## 2 Materials and Methods
### Taguchi Design of Experiments Method  
Nowadays, there is great interest in quality management. It seeks processes that provide products in the fastest, most efficient, and as economic as possible way. According to this interest, different procedures and statistic methodologies have been developed to evaluate and improve certain processes by analyzing the involved parameters of factors and taking actions. This can be applied to photogrammetric flights, which are nothing but a process aimed at taking photographs of the territory. As mentioned in the previous section, these processes count with a series of factors that are involved in the quality of the final product. This research is focused on the application of the Taguchi Design of Experiment (DOE) Method [18] for the optimization of the photogrammetric flight. This technique was developed by the Japanese engineer [PERSON]. It is an \"ad hoc\" experiment that allows choosing the process that works more consistently within a certain operative environment. The basic assumption is that not all the factors that cause variability can be controlled. The goodness of Taguchi Method is that it finds a good design (although it may not be the best) by developing a relatively reduced number of experiments, so that it reaches a good cost/benefit ratio. Although its initial uses were focused on the field of quality engineering [19], recent examples related to different disciplines such as mechanical [20] and oil [21] technologies, management of polluted soils [22], structural monitoring [23], or medicine [24] can be found. Considering its use in the field of photogrammetry with UAV platforms, it has been applied to the process of data management [25; 26], but not to the design of the flight. Before starting the experiment, noise and control factors must be identified. It can be stated that a photogrammetric flight designed with Taguchi DOE Method will be optimized, as all the factors will have been properly chosen. The technique is based on the application of an orthogonal matrix that indicates the experiments that must be developed. It is also known as orthogonal arrange, and it estimates the effects of the factors in the average response and the variation. In addition to this, as it is an orthogonal arrange, the design is balanced: the levels of the factors are equally weighted. This allows that every factor can be evaluated without taking into account the rest of factors: the effect of a factor does not affect the estimation of another. As the designs with orthogonal arranges are mainly focused on the key effects, the time, and costs associated to the experiment are reduced. Taguchi DOE Method can be developed in dynamic or static ways. The dynamic design applies the signal factors, that is to say, those that are controlled by the user during their application with a range of values. In a design with dynamic response, the characteristic of quality works through a range of values, and the final objective is to improve the relation between a signal factor and the output response. Taguchi DOE Method applies the fractional factorial designs or orthogonal arrays. However, when the number of factors is increased, the possible interactions also raise,and due to this, the difficulties to identify which are the specific conditions to experiment. [PERSON] developed a series of orthogonal arrays that called:  
\[\text{L}_{\text{a}}=(\text{b})^{\text{c}}. \tag{2}\]  
[PERSON]'s design for an experiment with four control factors and three levels of variability corresponds to the \(\text{L}_{9}\) matrix, which is shown in Table 1.  
According to the characteristic that is desired to obtain: there are three alternatives to calculate the signal-to-noise ratio: smaller is better, nominal is best and larger is better. In this case, since the error of geometry of the final model is assessed, it is aimed that the error tends to zero, which means that the model suits the reality that it represents.