# The UWB Radar Application in the Aviation Security Systems
## 4 Discussion  
The straight-line method was not verified for the accuracy of determining the position of a person behind the obstacle, because the measured data were not synchronized with the exact position of the person during the measurement. Our goal was to develop an algorithm that would allow tracking the movement of a person behind an obstacle. Determining the exact position of a moving person was not our main goal, because we did not have the measured data for it. In UWB radar safety applications, we generally do not require high accuracy to determine the position of a person behind the obstacle. It is required to detect the presence of a person behind the obstacle and the direction of his/her movement. As  
Figure 14: The trajectory of movement of the observed person after application of the straight-line method localization and linear Kalman filter.  
Figure 13: The trajectory of movement of the observed person after application of the straight-line method localization.  
follows from the description of our experiment, the position of a person behind a wall is determined by the rangefinder-rangefinder method. To determine the position of a person behind the wall, two independent radar systems are used, which we have designated as RS1 and RS2; see Figure 1. If we measure the distance of a person behind the wall from the receiving antennas of radars RS1 and RS2 and at the same time we know the coordinates of the antennas, then we can determine the position of the person. In this case, we will use the rangefinder-rangefinder method. If we denote the value of the linear error of the position line of the RS1 system by the symbol \(\delta_{1}\) and the value of the linear error of the position line of the RS2 system by the symbol \(\delta_{2}\), then we express the error of determining the position of the person \(\Delta\)l as follows:  
\[\Delta\mathrm{l}=(\sin\gamma)^{-1}\cdot[\delta^{2}_{1}+\delta^{2}_{2}+2\delta _{1}\cdot\delta_{2}\cdot\cos\gamma]^{0.5}, \tag{25}\]  
where \(\gamma\) is the angle between the position lines RS1 and RS2. The position line of the RS1 system is a circle with the center at the point of location of RS1 and of the radius determined by the distance the antenna RS1 from the position the person. The position line of the RS2 system is a circle with the center at the point of location of RS2 and of the radius determined by the distance of the antenna RS2 from the position of the person. From Relation (25), it is clear that the accuracy of determining the position of a person by such a system depends on the accuracy of measuring the distance (parameter \(\delta_{1}\), \(\delta_{2}\)) and the position of the person relative to RS1 and RS2 (parameter \(\gamma\)). In our case, if the errors of the measured distances between the systems RS1 and RS2 and the moving person are large and the angle \(\gamma\) is different than 90 degrees, then the position of the person is determined with a large error. This makes it possible to explain the errors in determining the position of a person moving behind the obstacle. The application of the linear Kalman filter effectively has suppressed these errors.