# 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 9: Average missed alarms under different \(\sigma\) using (**a**) GM; (**b**) ECM; (**c**) RWP. Figure 10: Number of false alarms under different \(T_{l}\), \(\sigma\), and \(R\) using (**a**) GM; (**b**) EGM; (**c**) RWP. If the \(\sigma\) is 25 m and the speed is 3 m/s, and assuming two drones enter each other's range and head to each other, this will give 8 s until the collision. Such conflict cannot be predicted before that. Therefore, a minimum of 8 s for look ahead is required in this case (\(\sigma\) = 25 and speed = 3) to detect such conflicts. However, we should avoid larger look ahead values with nonlinear mobility as they will negatively impact undetected conflicts and false alarms. Using GM and EGM, the drones will change their heading at each step (the considered time step (update interval) for both GM and EGM is 0.5 s), and the actual position in the near future may differ from the expected position by SLIDE. Figure 12 shows a sample of a GM path and compares it with the expected straight line path for 60 s. The distance between them reaches 7 m after 39 s.  
The same applies to the EGM, with the difference that with EGM, in the beginning, the difference between the paths is less than the GM case, then the drone starts heading in a completely different direction (Figure 13). Furthermore, for a specific \(T_{l}\) and \(\sigma\), the false alarms will rise by increasing the protected zone radius \(R\) from 1 m to 2.5 m. For example, with GM, when \(T_{l}=10\) s and \(\sigma=25\) m, the number of false alarms is 12 when \(R=1\) m and becomes 30 when \(R\) is increased to 2.5. We see the same behavior with the EGM; the false alarms increased from around 10 to 26. The reason for this rise is that the radius of the protected zone will increase the number of actual conflicts. For instance, with GM, the number of actual conflicts is 8 with a protected zone radius of 1 m and 60 conflicts with a protected zone radius of 2.5 m. This rise in the number of actual conflicts will increase the number of detected conflicts, and accordingly, the probability of false alarms will increase. In the same way, for a fixed \(T_{l}\) and \(R\), the number of false alarms will rise by increasing the communication range \(\sigma\) from 25 m to 65 m because each drone will have more nearby drones to consider, which will also increase the possibility of false alarms. Figure 11 shows the average maneuver time and its relation with \(T_{l}\), \(\sigma\), and \(R\). For both GM and EGM, the maneuver time increases by increasing \(T_{l}\), \(\sigma\), and \(R\) until it converges at some maximum value. From the analysis of Figures 10 and 11, we can conclude that the selections of \(T_{l}\) and \(\sigma\) are a trade-off between the disturbance alarms and higher safety margin. Raising \(T_{l}\) or \(\sigma\) will raise the maneuvering time but at the expense of raising the false alarms. On the other hand, lowering \(T_{l}\) or \(\sigma\) will reduce the false alarms at the expense of reducing the maneuvering time, which may become not enough for avoidance maneuver. Table 3 shows the number of false alarms under different airspace dimensions. We consider two speeds, \(v=3\) and \(v=5\), and two look ahead times, \(T_{l}=2\) and \(T_{l}=8\). The broadcast cycle is set to 2 s. We can see that the false alarms for all mobility models reduce as the airspace expands and the speed dropps. In larger airspaces, the drones will move in straight lines more frequently and have fewer turns, whereas in smaller airspaces and with faster speed, the drone will reach the boundaries faster, and the change of direction will be larger. Thus, to avoid large false alarms in smaller airspaces, we should use smaller \(T_{l}\). Figure 12: Sample of GM path and the expected straight line path for 60 s.  
Figure 13: Sample of EGM path and the expected straight line path for (**a**) 60 s; (**b**) 15 s.