# Anti-Collision System for Small Civil Aircraft
## 3 Design of the Anti-Collision System for the Category of Small Aircraft
### Model of Anti-Collision System  
The designed model assumes that all flying objects operate in the communication network of aviation and each flying object transmits information on its position. Another prerequisite for the operation of the anti-collision system designed by us is that the communication network must be synchronized. Every user is given a strictly specified time for the transmission of communication messages. Designing the anti-collision system, we started from the fact that if we know the location of a minimum of four points in the space and the distances of these points from an unknown point, we can calculate the position of the unknown point. In case we presuppose that based on message transmission by individual network users, the anti-collision system will know the location of those users. It will also be able to measure distances from those users because individual users will provide times of communication message transmissions. This method of position determining is a designated telemetric method. The principle of the telemetric method is described in detail in [1; 2]. In aviation, location is usually being expressed in geographical coordinates in WGS-84. Designing the anti-collision system, the rectangular Earth-Centered, Earth-Fixed coordinate system (ECEF) is used. Let us suppose that all users in the communication network in Figure 1 transmit in short time intervals, among other things, messages on their positions. The time of signals spreading from one user to the anti-collision system is directly proportional to the distance between that system's receiver and the source of transmission (ST). Measuring the distances of more users of the aviation communication network from the anti-collision system is possible to determine their location. The position of the anti-collision system P against other users of communication network P\({}_{i}\)t\({}_{i}\), i = 1 to 4, is demonstrated in Figure 2.  
Figure 1 reflects an air situation in the aviation communication system. The used symbols: P--position of the aircraft with the anti-collision system; P\({}_{1-4}\)--positions of other users 1-4 in the communication network; t\({}_{1-4}\)--times at which messages were sent; d\({}_{1-4}\)--distances of users from the anti-collision system. On condition that we have identified the coordinates of individual users of the aviation communication network (x\({}_{i}\), y\({}_{i}\), z\({}_{i}\)) and the distances of the anti-collision system from those users, we can determine its position P with the coordinates x, y, z:  
\[\mathrm{d_{i}}=\sqrt{\left(x-x_{i}\right)^{2}+\left(y-y_{i}\right)^{2}+\left(z -z_{i}\right)^{2}},\text{ where i }=1,2,3,4 \tag{1}\]  
If the user P\({}_{i}\) sends the message at the time t\({}_{i}\), the message will be received at the time t\({}_{\text{p}}\). Provided that the speed of electromagnetic waves spreading (c) is known, the distance between the source of transmission and the receiver of the user d\({}_{i}\) is as follows:  
\[\mathrm{d_{i}}=c\left(t_{\text{pi}}-t_{i}\right)=c\tau_{i}\text{ where i }=1,2,3,4 \tag{2}\]  
Figure 1: Position of aircraft in the airspace according to flightradar24. Figure 2: Position of the anti-collision system P concerning other users of the communication network. The calculated distance is burdened with several errors. For that reason, the distance is denoted pseudo-distance. If the time base of the user's receiver \(\rm P_{i}\) is shifted by an unknown time interval \(\rm\Delta t\), then this interval can be converted to a distance \(\rm b\) using the equation:  
\[\rm b=c.\rm\Delta t. \tag{3}\]  
The actual distance then will be equal:  
\[\rm D_{i}=d_{i}-b \tag{4}\]  
where: \(\rm d_{i}\)--measured pseudo-distance, \(\rm D_{i}\)--actual distance, \(\rm b\)--error of distance measurement. The delay \(\rm\Delta t\) causes a distance \(\rm D_{i}\) measurement error due to a shift in the time bases of the flying objects and the anti-collision system.