# Factorial Design Analysis for Localization Algorithms
## 1 Introduction  
Wireless Sensor Networks (WSN) are relevant in the real world because they can determine physical behaviors based on the collaborative work of many sensors [1]. There are several applications for this kind of network, and they can be classified into two categories: monitoring and tracking [2]. There is also a taxonomy of the application domains [3]. The taxonomy includes military and crime prevention [4], disaster prevention and reduction crime in the city [5], health care (Body Area Networks) [6; 7; 8], industry and agriculture [9; 10; 11], urbanization [12] and environmental monitoring applications [13; 14; 15]. The task of collecting data is well defined if the location of sensors is known [16]; localization information is also useful for coverage estimation, deployment, routing, location service, target tracking, and rescue [17; 18]. A solution is to add GPS receivers, but it is expensive and inconvenient for some application scenarios, such as indoors. Localization is one of the main problems in WSNs, since location information is essential for the detection of an event. In the field of underwater environments, localization is one of the most important technologies, since it plays a critical role in many applications. Some applications in underwater environments where location is useful are: data collection, climate change, aquatic animal life time and coral reef population variations, underwater exploration, naturaldisaster prevention (tornadoes, hurricanes, tsunamis, etc. ), ecological applications (pollution, water quality, environmental monitoring, etc. ), assisted navigation, military surveillance, etc. The localization problem in WSN is addressed with different approaches; nevertheless, the inherent characteristics of a WSN, such as limited processing resources, storage, and power, inevitably make localization an engineering challenge. In that sense, several proposals, including some novel solutions, have been developed; in most cases, the evaluation of proposals is done through simulations since their physical implementation involves a high cost and intensive work. The evaluation of all proposals is based on common metrics related to the estimation error and the cost, (i.e., accuracy, precision, and computational complexity [19; 20]). The network's performance can be influenced by the choice of key factors when a localization scenario is simulated, for example, node density [21], and propagation model, among others, and the simulation of all possible combinations can prove to be excessive. The main purpose of this paper is to qualitatively determine the key factors affecting the accuracy and precision performance metrics of localization techniques in some of the principal localization algorithms in a single-hop network, to concentrate on such parameters, thus reducing the amount of simulation time required. For this proposal, the \(2^{k}\) factorial design analysis methodology is used, and MATLAB simulations are carried out in different scenarios, i.e., the extremes values are used for each of the factors of interest and the impact of the interaction among them in the performance metrics is observed. It is important to point out that there is a high degree of variability in some of the simulation factors reported in the literature, and up to now no study has been done of the factors' impact in the performance of localization techniques or on the relations among them. In other words, the literature reports many proposals to improve localization algorithms, but their design is not based on the factors that have the greatest impact on performance metrics; they are only used to evaluate their algorithm. Thus, the main contribution of this paper is to formally identify these factors to generate more precise and accurate localization algorithms.