## 5 Performance Analysis
The lower bound of detection probability is analyzed in the earlier part of Section 5, the comparison between theoretical analysis and experimental results for the detection probability is shown in Figures 1 and 2, respectively. We vary the amount of mobile sensor nodes in sensor networks and the communication range between different sensor nodes. When \(N=1000\) and \(R=40\), the result of comparison is shown in Figure 1. When \(N=500\) and \(R=100\), the result of the comparison is shown in Figure 2. As is shown in both of Figures 1 and 2, the experimental detection probability is higher than the low bound of detection probability discussed before. The detection time is an important metric to evaluate the proposed scheme. Because the communication range reflects the encounter probability, and the encounter probability decides the time elapsed between each meeting, so that we would discuss the change of detection probability with over time on the effects of different communication ranges. As is shown in Figure 3, the detection probability under \(R=50\) is 51.1% and the detection probability under \(R=100\) is 82.1% about 250 s later; the detection probability under \(R=100\) is above 90% about 350 s later. To achieve the same  
Figure 1: Comparison of detection probability (\(R=40\), \(N=1000\)). Figure 2: Comparison of detection probability (\(R=100\), \(N=500\)). result in the case of \(R=50\), it takes at least 550 s to reach 90% detection probability. So the larger the communication range, the higher the detection probability. Simulations are conducted to demonstrate the impact of time synchronization and localization errors on the proposed protocol. We use ideal temporal synchronization and positioning method to measure the speed, and then the measured speed \(v\) is modified as \(v^{\prime}\), \(v^{\prime}\) is selected uniformly at random from the range of \(v-v\theta\) and \(v+v\theta\), where \(\theta\) is defined as the maximum speed error rate. \(\alpha_{0}\) and \(\alpha_{1}\) are set in accordance with the maximum speed error rate. Figure 4 shows how to take different values of \(\alpha_{0}\) and \(\alpha_{1}\) according to the maximum speed \(v_{\max}\) which is scientifically configured by the system. As shown in Figure 4, when the system-configured maximum speed \(v_{\max}\) is in the interval of 10-60 m/s, and the maximum speed error rate is 0.01 or 0.02. \(\alpha_{0}\) and \(\alpha_{1}\) are set to 0.1 and 0.95 respectively. When the predefined maximum value \(v_{\max}\) is in the interval of 60-80 m/s and the maximum speed error rate is 0.01 or 0.02, \(\alpha_{0}\) and \(\alpha_{1}\) are set to 0.05 and 0.9 respectively. When the system-configured maximum speed \(v_{\max}\) is in the interval of 80-100 m/s and the maximum speed error rate is 0.01 or 0.02, \(\alpha_{0}\) and \(\alpha_{1}\) are set to 0.01 and 0.8 respectively. When the system-configured maximum speed \(v_{\max}\) is in the interval of 10-60 m/s and the maximum speed error rate is 0.1, \(\alpha_{0}\) and \(\alpha_{1}\) are set to 0.2 and 0.9 respectively. When the predefined maximum value \(v_{\max}\) is in the range of 60 to 80 and the maximum speed error rate is 0.1, \(\alpha_{0}\) and \(\alpha_{1}\) are set to 0.15 and 0.85 respectively. When the system-configured maximum speed \(v_{\max}\) is in the interval of 80-100 m/s and the maximum speed error rate is 0.1, \(\alpha_{0}\) and \(\alpha_{1}\) are set to 0.1 and 0.8 respectively. So it is deduced that the configurations of \(\alpha_{0}\) and \(\alpha_{1}\) are inversely proportional to variety in the system-configured maximum speed \(v_{\max}\). Figure 4: The configurations of \(\alpha_{0}\) and \(\alpha_{1}\). Figure 3: Detection probability versus detection time. The average amount of samples for every tracked node is the amount of samples required for the witness node to judge whether a node has been cloned or not.