# Anti-Collision System for Small Civil Aircraft
## 4 Accuracy of Determining the Position of Flying Objects by Anti-Collision System
### Discussion and Results of Anti-Collision System Accuracy Evaluation  
In order to verify the sensitivity of the proposed algorithms to inaccuracies in measuring the distance of FO1-4 network users from ACS, we performed additional simulations for a straight flight of 1375 s and also for a flight with a maneuver of 1375 s. The maneuver flight contained two turns, each lasting 500 s. The initial coordinates of the FOs are given in Tables 1 and 2. In this simulation, the errors are added which are generated by the 12 random number generators to the exact coordinates of the FO1-4 users. This simulates the inaccuracies of the distance measurement from all network users to the ACS. The magnitude of the distance measurement inaccuracy is changed using the constant k following Equations (28) and (29). The constant k in the range from 0.2 to 3 is changed. In this variant, 11 simulations for straight flight and 11 simulations for flight with maneuver were performed. The simulation results are shown in Figure 7.  
Figure 7 shows the mean values m\({}_{\text{AP}}\) and dispersions \(\sigma^{2}_{\text{AP}}\) of ACS positioning errors for straight flight. The mean ACS positioning error values range from 1.45 m to 21.67 m. Dispersions of ACS \(\sigma^{2}_{\text{AP}}\) positioning errors range from 1.94 m\({}^{2}\) to 503.23 m\({}^{2}\). The results of the ACS positioning accuracy simulation confirmed that the ACS positioning errors depend on the accuracy of the distance measurement from FOs to the ACS d\({}_{1-4}\), according to which the ACS determines its position. The accuracy of the proposed system meets the requirements that are placed on such devices. Figure 8 shows the mean values m\({}_{\text{AP}}\) and dispersions \(\sigma^{2}_{\text{AP}}\) of ACS positioning errors for the maneuvered flight. The mean ACS positioning error values range from 2.04 m to 32.1 m. Dispersions of ACS \(\sigma^{2}_{\text{AP}}\) positioning errors range from 3.2 m\({}^{2}\) do 857.22 m\({}^{2}\). In addition, in this case, the results of the ACS positioning accuracy simulation confirmed that the ACS positioning errors depend on the accuracy of the distance measurement d\({}_{1-4}\). The simulation results showed that the accuracy of the proposed ACS deteriorated. Assuming that this is due to a more significant change in the geometry of the system that occurs during the maneuver flight simulation, some simulations were performed using a combination of precisely measured distances of individual FO1-4 from the ACS and pseudo-distances. They were burdened with errors to determine the position of the ACS. Initial conditions for FOs were the same as in previous simulations. FO1-4 coordinate errors were generated by generators under the same conditions as in previous simulations. The constant k was equal to 1. Simulations were performed for a straight flight with a flight duration of 1375 s. The results of all performed simulations are shown in Figure 9.  
Figure 7: Accuracy of ACS positioning for straight flight. The results of the simulation show that the mean values of the ACS positioning errors and the dispersion of the ACS positioning errors were smaller than if \(\Delta\)d\({}_{1-4}\
eq 0\). The best improvement occurred with the combination \(\Delta\)d\({}_{1}\) = 0, \(\Delta\)d\({}_{2}\) = 0, \(\Delta\)d\({}_{4}\) = 0, and \(\Delta\)d\({}_{3}\
eq 0\), where the mean value of the positioning error ACS was equal to 1.81 m and the dispersion of the positioning error ACS was equal to 3.18 m\({}^{2}\). The simulation results confirm that the time synchronization requirements of individual network users are high and inaccurate parameters in the transmitted message from individual FOs directly affect the accuracy of ACS positioning. Additional simulations were performed with the change of FO  
Figure 8: Accuracy of ACS positioning accuracy for maneuvered flight. Figure 9: Accuracy of ACS positioning for straight flight and various distance measurement: errors \(\Delta\)d\({}_{1}\)–\(\Delta\)d\({}_{4}\). position relative to the ACS.