## 5 Conflict Risk Assessment between Drones and Manned Aircraft  
Based on the predicted position of the manned aircraft and the predicted position distribution of the drone obtained in Sections 3 and 4, it is determined whether a conflict risk exists between the drone and the manned aircraft. Additionally, the conflict probability  
Figure 4: Performance comparison of the trajectory prediction models for drones. Figure 5: Illustration of the position distribution for the drone. between the drone and the manned aircraft with the conflict risk is calculated. The specific process is as follows:  
First, it is determined whether there is an intersection between the predicted position of the drone under each quartile at the prediction time and the protected area of the predicted location for the manned aircraft. If the predicted value of the drone at the \(\tau\) quartile at the \(i\)-th time is in the protected area of the manned aircraft in the \(x\), \(y\), and \(z\) directions, that is, when Formula (9) is satisfied, it means that the drone is in the risk of conflict with manned aircraft. The horizontal and vertical distance between the predicted position of the drone and the protected area of the manned aircraft is judged as follows:  
\[\left\{ \begin{array}{c}\sqrt{\left(O(x)_{\tau i}-P(x)_{i}\right)^{2}+\left(O (y)_{\tau i}-P(y)_{i}\right)^{2}}<dis_{e}\\ \left|O(z)_{\tau i}-P(z)_{i}\right|<dis_{f}\end{array} \right. \tag{9}\]  
In the formula, \(dis_{e}\) is the horizontal distance between the predicted position of the drone and the protected area of the manned aircraft, \(dis_{f}\) is the vertical distance between the predicted position of the drone and the protected area of the manned aircraft; \(O(x)_{\tau i}\), \(O(y)_{\tau i}\), \(O(z)_{\tau i}\) are the predicted values of the drone at the \(\tau\) quartile at the \(i\)-th time in the \(x\), \(y\), and \(z\) axes; \(P(x)_{i}\), \(P(y)_{i}\), \(P(z)_{i}\) are the predicted values of the manned aircraft in the \(x\), \(y\), and \(z\) axes. Second, the probability of collision between the drone and the manned aircraft at the predicted time can be estimated. According to the conflict risk assessment, the number of predicted position points of the drone under all the quartiles at the prediction time in the protected area of the manned aircraft is obtained. The ratio of the number in the protected area to the number of total predicted position points of the drone under all quartiles is the collision probability between the drone and the manned aircraft at the predicted time. The collision probability \(Prob_{i}\) between the drone and the manned aircraft at the \(i\)-th moment is expressed as:  
\[Prob_{i}=\frac{\sum\limits_{\tau=1}^{m}b_{\tau|i}}{m} \tag{10}\]  
In the formula, \(m\) is the number of predicted position points of the drone under all quartiles, and \(b_{\tau|i}\) represents the conflict between the predicted position of the drone and the manned aircraft under the \(\tau\) quartile at the \(i\)-th time. When there is a conflict risk, \(b_{\tau|i}\) takes the value of 1, and otherwise, \(b_{\tau|i}\) is 0. The conflict probability threshold is set to 50%. The threshold is the same as that set in previous research [27; 29]. If the probability of conflict at the predicted time is greater than or equal to the conflict probability threshold, it is considered that there is a conflict between the drone and the manned aircraft. If it is less than the conflict probability threshold, it is considered that the drone and the manned aircraft are not in conflict. Then, the correct detection rate and false alarm rate of collision probability prediction are calculated. In reality, it is difficult to carry out a collision test between a manned aircraft and a quadrotor. Therefore, a collision simulation test is carried out based on the real trajectory data, which not only ensures that the trajectory data in the simulation test conforms to the actual flight situation but also reduces the test risk and cost.