## 5 Experimental Results and Analysis  
Experimental analyses are carried out under four different network simulation conditions to show the effectiveness of the proposed algorithm, listed as random topology, grid topology, C-Shaped random topology, and C-Shaped grid topology, as shown in Figure 2 respectively. In random topology, all nodes are randomly deployed in the corresponding experimental area, while in grid topology, each node is deployed at the intersection of gridlines and differentiated according to the proportion of the deployment deviation, in which ratio of 0 means that the nodes are precisely distributed at the gridline intersection. In comparison with random topology, the node distribution of grid topology is uniform. When designing the C-shaped area, we considered excavating a part of the square area during the simulation. The cut-out area is \(30\times 70\) m\({}^{2}\) (the original area was \(100\times 100\) m\({}^{2}\)). The DEIDV-Hop algorithm is compared with DV-Hop, PSODV-Hop [43], and GSODV-Hop [44] through simulation implemented on MATLAB 2014a [45], running on a desktop PC with one Intel(R) Core(TM) i5-6500 CPU @3.20 GHz processor, 8 GB RAM, and Windows 7 OS. In this investigation, only the two-dimensional coordinate plane is considered. All experimental results are averaged by running 100 times independently, and the size of the experimental area is \(100\times 100\) m\({}^{2}\). The localization error of unknown nodes \(u\) is:  
\[Error_{u}=\sqrt{\left(x_{u}^{est}-x_{u}^{act}\right)^{2}+\left(y_{u}^{est}-y_{ u}^{act}\right)^{2}} \tag{22}\]  
Figure 2: **(a)** Node error distribution diagram in square random topology; **(b)** Node error distribution diagram in a square grid topology; **(c)** Node error distribution diagram in C-Shaped random topology; **(d)** Node error distribution diagram in C-Shaped grid topology. The average localization error (ALE) is taken as the evaluation criterion, and calculated as:  
\[\text{\emph{Average Localization}}\quad Error(ALE)=\frac{\sum_{i=1}^{n}\sqrt{ \left(x_{u}^{est}-x_{u}^{act}\right)^{2}+\left(y_{u}^{est}-y_{u}^{act}\right)^{ 2}}}{n\times R} \tag{23}\]  
where \(\left(x_{u}^{est},y_{u}^{est}\right)\) and \(\left(x_{u}^{act},y_{u}^{act}\right)\) is the estimated location and actual location of the unknown node \(u\). ALE is the average localization error, \(N\) the total number of nodes, \(n\) is the number of unknown nodes. In Equation (23), the numerator represents the Euclidean distance between the estimated location and the actual location of the unknown node, and the estimated error distance. This article includes R in the denominator, thus, Equation (23) with R is called the normalized average localization error. Thus, \(n\) is given as:  
\[n=N-m \tag{24}\]  
Experiments verify its influence on the average localization error in three aspects: the communication radius of nodes, the percentage of anchor nodes, and the total number of nodes. The parameters used in the DEIDV-Hop experiment are shown in Table 1, while the parameter settings for PSODV-Hop [43] and GSODV-Hop [44] are identical to original references and shown in Tables 2 and 3, respectively. The error graphs of nodes in four topologies, namely square random topology, square grid topology, C-Shaped random topology, and C-Shaped grid topology are listed in Figure 2. As settings for the investigation, the communication radius R of the node is 20 m, the total number of deployment nodes is 100, and the percentage of anchor nodes is 20%. As shown in Figure 2, when the node deployment area changes from square topology to C-shaped topology, the average localization error of the node rises sharply. On the other hand, from the perspective of node distribution, random topology and grid topology can be considered a sparse network and intensive network. It can be observed that the nodes of the grid topology are evenly distributed if compared with the random topology; the error of nodes is smaller as well.