## 6 Conclusions  
As mentioned in the literature review, only in Europe and the USA are there several localization systems focusing on regional and monorail lines. Most of these solutions use the GNSS as the primary source of vehicle location information, but they also use balises (physical or virtual) and odometers for additional location information. However, the main objective of this article was to present a proposal for the supplementary support of railway traffic control on monorails where the GNSS system is used as the only supplier of information about the position of the rolling stock (i.e., the use of balises, etc., is not assumed). The originality of the proposed solution lay in the design of the methodology for building a multilayer model of the railway network over which the original localization algorithms were subsequently implemented, both for the localization of rolling stock and for the detection of nonstandard and crisis situations. Firstly, it was essential to design a set of algorithms for the building of a multilayer railway network model that reflected the data structure of an undirected graph. The official base data describing the railway infrastructure were used to build the actual model. Subsequently, the attention was focused on the detection of nonstandard or crisis situations on single regional tracks. Two attitudes were mainly applied: (i) the occurrence of two rail vehicles on an identical model edge and (ii) the occurrence of two rail vehicles on two neighbouring edges where the incidental vertex of the two edges did not dispose of any track branching enabling vehicle crossing. The article further dealt with the braking distance of rail vehicles on the basis of the characteristics of a selected train set and railway infrastructure, for which the real track profile was substituted by a reduced set of temporary gradients. The last part of the article dealt with experiments focusing on (i) the mutual position (distance) of two vehicles at the time of nonstandard situation detection and (ii) the braking distance and mutual position (distance) of both vehicles after stopping. Both experiments used a computer simulation inducing rail vehicle operation. The simulator used both the data resulting from a real situation (based on processing of the train passage historical data) and generated data. The experiments focused mainly on testing (i) the occurrences of two different trains on an identical model edge and (ii) the occurrences of these trains on two adjacent model edges (these situations in the model reflected the potential risk of train collisions). From the experimental results presented in the Results section, it was found that, if the speed of the above trains (moving towards each other at 65 km/h) was increased by 15%, then the total stopping distance of the trains increased by 34%. It was also clear that, for the identification of crisis situations for train speeds of 65 km/h, a current position detection period of 30 s was sufficient, but for speeds of 75 km/h, this period may already be inadequate in some cases, and the trains would no longer be able to stop safely. It should be noted that the above results obtained from the experiments did not include the reaction time (of both the software system and human operators). Therefore, for the deployment of the presented solutions in real operation, it would still be necessary to take these reaction times into account. Overall, however, the results of the experiments showed new possibilities of using the proposed concept in the field of supplementary support of dispatch control on regional lines, as well as in the timely detection of nonstandard and crisis situations. Conceptualization, J.F. and A.K. ; methodology, J.F. and A.K. ; software, J.F. ; validation, A.K. ; formal analysis, A.K. ; investigation, J.F. ; resources, J.F. ; data curation, J.F. ; writing--original draft preparation, J.F. ; writing--review and editing, A.K. ; visualization, J.F. ; supervision, A.K. ; project administration, J.F. ; funding acquisition, J.F.