# 3D Positioning of Drones through Images
## 4 Experimental Setup
### Altitude Determination-Related Experimental Results  
In our proposed fixed-height method, the core idea is to calculate the flight height by converting the area of the captured range, computed from ground coordinates, using a proportional relationship. Through Sequential Quadratic Programming (SQP), we comprehensively evaluate multiple predicted values generated from each coordinate point to calculate the optimal ground range. In this study, each UAV aerial photograph is matched with 12 satellite images containing the UAV image at different spatial scales. Satellite images of different sizes produce varying degrees of accuracy during the matching process. These accuracies are reflected as weights in the objective function of the sequential quadratic programming, essentially seeking an optimal solution in space that both satisfies geometric constraints and fits all predicted data as closely as possible, embodying balance and compromise. Figure 13 shows the partial meter-level (3 m, 5 m, 20 m) matching accuracies produced by satellite images of different sizes. The satellite image cropping range is from 700 to 1800, corresponding to real-world distances from 180 m to 463 m. \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Model** & **Parameter (M)** & **GFLOPS** & **RDS** & **\textless{3 m (\%)**} & **\textless{5 m (\%)**} & **\textless{20 m (\%)**}** \\ \hline MH-FPI & 17.27 & 15.39 & 76.32 & 21.37 & 50.62 & 81.28 \\ OS-FPI & 14.76 & 10.42 & 68.57 & 17.34 & 40.19 & 76.52 \\ WAMF-FPI & 48.5 & 13.55 & 60.49 & 10.45 & 27.83 & 57.72 \\ FPI & 44.48 & 14.88 & 57.15 & 9.86 & 22.39 & 53.77 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Different model parameters, calculation amount, RDS scores and partial meter-level accuracy. Figure 12: Visualization results. In the fixed-height calculation process, to comprehensively consider the coordinates produced by matching satellite images of different sizes and the varying accuracies of different matching results, Sequential Quadratic Programming (SQP) iteratively seeks the minimum value of the objective function J while satisfying geometric constraints. In the test set, the function converged after an average of 14 iterations. This is a gradual process of convergence. After SQP optimization, while maintaining the accuracy of each predicted point, the irregular shape in the second image from the left in Figure 14 was dynamically adjusted to the ideal square shape we envisioned. Figure 15 below shows the relative errors of the original height calculation and the height after SQP processing. Testing revealed that the fixed-height method achieves higher accuracy in the 140-160 m range. We believe this is because localization accuracy reaches an optimal level at this  
Figure 14: The first column is the original image of the drone, and the blue marked point is the center point of the drone mini image that is ready to be cropped. The second column shows the positions of multiple predicted coordinates generated by the cropped drone image on the satellite image (The four colored dots represent drone images that have been cropped into quarters, and each drone image predicts the resulting location,excluding outliers), the coordinates generated by taking the average, and the shape enclosed. The red part in the third column represents the predicted coordinates and the regular shapes enclosed by each drone small image with the minimum objective function after multiple predicted coordinates have passed through SQP. The orange part represents the true position of the center point coordinates of the drone image on the satellite map. Figure 13: Meter-level matching accuracy produced by satellite images of different sizes. height, while the impact of image cropping on the model's localization gradually decreases with increasing altitude. These two factors achieve a balance in the 140 m to 160 m interval. The comprehensive relative height error obtained through direct calculation was 23.17%, which was reduced to 18.16% after SQP processing.