## 2 Related Work
### Hybrid PSOGWO Principle
#### 2.2.2 Gwo
As shown in Figure 7, when three reference points are collinear, there may be the following three situations: the first is that there is no intersection region, as shown in Figure 7a; the second is that there is a large intersection region, as shown in Figure 7b; and the third is that there are multiple intersection regions, as shown in Figure 7c. The above three cases increase the difficulty of locating the target node. To avoid the above situation, this paper limits the reference point location. When the number of reference points is equal to or greater than 3, we limit the selection of the third reference point location, so that the third reference point location is not on the extension line or reverse extension line between the first two reference point locations. In this way, we can realize that at least three reference point locations are non-collinear, and the concrete example is shown in \[L(t+1)=L_{p}(t)-A\times D,A=2a\times r_{1} \tag{4}\]6 As shown in Figure 8, we select the first two reference point locations \(A\) and \(B\). To avoid the collinearity of the three reference point locations, the selection of the third reference point location has the following three cases: the first is shown in Figure 8a, where the third reference point location \(C\) or \(C^{\prime}\) is on the vertical line of the \(AB\) line segment; the second case is shown in Figure 8b, where the location \(C\) or \(C^{\prime}\) is on the perpendicular of the \(AB\) extension; the third is shown in Figure 8c, where the location \(C\) or \(C^{\prime}\) is on the perpendicular of the \(AB\) reverse extension. At this time, it can be ensured that the ring formed by the three reference points has only a small intersection region. \[L(t+1)=L_{p}(t)-A\times D,A=2a\times r_{1} \tag{4}\]7 The region where the target node is. \[L(t+1)=L_{p}(t)-A\times D,A=2a\times r_{1} \tag{4}\]8 Collinear situation of reference points. (**a**) Case 1. (**b**) Case 2. (**c**) Case 3. #### 3.2.3 Weighted Distance Strategy for Selecting Reference Points

The RSS and stability of the target node are different from the reference point location. As shown in Figure 9, this paper selects four different reference points \(D_{1}\), \(D_{2}\), \(D_{3}\) and \(D_{4}\). The RSS mean values of these four reference points are \(-30.26\), \(-50.24\), \(-65.05\) and \(-80.54\), respectively, and the variances are \(1.952\), \(7.822\), \(6.868\) and \(3.028\), respectively. Therefore, although the RSS at the reference point \(D_{2}\) is strong, the signal stability is the worst. If the RSS is considered as the only criterion for selecting reference points, the localization precision may be reduced. Therefore, to select the reference points with strong and stable RSS, this paper records the variance of the RSS of the target node received by reference points to improve the reliability of reference point selection. According to the recorded variance, different weight coefficients are assigned to different reference points. The RSS collected continuously for \(N\) times at the \(i\)th reference point can be expressed as follows:

\[L(t+1)=L_{p}(t)-A\times D,A=2a\times r_{1} \tag{4}\]9

According to the obtained \(RSS_{i}\), we can calculate the variance \(\sigma^{2}\) of the reference point. The larger the variance of the reference point is, the more unstable the RSS is and

\[D_{\alpha}=|C_{1}\times L_{\alpha}-L|,D_{\beta}=|C_{2}\times L_{\beta}-L|,D_{ \delta}=|C_{3}\times L_{\beta}-L| \tag{5}\]0 Deployment process of reference points. (**a**) Case 1. (**b**) Case 2. (**c**) Case 3. \[D_{\alpha}=|C_{1}\times L_{\alpha}-L|,D_{\beta}=|C_{2}\times L_{\beta}-L|,D_{ \delta}=|C_{3}\times L_{\beta}-L| \tag{5}\]1 Collect the RSS. the smaller the weight that should be allocated. The weight \(w^{i}\) of the \(i\)th reference point is calculated as follows:

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

where \(t\) represents the number of reference points.