# Collision Risk Evaluation and Verification of GNSS-Based Train Integrity Detection
## 5 Simulation and Results  
To obtain different scenarios and positioning states, raw data are collected as follows: the runs of a train equipped with a GPS receiver and reference system are tested in order to evaluate the positioning errors. The GNSS and the reference location data were collected along the High Tatra Mountain railway line from May 2008 to February 2009 (see Figure 8) [23; 24; 25; 26], and the deviation between GNSS receiver and reference locations is calculated for performance evaluation. Figure 8: Map of the field data. Figure 7: Verification procedure based on the analysis of experiments data. The High Tatra Mountain railway line is 29.1 km long from Poprad to Smokovec until Strbske Pleso. There are open areas and forests but no tunnels or railway bridges. The thresholds for the required train localization function are set as an upstate threshold of 10 m, and the positioning deviations bigger than 10 m and lower than 20 m are set as the degraded state. A faulty state is defined when the deviation is bigger than 20 m, which indicates it ceases to be a localization function and is no longer available as a resource for the localization function. Then, the statistics of positioning errors in different scenarios (open area and forest) and localization states (upstate, degraded state and fault state) are found out [27], as shown in Table 4. Since the mean and variance of deviation normal distribution in upstate from the test run are chosen, the mean and variance of the other two states are set depending on the thresholds. Not only the localization states but also the transitions between the states are considered here. The mean time of the six transitions can be found out from the measured individual time span staying in one state to another. The mean times from one state transition to another are categorized, and the results [27] of all six transitions are estimated in Table 5.  
The procedure is based on the statistically processed fieldmeasurements. One scenario is a sequence constituted of a succession of states associated with the localization function. The transition between the different states is also associated with time. Figure 9 illustrates scenarios (open area with white color and forest with grey color) in which states (upstate with green color, degraded state with yellow color, and fault state with red color) are distinguished at each sampling instant using unit steps and colors. Because of the timed and stochastic nature of the GNSS-based positioning system, formal and simulation-based verification are combined to generate the GNSS positioning errors. The CPN model of the GNSS positioning errors is shown in Figures 10 and 11. In order to evaluate the existing or planned systems, a performance analysis is conducted. In CPN, each token can be parameterized with the required meaning, which is not available in low-level Petri Nets. By adapting values to corresponding quantities, the system can be easily understood and changed, then described in executable code. During simulation-based performance analysis, data is collected from the occurring binding elements, and the markings reached [15]. With the data obtained from the model, performance measures of the GNSS-based TIMS are available.