## 4 UAV-TPUA: UAV Trajectory Progress Updating Algorithm
### Updating Trajectory Progress
Experimentation employs 12 PRS beams for fine-grained beam scanning, which improves the accuracy of positioning, especially in the precise location determination of UE within complex wireless environments. This meticulous allocation and strategic beam management are pivotal for optimizing the performance of positioning services in 5G networks, ensuring reliable and high-precision positioning outcomes. ### Channel Propagation Model

The channel is modeled according to the standard using the Clustered Delay Line (CDL) impulse response, which can be defined up to a maximum bandwidth of 2 GHz. Additionally, the simulations employ the Shooting and Bouncing Rays (SBR) method to analyze the characteristics of the wireless channel. Noise power spectral density can be modeled by the following formula:

\[N_{0}=k_{\text{B}}\cdot BW\cdot T_{e} \tag{12}\]

where \(k_{\text{B}}\) denotes the Boltzmann constant [JK\({}^{-1}\)]. \(BW\) is the bandwith [Hz]. \(T_{e}=T_{ant}+290(NF-1)\) represents the noise temperature [K]. NF is the linearized noise figure, both referring to the receive antenna. For DL measurement, \(NF=10\) dB and we set \(T_{ant}=298\) K (\(25\,^{\circ}\text{C}\)). ### SAR Setting

The UAV is configured with a flight speed of 100 km/h, with the UE position remaining stationary. The positioning update intervals for the first, second, and third phases are set to 90 ms, 30 ms, and 10 ms, respectively. When the UAV's flight altitude is less than 200 m, the second phase of dual-beam downlink positioning strategy using SSB and PRS is initiated. Upon reaching an altitude below 50 m, the third phase of hovering positioning strategy is activated. The positioning process is concluded and converged when the distance of the UE's positioning results for five consecutive instances is less than 1 m from the mean value. ### Simulation Result

As illustrated in Figure 2, lowering the UAV's altitude and reducing the distance between the UAV and the victim result in a decreased overall localization error. Building upon this finding, we introduce a two-stage trajectory updating algorithm designed to progressively guide the UAV towards the victim over time. Figure 3 depicts the UAV's trajectory with two different flight strategies, which are \"SSB only\" and \"SSB+PRS\", respectively. The red triangle represents the destination position of the victim (or target) in the simulated scenarios. It can be observed that using PRS can

Figure 2: Localization error vs. distance between the UAV and the victim. enhance the trajectory accuracy. However, the improvement of the \"SSB+PRS\" flight strategy compared to \"SSB only\" is not very significant. In light of this scenario, we have included the PRS beam sweeping time in the simulation analysis to assess the merits and demerits of these two strategies, whose results are shown in Figure 4.

The curve on the left vertical axis represents the deviation in distance to the UE compared to the ideal trajectory at different time points under the two updating strategies. Although PRS can improve trajectory accuracy, the red curve gradually deviates more over time due to the fact that during the time required for PRS sweeping, the UAV is actually able to continue moving in the SSB only scheme. The curve on the right represents the distance from the base station to the UE starting from the same initial point at different time points. Figure 4: The distance to UE over time with two different flight strategies. Figure 3: The UAV trajectory with two different flight strategies. It can be observed that the SSB scheme is closer to the UE in the same amount of time spent. Therefore, based on the above observations, SSB only is chosen as the first-stage strategy. According to the resource high-frequency band base station's maximum coverage range of 1 km-2 km, following the principle of a 45\({}^{\circ}\) elevation angle, the drone flies at a height of 700 m to a specific location to access the UE in need of search and rescue.