# Using Ground-Based Passive Reflectors for Improving UAV Landing
## 4 Results  
Consider the described landing system's effectiveness on a specific example of landing an aircraft-type UAV along a trajectory, which the horizontal and vertical sections shown in Figure 8 and the course difference defined as the difference in the y-coordinate (see Figure 3) between the intended touchdown point of the UAV and its position at the \(k\)-th observation moment. The trajectory initial height was 35 m, the range to the touch point was 500 m, and the push down angle was 5 degrees. The dots show the reflectors placed for landing UAVs using the radar. Figure 9 shows the runway plan and the reflectors' locations, indicating the distances between them. The intended touchdown point was the intersection of the runway longitudinal axis and the segment connecting the side reflectors. The model of the landing trajectory and runway were indicative and could be refined for UAV-specific types and landing conditions. Figure 8: Gliding line model. The study of the UAV's positioning errors occurring along its trajectory is a problem whose analytical solution in closed-formed is extremely difficult. Therefore, we proposed using the simulation of the UAV equipped with an onboard radar during its final approach in the vicinity of the runway. A sequence of coherent radio pulses with a duration of 50 ns was used as a probing signal. Figure 10 shows the UAV's push-down trajectory and the marks obtained determining its coordinates by solving Equation (3) for successive moments of time and illustrates errors in the vertical plane (top) and in the horizontal (bottom). As can be seen from the above figures, the errors in the horizontal plane were quite small, and the UAV's estimated location did not differ from its actual position by more than 1 m. The worst situation was in the vertical plane, where the error values could be up to three meters, an unsatisfactory result. The latter was explained by the large value of the geometric factor (9), connecting the location determination errors with the errors of the distance primary measurements to the reflectors. The geometric factor, in turn, depended on the base of the positional navigation system, that is, on the distance between its reflectors. Figure 10: Mark deviations from the calculated trajectory in the vertical plane (**top**) horizontal plane (**bottom**). Figure 9: Landing system reflector location. Figure 11 shows the total error dependence in determining the UAV's location in the time from the beginning of the approach to the landing trajectory. Dotted lines represent the raw value of the absolute error and the solid lines account for the Savitzky-Golay filter [55; 56] application (open-loop filter of order three). Data were obtained as a result of the numerical simulation for both the default case and the case with one reflector in a higher position. A single simulation was performed and a single realization of the noise vector was generated. That dataset was then processed by the two systems with different reflector heights representing the two presented cases. Thus, no ensemble averaging was employed. The dependency of the location determination error shown in Figure 11 allowed to conclude that, as the UAV approached the calculated landing point, the error values decreased and reached a value of one meter. If such a value was quite acceptable for errors in the planned plane, then, for errors in the vertical plane, such values would not allow a soft landing on the runway. To reduce vertical errors, one would further consider the reflector height influence located on the edge of the runway opposite to the landing point on the accuracy of estimating the UAV coordinates' vertical component.