# Factorial Design Analysis for Localization Algorithms
## 2 Related Work  
### Classification of the Localization Techniques  
Localization techniques are classified into two categories: range-free [31] and range-based [19]. The former use connectivity information from the network to estimate the distance between the Node of Interest (NOI) and the Reference Nodes (RNs). This group includes techniques such as centroid; Distance Vector-Hop (DV-Hop) [32]; Approximate Point In Triangle (APIT); circular, rectangular, and hexagonal interaction, respectively; among others. Range-free localization techniques are more inaccurate in localizing the NOI than range-based localization techniques, but they are less complex in terms of computational cost [19]. Range-based techniques, for their part, need distance between the NOI and the RNs to estimate the position of the NOI. The distance between the NOI and the RNs can be calculated using the Received Signal Strength (RSS), Time of Arrival (ToA), Time Difference of Arrival (TDoA) or Angle of Arrival (AoA) [19]. Some range-based localization techniques are multilateration, Multidimensional-Scaling (MDS), hyperbolic and weighted hyperbolic positioning algorithm, circular and weighted circular positioning algorithm, and Weighted Least-Squares (WLS) multilateration [19]. In [19; 31] the range-free and range-based localization techniques are evaluated using three performance metrics: Mean Squared Error (MSE), Cumulative Distribution Function (CDF), and computational complexity. [PERSON] and [PERSON]. [22], as in [23], use the Average Localization Error (ALE) and the CDF to measure the performance of free-range localization techniques and [23] also uses them in range-based techniques. In multi-hop scenarios the DV-Hop, Improved DV-Hop (IDV-Hop) and Weighted DV-Hop (WDV-Hop) algorithms are used to estimate the distance between the NOI and the RNs using the number of hops between them [32]. The algorithms DV-Hop and its variations IDV-Hop and WDV-Hop use the network connectivity information to estimate the average distance per hop. Once the average distance per hop is obtained, the distance separating the NOI and the RNs is obtained to estimate the position of the NOI. There are different localization techniques to estimate the position of the NOI. In [33] the Least-Squares DV-Hop (LSDV-Hop) algorithm is used; this improves the accuracy of the localization of the NOI by extracting a minimum-squares transformation vector between the real and estimated position of the RNs, which are chosen at random. This method does not require extra hardware to estimate the position of the NOI, and it is more suitable for networks with high node densities and long scale. In [32] the hyperbolic and weighted hyperbolic algorithm is used to estimate the position of the NOI; the weighted hyperbolic algorithm offers better performance than the hyperbolic algorithm in terms of the accuracy of the position of the NOI, because this method uses a covariance matrix, whose elements from the main diagonal depend on the estimated distance between the NOI and the RNs. In [34] the meta-heuristic optimization algorithm is used based on Particle Swarm Optimization (PSO) to estimate the position of the NOI through an iterative process that minimizes one cost function. In [35] the PSO algorithm is also used with learning strategies; this technique improves convergence speeds and the PSO algorithm's search efficiency, thus solving the problem of the local minimum of the PSO algorithm. In other multi-hop scenarios, ToA is used to estimate the distance separating the NOI and the RNs [36], where the localization algorithms used are the Vertex-Projection (VP) based on a pyramid-shaped structure; the VP with correction factor, which diminishes the localization error; and the maximum-likelihood algorithm, which shows less localization error than the VP algorithm with the correction factor for high noise levels.