## 2 UTM Monitoring Framework
### Conflict Detection Algorithm  
The inverted teardrop shape algorithm for UAS conflict detection in 3D space was used in this research. It employs a new shape of a teardrop as the horizontal detection area with the sharp edge pointing toward the direction of the UAV flight movement, as shown in Figure 2. However, the inner near-collision area still used a circle shape. The teardrop shape gives two advantages, which are providing a larger buffer area in UAV movement and allowing a higher traffic capacity. The radius of the near-collision circle is based on the research from MIT Lincoln Laboratory (MIT LL) and the John Hopkins University Applied Physics Laboratory (JHU APL) [29; 30; 31] as 50 ft or 15 m plus the horizontal accuracy from the GNSS system. This fixed separation concept was demonstrated successfully in an Airborne Collision Avoidance System for a small UAS (ACAS sXu) system to mitigate the likelihood of a loss of separation. While the teardrop round shape was selected to be 3 times the near-collision circle with an assumption that the near-collision circle was equal to the average distance of the UAV traveled in 1 s plus another 2 s to allow for the UAV to react to and avoid the conflict. The sharp edge of the teardrop shape has a distance of two times the circle radius of the round shape. This distance definition is based on the proportionality of a teardrop shape that produces a larger buffer area at a 120\({}^{\circ}\) wide angle in front of its movement direction. This 120\({}^{\circ}\) angle is the same as the maximum horizontal binocular vision of a human [32]. Figure 1: Remote ID conceptual overview [27]. Figure 2: Inverted teardrop detection volume in 3D space with the big arrows as UAV symbols: black is the own UAV and red is the intruder UAV. This shape combination gives a larger buffer zone on the front side of the UAV movement to reduce the possibility of a collision event. For three-dimensional (3D) consideration, the height range was adopted for vertical area detection in accordance with what is mostly used in the concept of aviation airspace and suggested by other research [33]. Like horizontal detection, the size of the height range for conflict detection was selected to be 3 times the height range of the near-collision height. The algorithm for conflict detection of UAVs in 3D space is shown in Figure 3.  
It starts with the calculation of the UAV flight direction, horizontal relative distance, relative direction, and relative height between UAVs based on the position of two UAVs at the same timestamp. For UAV flight direction \(\psi\) in geographical standard (0 degrees pointing to the north), it can be calculated using the trigonometry principle from the speed vector as shown in Equation (1):  
\[\psi=tan^{-1}\bigg{(}\frac{V_{e}}{V_{n}}\bigg{)} \tag{1}\]  
where \(V_{e}\) is the speed in the east direction and \(V_{n}\) is the speed in the north direction. The relative horizontal directions \(\theta\) and relative height h are calculated as in Equations (2) and (3), and the horizontal distances between UAVs d are calculated using the haversine method, which uses the great circle reference, as shown in Equations (4) and (5), where R is Earth's reference radius of 6,378,137 m [34]. \[\theta=\psi_{1}-\psi_{2} \tag{2}\]  
\[h=h_{1}-h_{2} \tag{3}\]  
\[\mathit{hav}\ (\theta)=sin^{2}\bigg{(}\frac{\theta}{2}\bigg{)} \tag{4}\]  
\[d=2R\times sin^{-1}(\sqrt{\mathit{hav}(\theta)}) \tag{5}\]  
Figure 3: Conflict detection algorithm based on the inverted teardrop shape. Based on the calculated parameters, the algorithm can define whether a conflict is detected based on the position of the intruder UAV relative to the teardrop detection volume. First, if the distance d between UAVs is more than 6r, then there is no conflict detected and no warning produced. The \"r\" is the radius of the circle used in the near-collision area.