## 5 Experimental Results and Analysis
### Over-the-Horizon PTV Perception Algorithm
#### 5.4.2 Result Analysis  
In order to analyze the influence of the ETC gantry distribution interval on the detection of PTVs, the experiment uses an ETC simulation platform to select a part of the expressway section test area and set different ETC gantry distribution intervals, such as 1 km, 2 km, 3 km, and so on [39]. In the ETC simulation application system function, the platform can simulate the actual situation of multiple concurrent expressways, providing micro-level multitask debugging technical support for traffic flow and single vehicles in transit supervision. The random number generator is used to simulate the driving of three types of Class I passenger cars, as well as other passenger cars and trucks in the test area. At the same time, the ETC gantries are used to collect information on the passage time and speed of the vehicles, and to record the PTVs that are monitored. It should be noted that in order to facilitate the use of data collected by ETC gantry for PTV detection, we represent the distance distributed by the gantry as the distance for over-line-of-sight detection. After data preprocessing, the ETC transaction data of some sections are randomly extracted, the time series of vehicle traffic speed is generated, and 1000 groups of PTVs are selected for testing and evaluation. In order to analyze the rationality of gantry distribution, this article used 11 sets of data collected at different gantry intervals for comparison and analyzed the impact of gantry density in different kilometers on PTV detection. The results are shown in Figure 14.  
Figure 14: Comparison of different gantry intervals. It can be seen from Figure 14 that the recognition accuracy of PTVs gradually decreases with the increase of the distribution interval of the gantry, especially at 6 km, which may be due to the fact that PTVs exceed the over-the-horizon vehicles during the refresh interval. Take the Class I passenger car and truck with the highest and lowest average speed as an example: the average speed difference is 30-40 km/h. If the safety distance is 2 km, it takes 3-4 min for the Class I passenger car to catch up with the truck. If the speed of the Class I passenger car is 100-120 km/h, the three-minute driving distance is 5-6 km. Therefore, if the gantry is not deployed within 6 km, it will largely lead to the Class I passenger car in the rear having exceeded the truck before refreshing the location information of the Class I passenger car, which will greatly reduce the accuracy of recognition. However, from an economic perspective, if the construction cost of ETC gantries is high and the distribution is too dense, this will cause pressure on the economy. If the distribution is too sparse, it will affect the real-time road condition refresh frequency, resulting in the delay of road condition information updates and misleading the driver. Therefore, according to the analysis of the gantry refresh frequency and the consideration of the actual construction cost, the gantry distribution interval of 2 km is the best. The experiment also tracked and counted different types of over-the-horizon PTVs with 600 s (10 min) slices. A statistical analysis of PTVs at different safety distances of 2 km, 4 km, and 6 km was conducted. Due to the lack of transaction data of special operation vehicles, the experiment only analyzes two types of vehicles, such as passenger cars and trucks. The experimental results are shown in Figure 15. The model indicated in orange is trucks, and the model indicated in blue is passenger cars. The safety distance in Figure 15a is 2 km. Since the speed of the trucks fluctuates less throughout the whole process, the surrounding PTVs are more stable than passenger cars, generally around 2. These PTVs may be caused by other trucks in order to ensure timeliness, leading to relative speeding. At 9:00 for the passenger car, there were approximately two PTVs around, and in the next half hour, the number of PTVs within 2 km reached approximately six.