review & editing, F.G.R., L.G., 5.G. and T.E.; Visualization, F.G.R.; Project 
administration, 5.G.; Funding acquisition, 5.G. All authors have read and agreed to the published 
version of the manuscript. 
Funding: This research received no external funding 
Institutional Review Board Statement: Not applicable. 
Informed Consent Statement: Not applicable. 
Data Availability Statement: Not applicable. 
Acknowledgments: This research was conducted within the framework of the R-Mode Baltic project, 
which aims to set up the first combined MF and VDES R-Mode testbed in the southern Baltic Sea and 
demonstrate that the R-Mode fulfils the maritime user requirements. The authors thank the entire 
R-Mode Baltic project team. Furthermore, the authors thank the European Union for co-financing the