# Collision Risk Evaluation and Verification of GNSS-Based Train Integrity Detection
## 4 Experiments Based Simulation for Collision Risk Verification  
For each specific scenario in GNSS-based TIMS constructed from the attributes of the operating situation (both GNSS positioning situation and train motion situation), the probability of a specific event in a scenario depends on the frequency range assigned to the safety function [21]. To consider the influence of the environment along train routes, it is obviously impossible to describe a limited number of representative geometries to cover all situations of signal visibility. Environmental configurations along the train itinerary present identical geometry features. The area around this itinerary constitutes a \"typical\" environment. Safety results can then give representative characteristics for the different typical environments observed [21]. The GNSS-based positioning system can be decomposed as a state to help \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Velocity (km/h)** & **300–0** & **250–0** & **200–0** & **160–0** & **100–0** \\ \hline Emergency braking time (s) & 74.2 & 60.6 & 47.1 & 37.5 & 23.2 \\ Full-service braking time (s) & 113.1 & 88.1 & 63.6 & 48.1 & 31.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Train braking time in train control system. identify the system performance level. These states of GNSS in TIMS are related to location measurements. So from the GNSS receiver perspective, three states are defined for the GNSS receiver locations. These three states [21] are upstate, degraded state, and faulty state, as shown in Figure 6.  
The measured position of the GNSS-based positioning unit is the most important factor for train parting incident detection. So, a hazardous event is more likely to occur when the localization function reaches the degraded state and fault state. A train, which has been wrongly positioned, can lead to unexpected estimated train length and false detection results. This situation can lead to a rear-end collision. Safety activities on a GNSS-based TIMS concentrate on these states of GNSS-based localization. The Monte Carlo simulation is a numerical process that is able to generate both GNSS positioning errors and train parting sequences composed of dependent situations where failure frequencies are subject to uncertainty [22]. Several possible evolutions in the life of the system (i.e., the dynamic transitions of the GNSS positioning system in an up or degraded state) can be obtained with a Monte Carlo simulation. In GNSS-based applications in railways, we use an Experience Statistics (ES) methodology [7] to obtain an efficient procedure capable of managing a huge quantity of data in order to evaluate the safety properties of GNSS-based positioning. This approach follows the usual steps that we have here adapted to the GNSS localization. To determine the accuracy of an estimated position, a reference is needed. The inertial navigation sensors and other technical solutions-based reference systems can provide an accurate reference for measurement data evaluation. Figure 7 illustrates the proposed ES-based Monte Carlo simulation procedure, which begins with this data collection and continues with several processing steps:  
* Step 1, a selection is carried out by the amount of collected data stemming from receiver output files. They constitute raw data that are unworkable for a safety evaluation. Useful data leading to the position estimation are extracted at each sampling instant. Then the useful data are processed to obtain information related to correct and hazardous states. To determine if there is a failure or not, a position has to be compared with the true position (the reference). The obtained information leads to quantitative values that can be subsequently analyzed statistically in order to get safety results
* Step 2, the typical testing scenarios can be simulated by different probabilities from Step 1. The system states of GNSS-based positioning in each scenario will be defined and transformed to each other.