# Anti-Collision System for Small Civil Aircraft
## 4 Accuracy of Determining the Position of Flying Objects by Anti-Collision System
### Verification of the Functionality of Derived Algorithms  
To simulate the operation of the anti-collision system, five FOs motion models in three-dimensional space were created. We chose the initial positions of the FOs to correspond to the real operation in the airspace according to flightradar24. Based on the observation of the movement of aircraft over the territory of the Slovak Republic, there were randomly selected five aircraft and their coordinates were found out at a given time. Since the data come from GPS, it is determined by latitude, longitude, and altitude according to WGS-84. Figure 3 shows a random selection of four transmission sources (aircraft) with a known position and the fifth aircraft, highlighted in red, on which the anti-collision system is located. The position of this aircraft was calculated by applying algorithms that were created during the research which verifies the correctness of the solution. In Tables 1 and 2, the initial position of the selected FOs is listed. In the following simulations, it is assumed that the anti-collision system is located on FO LOTSMF. The selected situation corresponds to real air traffic. An anti-collision system is located on board the LOT5 MF, which, based on the received messages regarding the positions of other FOs, can detect the surrounding traffic and determine the aircraft's position. The created model of the anti-collision system by simulation was verified. Based on algorithms, the position of LOT5 MF was calculated. In the calculation, the initial coordinates LO from Table 1 and 2 are used. The assumption is that the undulation of the geoid is 40.0 m.  
Table 3 shows the LOT5 MF coordinates, calculated using algorithms. The calculations confirmed that the derived algorithms are correct. After verifying the correctness of the algorithms for position calculation, we can proceed to the visualization of models of movements of the users. The FO flight trajectory model is designed to verify the accuracy of the anti-collision system. Based on the created FO models, information about their geocentric position in space can be obtained. Abstracting from the forces acting on the FO during the flight, to simulate anti-collision systems, this fact can be considered irrelevant. The methodology for creating flight trajectory models of FOs is analyzed in detail in [22]. The initial coordinates of the FOs are determined according to flightrad24 in geographical coordinates (LLH). See Table 1. When modeling FOs' trajectories, each part of their trajectory is modeled in a geocentric coordinate system (ECEF). See Figure 4. Therefore, it was necessary to transform the initial coordinates of the FOs into a geocentric coordinate system (Table 2). Five models of straight flight trajectory FOs and five models of flight trajectories with maneuvers were created, which consisted of straight flight and two turns. Based on this, it is possible to evaluate the accuracy of the anti-collision system during straight flight and FO maneuvers. The input parameters of the flight trajectory model, which can be changed according to current requirements, are the initial position of the FO, the time of straight flight or flight in turns, the flight speed, and the radius of curvature. After performing the simulation, we can visualize the FO motion model in the ECEF system. The position of FOs is determined by the coordinates xi, yi, and zi, i = 1 to 5, in meters. The straight flight model lasted 1375.0 s. The flight speed of the flying objects was 100 m.s\({}^{-1}\). We used the equation of a line in three-dimensional space. We assume that the line is uniquely given by two points or one point and a direction vector. The initial coordinates of the FOs' flight trajectories are given in Table 2. The flight altitudes were constant. The initial coordinates of the FOs in  
Figure 3: FOs’ flight trajectories for straight flights.