## 2 Related Work
### Hybrid PSOGWO Principle
#### 2.2.2 Gwo
The weighted distance \(d_{ij}\) between the reference point and the target node after improvement can be calculated as follows:

\[D_{\alpha}=|C_{1}\times L_{\alpha}-L|,D_{\beta}=|C_{2}\times L_{\beta}-L|,D_{ \delta}=|C_{3}\times L_{\beta}-L| \tag{5}\]3

where \(j\) represents the target node, and \(d_{i}\) represents the distance between the \(i\)th reference point and the target node. Taking the deployment of three reference points as an example, as shown in Figure 10a, \(S\) is the first deployed reference point. To deploy the next reference point closest to the target node, we select a location in the upper, lower, left and right directions of location \(S\), respectively, and compare the RSS of these four locations. Then, we select the location with the strongest RSS (i.e., \(S_{2}\)) as the candidate location for the second reference point. In Figure 10b, \(P_{1}\), \(P_{2}\) and \(P_{3}\) represent three reference points selected within the range [\(R_{1}\), \(2R_{1}\)] of distance \(S\). According to the weighted distance strategy, if the weighted distance at \(P_{1}\) is the shortest, this location is selected as the second reference point. Figure 10c shows the selection process of the third reference point. According to the deployment strategy of reference points, this paper selects the third reference points on the vertical bisector of location \(S\) and \(P_{1}\), namely \(Q_{1}\), \(Q_{2}\) and \(Q_{3}\). The connecting distance between the third reference points and the first two reference points meets the range [\(R_{1}\), \(2R_{1}\)]. According to the weighted distance strategy, \(Q_{2}\) will be selected as the third reference point. Finally, the third reference points, \(S\), \(P_{1}\) and \(Q_{2}\) are selected in turn. ### Locating the Target Node

As shown in Figure 11, simply taking the centroid of the intersection region of the three rings (i.e., the green hexagonal star) as the true location of the target node will cause a reduction in localization precision. Therefore, this paper uses hybrid PSOGWO to locate and optimize the target node location. The main processes of locating are as follows. \[D_{\alpha}=|C_{1}\times L_{\alpha}-L|,D_{\beta}=|C_{2}\times L_{\beta}-L|,D_{ \delta}=|C_{3}\times L_{\beta}-L| \tag{5}\]4 Select reference point. (**a**) Select the first reference point. (**b**) Select the second reference point. (**c**) Select the third reference point. * **Step 1:** As shown in Figure 11(a), initialize the gray wolf population \(N\) in the target region, and each gray wolf represents the potential location of the target node. * **Step 2:** Calculate the fitness of gray wolf individuals and save the first three gray wolves with the best fitness \(\alpha\), \(\beta\) and \(\delta\). The calculation equation of fitness value is as follows: \[D_{\alpha}=|C_{1}\times L_{\alpha}-L|,D_{\beta}=|C_{2}\times L_{\beta}-L|,D_{ \delta}=|C_{3}\times L_{\beta}-L| \tag{5}\]5 (18) where \[D_{\alpha}=|C_{1}\times L_{\alpha}-L|,D_{\beta}=|C_{2}\times L_{\beta}-L|,D_{ \delta}=|C_{3}\times L_{\beta}-L| \tag{5}\]6 (19) \[D_{\alpha}=|C_{1}\times L_{\alpha}-L|,D_{\beta}=|C_{2}\times L_{\beta}-L|,D_{ \delta}=|C_{3}\times L_{\beta}-L| \tag{5}\]7 (20) where \(RMS_{i}\) represents the fitness value of gray wolf \(i\). The smaller the fitness value, the closer the actual location of the gray wolf and target node. \((x_{t},y_{t})\) and \((x_{p},y_{p})\) represent the reference point location and each gray wolf, \(d_{t,p}\) is the distance from the reference point to each gray wolf, \(d_{t,ap}\) is the distance from the reference point to the target node and \(n\) is the number of reference points. The fitness ranking of the gray wolf may encounter the situation of equal fitness values, as shown in Figure 11(b); the distance between gray wolf \(i\) and \(j\) to the three reference points are equal, that is,

\[D_{\alpha}=|C_{1}\times L_{\alpha}-L|,D_{\beta}=|C_{2}\times L_{\beta}-L|,D_{ \delta}=|C_{3}\times L_{\beta}-L| \tag{5}\]8 Locating target node.