# The Impact of Nonlinear Mobility Models on Straight Line Conflict Detection Algorithm for UAVs
## 5 Performance Evaluation
### Slide Behavior with Different Mobility Models
#### 5.2.1 Effect of Simulation Parameters  
Figure 6 shows the number of missed alarms using various broadcast cycles and velocities for SLIDE using GM, EGM, and RWP, respectively. The number of drones N is 40, the protected zone R is 1 m, and the look ahead time is 8 s.  
As expected, increasing the broadcast cycle leads to an increase in missed alarms. With the RWP, the broadcast cycle should be less than \(\frac{\sigma-2R}{2\
u}\) to avoid missed alarms, thus, less than 3.8 s when the speed equals 3 s and 2.3 s when the speed equals 5 s. With the nonlinear mobilities, as there is a randomness factor, the drone's next position may differ from the expected position. For EGM, the direction standard deviation is 2.49, which will make the next angle vary approximately by the range \([-5.6,+6.4]\) (the range is different around the boundary). For the GM, we set the angle standard deviation to 10, so the next  
Figure 6: Average missed alarms under different \(T_{b}\) using (**a**) GM; (**b**) EGM; (**c**) RWP. angle varies approximately by the range \([-17+17.7]\). For instance, when speed equals 3 m/s and the time step equals 0.5, if the angle changes by 4.5 degrees, the distance between the expected and the actual location will be around 15 cm. These values have a small but cumulative effect on the drone's path, so GM and EGM performance are close for lower broadcast cycles and speed. However, as the broadcast cycle and speed increase, we can see that the EGM outperforms GM because the angle change is less using EGM. Besides that, EGM produced more smoothed paths around the borders; Figure 7 shows examples of how GM and EGM behave around borders. Notably, the number of missed alarms for higher broadcast cycles is lower than that of the RWP. It is because the number of actual collisions is lower using GM and EGM. A possible reason for this is their movement pattern. Several works in the literature compared RWP with GM and concluded that GM leads to uneven node distribution, and they became  
Figure 7: Samples of the paths around the boundary using (**a**) GM; (**b**) EGM. more isolated for some time [28]. Figure 8 shows the movement pattern for three nodes with RWP and GM. Figure 9 shows the number of missed alarms using different communication ranges and velocities for SLIDE using RWP, GM, and EGM, respectively. The considered broadcast cycle is 2, protected zone R is 1, and the look ahead is 8. These figures show clearly that the number of missed alarms decreases when the communication range increases. The algorithm will receive additional state information with larger communication ranges, enhancing the general performance. Figure 10 shows the impact of the look ahead time \(T_{l}\), communication range \(\sigma\), and protected zone radius R on the number of false alarms. The figures clarify that increasing \(T_{l}\), R, and \(\sigma\) lead to an increase in false alarms. For a particular R and \(\sigma\), when \(T_{l}\) increases, false alarms increase until they reach some maximum value. For instance, with RWP, when R = 2.5 and \(\sigma\) = 25, there were around two false alarms when \(T_{l}\) = 2 s, and 4.9 false alarms when \(T_{l}\) = 10 s, then the false alarms stabilize at this point. Similar behavior appears with GM and EGM but with larger false alarm values. This indicates that the prediction performance depends directly on the accuracy of the expected paths. The more distant in advance a prediction is, the less likely it is that such a prediction will be accurate because unexpected turning maneuvers are more likely to occur. SLIDE is a straight line conflict detection algorithm, yet it can provide acceptable performance for some small look ahead times with nonlinear mobilities such as GM and EGM. In fact, when the \(\sigma\) is 25, the benefit of a large look ahead is reduced, as this communication range gives us around 4 s on average for maneuver  
Figure 8: Traveling patterns of nodes with (**a**) RWP; (**b**) GM.