## 2 Materials and Methods
### Methodological Proposal Adapted for the Optimization of Flights  
Starting from the premise of this research, the optimization of the potential photogrammetric flights over archaeological sites, to obtain a 3D model that allows for virtualization with the added advantage of good metrics, Taguchi DOE Method is applied to enhance the most relevant parameters that the pilot can modify (control factors). After the analysis that was developed in Section 2.1, it seems reasonable that the most determinant factors are the ones included in Table 2. The levels for each parameter range according to the recommendations and values applied in several works of research related to the application of aerial photogrammetry with UAV to the analysis of archaeological sites and structures [1; 28; 29; 30; 31]. Taguchi DOE Method applied to four factors with three different levels implies a matrix with nine arranges or tests. It is worth noting that there are other procedures such as Fisher DOE Method, that require \(3^{4}\) tests. This entails the development of 81 flights, in order to obtain 81 models to contrast the variation of their accuracy. This large volume of experiments, which implies important costs and time, justifies the application of Taguchi DOE Method. For this particular case, the resulting matrix is shown in Table 3.  
It is worth noting that the meteorologic conditions related to the wind speed and direction, and the lightning, are left as noncontrollable or noise factors. However, their incidence can be reduced with a proper planification of the flight in terms of date and hour. For the analysis, a statistical value is proposed for every test: the average signal-to-noise ratio, which is obtained from the measurements taken in each of them. Otherwise, the dependence of the parameter of interest with respect to the controllable variables can be analyzed, and the effects of noise factors can be compensated, with the identification and optimization of those upon which it is possible to act. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Factors**} & \multicolumn{3}{c}{**Levels**} \\ \cline{2-4}  & **1** & **2** & **3** \\ \hline Height of flight & 15 m & 45 m & 75 m \\ Forward overlap & 60\% & 70\% & 80\% \\ Lateral overlap & 60\% & 70\% & 80\% \\ Inclination angle of the sensor & \(0^{\circ}\) & \(30^{\circ}\) & \(60^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Control factors and levels for the application of Taguchi Design of Experiments (DOE) Method. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Flight**} & \multicolumn{3}{c}{**Control Factors**} \\ \cline{2-5}  & **Height of Flight** & **Forward** & **Lateral Overlap** & **Inclination Angle** (\({}^{\circ}\)) \\ \hline
1 & 15 & 60 & 60 & 0 \\
2 & 15 & 70 & 70 & 30 \\
3 & 15 & 80 & 80 & 60 \\
4 & 45 & 60 & 70 & 60 \\
5 & 45 & 70 & 80 & 0 \\
6 & 45 & 80 & 60 & 30 \\
7 & 75 & 60 & 80 & 30 \\
8 & 75 & 70 & 60 & 60 \\
9 & 75 & 80 & 70 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Proposal for the application of Taguchi DOE Method to photogrammetric flights. Given the objective of this research, the error that is committed when measuring a distance is adopted as fundamental variable for its determination. For this purpose, eight 1-m-long stadias were evenly distributed on the archaeological site before developing the flights, so as to be able to determine the geometric accuracy of the model. These elements have been selected, rather than other structures that already existed in the site, due to their easy identification in photographs, and the accuracy that, as a standard [32; 33], they must have. From these measurements, it will be possible to establish the signal-to-noise ratio proposed by [PERSON], thus analyzing the dependence of the final result geometry with respect to the design variables of the flight project.