# Vehicle Collision Prediction under Reduced Visibility Conditions
## 4 Experiments
### Experiment Results
#### 4.2.4 Comparison with Different Methods  
For the non-congested traffic scenario, we experimented with different target visibility (\(D_{\text{eb}}\)) conditions [19]. Between the time slots 1 to 19, the target visibility is 400 m. Between the time slots 20 to 39, the target visibility is 120 m due to a heavy fog. Between the time slots 40 to 71, the target visibility is 160 m due to a medium fog. The computed prediction horizons are shown in Table 3. Figure 13a shows the final result compared with the Forward Collision Probability Index (FCPI) method [29]. The FCPI method alerts SV in the 65 th time slot, which gives 0.6s for the driver to react before collision. Our proposed ViCoWS method alerts SV between the 26 th time slot to the 46 th time slot, and between 50 th time slot to 71 st time slot. The collision warning level decreases between the 43 th time slot to the 48 th time slot because of the SV slowing down. The proposed ViCoWS method alerts the SV after the 50 th time slot because the SV speeds up which leads to headway decreasing at a faster rate. If the SV did not brake between the 26 th time slot to the 71 st time slot, a collision will occur after 4.5 s. Further, if the SV did not brake in the 50 th time slot to the 71 st time slot, a collision will occur after 2.1 s.  
As shown in Table 3, the warning time by ViCoWS (\(T_{\text{ViCoWS}}\)) is always greater than the safe PRT (\(T_{\text{PR}}\)) irrespective of the different visibilities, thus ViCoWS can safely warn drivers before it becomes dangerous. However, the warning time by FCPI (\(T_{\text{FCPI}}\)) is safe only the normal visibility condition (400 m). The warning time of 0.6 before possible collision is much less than the PRT (2.0864 s under 120 m visibility and 1.6101 s under 160 m visibility). For the congested traffic scenario, we also experimented with different target visibility (\(D_{\text{eb}}\)) conditions. Between the time slots 1 to 39, the target visibility is 400 m. Between the time slots 40 to 79, the target visibility is 120 m due to a heavy fog. Between the time slots 80 to 115, the target visibility is 160 m due to a medium fog. The computed prediction horizons are shown in Table 4. Figure 13b shows the final result compared with FCPI, which alerts SV in the 103 rd time slot, giving only 1.2 s for  
Figure 12: Relationships between prediction horizon and PRT. (**a**) Non-Congested Traffic Scenario; (**b**) Congested Traffic Scenario. Figure 13: Comparison between ViCoWS and FCPI. (**a**) Non-Congested Traffic Scenario; (**b**) Congested Traffic Scenario. the driver to react before collision. Our proposed ViCoWS method alerts the SV between the 96 th time slot to the 115 th time slot. If the SV did not brake in time, a collision will occur after 1.9 s.  
As shown in Table 4, under the 160 m visibility the safe warning time is \(T_{pr}\) = 1.6101. The warning time by ViCoWS (\(T_{ViCoWS}\)) is 1.9 s which is greater than the safe PRT (\(T_{pr}\)) under the 160 m visibility, thus ViCoWS can safely warn drivers before it becomes dangerous. However, the warning time by FCPI (\(T_{FCPI}\)) is 1.2 s before possible collision which is less than the safe PRT of 1.6101 s under 160 m visibility, thus FCPI is not able to cope with low visibility warnings. It is shown that corresponding to different vehicle velocities, the ranges of prediction horizon must also be different so that collisions can be avoided. In the non-congested traffic scenario, the prediction horizons are in the range of 14 to 25 time slots. However, in the congested traffic scenario, the prediction horizons are in the range of 1 to 13 time slots. This shows that a vehicle with higher velocity should be warned earlier via a larger prediction horizon (more time slots) so that collisions can be avoided. Further, more experiments were conducted to check the validity of the proposed ViCoWS method and to compare it with FCPI.