## 2 Materials and Methods
### Determination of the Cardinal Direction
The topological sequence for these events is shown in Figure 1:1

As the final case of the experiment, after a certain period of time, the results showed that all four vehicles participating in the experiment formed a fully connected group; further, the results indicated the relative position of all vehicles by recognizing the topological sequence of vehicles within the connected group. The images of screens displaying the results are shown in Figures 11 and 12. Figure 1:2 Conceptual illustration of the topological vehicle sequence shown in Figure 1:3

Figure 1:4 Screen images of the connected group’s reformation and overtaking. As shown in Figure 11, the topological sequence of all vehicles shown on the upper left of all screens indicated A\(\rightarrow\)D\(\rightarrow\)B\(\rightarrow\)C, and the geographical location of all vehicles was also the same. The illustration for this sequence is shown in Figure 1:5 In addition, as the boxes at the bottom of each screen of Figure 11 showed the formation of a fully connected group, the driving information of other vehicles including its own appeared for each vehicle at the same time. Therefore, each vehicle knows which vehicle is ahead and which is behind in the current group. Most vehicles run at a constant speed on the road, but they often overtake other vehicles by accelerating to overcome any delay or to avoid traffic congestion. It is important for autonomous vehicles to gauge the geographic location on the road with respect to the surrounding vehicles even

Figure 1:6 Screen images showing the formation of a fully connected group and the sequence of all vehicles. Figure 1:7 Conceptual illustration of the topological vehicle sequence shown in Figure 1:8

when a situation of departure from the current sequential vehicle group occurs. The necessity to know the situation of preceding vehicles is to prevent vehicle accidents while overtaking. Figures 13 and 14 show that vehicles in the connected group recognize each other by incorporating an overtaking situation's information. As shown in Figures 13 and 14, after approximately 3 min had elapsed from the current time in each vehicle shown in Figure 11, vehicles A and D accelerated, and their speeds surpassed those of vehicles B and C. Here, if an overtaking situation occurs, the topological sequence of all vehicles should also be changed and recognized. The upper left parts of each screen image in Figure 13 show that the sequence information among vehicles is correctly reflected from the previous sequence A\(\rightarrow\)D\(\rightarrow\)B\(\rightarrow\)C to sequence B\(\rightarrow\)A\(\rightarrow\)C\(\rightarrow\)D.

Figure 1:9 Images of screens when each vehicle overtakes the other. ## 4 Discussion

Although the connected car technology is applicable to future autonomous vehicles and smart cars, it does not apply to vehicles that are currently being produced [4; 10]. If this technology is to be applicable to existing vehicles, it will require the attachment of additional devices such as an on-board unit (OBU). To prevent accidents, Advanced Driver Assistance Systems (ADAS) installed on existing vehicles are not optimum systems for the driver, and they provide neither the connected car technology nor self-driving [31]. Even if a vehicle is equipped with the Autonomous Emergency Braking (AEB) system, the vehicle will automatically apply the emergency brakes when other vehicles driving around the vehicle overtake and intervene. In this case, vehicles that immediately follow may cause a collision. Therefore, it is also important to understand the situation information of other vehicles that are currently driving around a vehicle. Hence, it is necessary to form a connected car subgroup. Therefore, this paper proposed and experimented three algorithms that improve the performance of the CMVF system using smartphones and the connected car technology. The proposed algorithms distinguish the representative direction in which vehicles are driven and allow vehicles in the connected group to recognize each other's topological sequence.