# C Band 360\({}^{\circ}\) Triangular Phase Shift Detector for Precise Vertical Landing RF System
## 4 Landing Algorithm and Evaluation  
The landing algorithm used in [25; 27] is formulated in terms of the voltages measured at the output of each of the analog phase detectors because there is a bijective relationship between phase and voltage. However, the voltages directly measured at the dual multiplier phase detector do not provide direct information to be used in the landing algorithm. The landing algorithm is based on the offsets between the input signals to each of the three receiving points located on the drone when transmitting from the LP (Equation (3)). The objective is to locate the incenter of the drone over the LP. In that case, the distances between the LP and the vertices of the receiving triangle are identical, and hence, the three phase shifts will be zero. If the drone is considered to be at a height \(z_{D}\) and the LP is at a distance \(r_{L}\) and rotates around according to angle \(\phi_{L}\), the input phase shifts vary as shown in Figure 14. The crossing points between the detector curves determine the limits of each of the six sectors in which the LP can be located. Figure 14 includes the relationships between the phase shifts for the different sectors and the relative location of the drone, which will serve as the basis for performing the landing algorithm with the maneuvers that guide the drone towards the LP. Figure 15 shows the landing algorithm to be used in this case, which should be in terms of the offset between the input ports. Unlike the algorithms used in [25; 27], where \(\pm 60^{\circ}\) turns were performed to orient the drone so that the landing point was in Sector 1, this algorithm proposes to reach that situation through smaller corrections. This leads to a more realistic correction adapted to the drone dynamic movements, as is performed in the stabilization phase with pitch and roll data [47; 48]. The flight maneuvering algorithm detailed in Figure 15 has been validated using a simple program. From the positioning of the drone and the LP, the three phase shifts \begin{table}
\begin{tabular}{c|c|c c c c c c c c c|c} \hline \hline  & & & & & & & \multicolumn{6}{c}{_Frequency_ (GHz)} \\ \hline  & 4.7 & 4.8 & 4.9 & 5.0 & 5.1 & 5.2 & 5.3 & 5.4 & 5.5 & 5.6 & 5.7 \\ \hline \(S_{in}\) (dBm) & \(-46\) & \(-49\) & \(-51\) & \(-51\) & \(-50\) & \(-52\) & \(-52\) & \(-52\) & \(-50\) & \(-50\) & \(-45\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Minimum input power versus frequency that stabilizes the reference point power to 0 dBm (Figure 7). The 3 dB bandwith extends from 4.8 GHz to 5.6 GHz. Figure 14: Phase shifts between RF (\(\Delta\theta_{ij}\)) inputs when the LP is moved around the drone (\(\phi_{L}\)). The figure includes the relationships between the phase shifts associated with each of the 6 sectors that determine the relative location of the LP. between the RF inputs are calculated (Equation (3)). The phase shifts can exceed the range \(\pm 180^{\circ}\). Next, the three pairs of voltages \(V_{dQ}\) and \(V_{dI}\) are obtained using both Equation (3) and coefficients from Table 3. The new phase shifts (\(\Delta\theta_{12}\), \(\Delta\theta_{23}\) and \(\Delta\theta_{31}\)) are calculated from these voltages and following the procedure described in Section 2.3. This operation is going to provide an offset between \(\pm 180^{\circ}\). The phase shift values are used in the landing algorithm (Figure 15) to determine the maneuver to be performed. This process and the descent are performed continuously until the drone lands (\(z_{D}=0\)). The simulation uses \(1^{\circ}\) increments for the rotation and 1 cm for the forward/reverse. The descent increment starts at zero and increases progressively up to 1 cm when the drone is on the LP perpendicular. Figure 16 shows the evolution of the drone in cylindrical coordinates when it starts from position \(\{0,0^{\circ},500\}\), oriented along the positive \(Y\) axis, and the LPs are located at angles multiples of \(60^{\circ}\) about an initial reference of \(-35^{\circ}\) (\(490,(-35+n\cdot 60)^{\circ}\), \(0\)).