## 6 Convergence Speed of the Algorithm and the Localization Error of Unknown Nodes
### The Localization Error of Unknown Nodes  
In this section, the percentage of anchor nodes is 20% and the number of nodes is 100. The communication radius is 20 m. Experimental results are shown in Figure 11. In this section, \(ALE\geq 1\) is considered as an isolated node, and it is considered as a node that cannot be located.  
As in Figure 11, boxplots are applied to show the following ALE results: minimum/maximum of the localization error, the median, and the 25 th and 75 th percentiles of the independent simulations of each unknown node in the algorithms of four network topologies. The DEIDV-Hop algorithm is relatively stable, and the localization error is lower than the original algorithms DV-Hop algorithm, PSODV-Hop algorithm, and GSODV-Hop algorithm,  
Figure 11: (**a**) The ALE of each unknown node in square random topology; (**b**) The ALE of each unknown node in a square grid topology; (**c**) The ALE of each unknown node in C-Shaped random topology; (**d**) The ALE of each unknown node in C-Shaped grid topology.  
* In the square random topology, there are four nodes in the DV-Hop algorithm that cannot be located, and 33 nodes are higher than the average of the localization error. In the PSODV-Hop algorithm, one node cannot be located, and the localization error of 44 nodes is higher than the average. In the GSODV-Hop algorithm, two nodes cannot be located, and the localization error of 38 nodes is higher than the average. In the DEIDV-Hop algorithm, one node cannot be located, and 28 nodes are higher than the average.
* In the square grid topology, among the four algorithms, no unknown node cannot be located. In the DV-Hop algorithm, the localization error of 41 nodes is higher than the average of the localization errors. The localization error of 36 unknown nodes in the PSODV-Hop algorithm is higher than the average. In the GSODV-Hop algorithm, the localization error of 36 nodes is higher than the average. In the DEIDV-Hop algorithm, the localization error of 36 nodes is higher than the average.
* In the C-shaped random topology, there are 46 nodes in the DV-Hop algorithm that cannot be located, and the localization error of 37 nodes is higher than the mean of the localization error. In the PSODV-Hop algorithm, there are 25 nodes cannot be located, and the localization error of 29 nodes is higher than the average. In the GSODV-Hop algorithm, 25 nodes cannot be located, and the localization error of 26 nodes is higher than the average. In the DEIDV-Hop algorithm, 14 nodes cannot be located, and the localization error of 36 nodes is higher than the average.
* In the C-shaped grid topology, there are 38 nodes in the DV-Hop algorithm that cannot be located, and the localization error of 34 nodes is higher than the mean of the localization error, where 26 nodes cannot be located and the localization error of 31 nodes is higher than the average in the PSODV-Hop algorithm. In the GSODV-Hop algorithm, 20 nodes cannot be located, and the localization error of 31 nodes is higher than the average. In the DEIDV-Hop algorithm, 18 nodes cannot be located, and the localization error of 30 nodes is higher than the average.  
When the number of deployed nodes and the communication radius are the same, the four network topologies of the nodes will affect the distribution of the nodes. The grid topology will make the distribution of the nodes more uniform, denser, and tend to be intensive networks. In this way, each node has more single-hop connection nodes, and the hop-count value between nodes will become smaller and more regular. Thus, network connectivity is stronger. In random topology, the random distribution of nodes makes the hop-count value between nodes irregular, the connectivity between nodes deteriorates, and it tends to lead to sparse networks. There will be some isolated nodes that cannot be located, which increases the average localization error of nodes.