# Collision Risk Evaluation and Verification of GNSS-Based Train Integrity Detection
## 5 Simulation and Results
Therefore, through the Monte Carlo simulation process of multi-level state transition, train integrity detection results of all simulation operation scenarios, environment scenarios, train positioning status, train integrity status, and other system's multi-level state evolution can be completed. For accelerometers, the sensor error includes three parts: bias, temperature drift, and random interference. Taking the measurement result of the x-axis of the accelerometer as an example, the error model [28] is as follows:  
\[\hat{a}=(1+S)a+B_{f}+n \tag{11}\]  
The meaning of each symbol in the formula is as follows: \(\hat{a}\) is the measured value of acceleration; \(a\) is the actual acceleration; \(S\) is the scale factor error; \(B_{f}\) is the zero bias error; \(n\) is the random noise error. In order to verify the performance of the proposed train integrity detection based on autonomous perception, this paper takes the actual operation of the Ge NJ2 train on Qinghai Tibet Railway as an example and uses the combination of measured data and numerical simulation data to verify the performance of the train operation state estimation, train integrity detection and collision risk evaluation and verification. See Table 6 for the main parameters of the Ge NJ2 train. The simulated train operation time of the train parting process in every single simulation is 100 s. Every set of simulation tests include 2700 simulation tests, in which the velocity increases from 0 to 50 m/s (almost the maximum velocity that a freight train can reach) by 1 m/s and the acceleration from 0 to 0.54 m/s\({}^{2}\) (maximum traction acceleration) \begin{table}
\begin{tabular}{c c} \hline \hline
**Performance Parameter Category** & **Parameter Characteristics** \\ \hline Locomotive length & 21 m \\ Maximum operating speed & 120 km/h \\ Brake type & CCBII \\ Maximum acceleration & 7.2 km/h/s \\ Maximum deceleration & 14.4 km/h/s \\ Dead-weight & 13.8 t \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Main parameters of NJ2. Figure 12: Simulated positioning error and velocity error. by 0.01 m/s\({}^{2}\). Kalman filtering is employed to smooth the data and compute the protection level. Based on the positioning errors and protection level (see Figure 13), the train integrity detection threshold is set to be 50 m. Then a safety evaluation procedure is launched, and plenty of PFDs in different simulations are computed. As presented in Figure 14, a set of simulation tests with all the train motion situations show the calculated PFD. The results show that the PFD varies from \(10^{-20}\) to \(10^{-50}\), and higher FFD's have smaller velocity and acceleration. Due to the limit of computing performance, 50 sets of simulation tests are carried out, and the total simulated train operation time is \(1.35\times 10^{-7}\) s. Plenty of PFD in both different GNSS localization scenarios and states and train motion states are calculated and followed by the PFH with simulated train operation time. The calculated PFH (see Figure 15) in the 50 sets of simulation range from \(10^{-23}\) per hour to \(10^{-35}\) per hour. An average PFH = \(10^{-25.1482}\) is found, in reference to the corresponding relationship of SIL and PFH, the value of the PFH goes into SIL4. Additionally, in the simulated 3750 h of train operation, no collision accidents happen. Consequently, GNSS technologies can be applied in safety-related TIMS. Yet it is worth more time to verify, since the results of SIL quantities were gained over a limited time period. To improve the performance of GNSS-based train integrity detection, an innovative method should be offered. Figure 14: Collision risks in one simulation test. Figure 13: Simulated positioning error and protection level.