## 2 Related Work
### Hybrid PSOGWO Principle
#### 2.2.2 Gwo
\[D_{\alpha}=|C_{1}\times L_{\alpha}-L|,D_{\beta}=|C_{2}\times L_{\beta}-L|,D_{ \delta}=|C_{3}\times L_{\beta}-L| \tag{5}\]9 Optimizing the target node location using PSOGWO. (**a**) Optimizing the target node location. (**b**) The situation of equal fitness values. \(d_{1}+d_{2}+d_{3}=D_{1}+D_{2}+D_{3}\). At this time, the fitness values of the two gray wolves are also equal, indicating that the gray wolf locations coincide, but in practice, gray wolf \(i\)'s location is not equal to gray wolf \(j\)'s location, which will affect the target node location. Therefore, if the fitness values of gray wolves are equal, this paper proposes to use the following conditions for exclusion:

\[L_{1}=|L_{\alpha}-A_{1}\times D_{\alpha}|,L_{2}=|L_{\beta}-A_{2}\times D_{ \beta}|,L_{3}=|L_{\delta}-A_{3}\times D_{\delta}| \tag{6}\]0

where \(d_{1,i}\) and \(d_{1,j}\) represent the distance from gray wolf \(i\) and \(j\) to the first reference point, respectively. * **Step 3:** Update the current location of the gray wolf. * **Step 4:** Update \(a\), \(A\) and \(C\). * **Step 5:** Calculate the fitness of all gray wolves. * **Step 6:** Update the fitness and location of \(\alpha\), \(\beta\) and \(\delta\). * **Step 7:** Judge whether the maximum number of iterations or the fitness threshold is reached. If yes, exit the loop and output the target node location. Otherwise, go to Step 3 and continue. The time complexity will affect the execution efficiency of the algorithm. The time complexity of ILP-PSOGWO is mainly composed of two aspects: the first is the dichotomy used to narrow the selected region of reference point, and the second is the hybrid PSOGWO used to optimize the target node location. The optimal time complexity of dichotomy is \(O(1)\), and the worst time complexity is \(O(\log_{2}n)\). The time complexity of hybrid PSOGWO is \(O(t\times n)+O(t\times n\times d)\). Therefore, the time complexity of the two methods is \(O(\log_{2}n)\) and \(O(n^{3})\), respectively. The time complexity of ILP-PSOGWO is \(O(n^{3})\). ## 4 Experiment

To verify the effectiveness and feasibility of ILP-PSOGWO, this paper obtains data sets in the actual environment, conducts experiments many times and compares the experimental results with the existing methods particle swarm optimization (PSO), gray wolf optimization (GWO) and extended weighted centroid localization (EWCL). ### Experiment Setting

In real scenarios, the transmission environment of wireless communication systems is usually divided into line of sight (LOS) and not-line of sight (NLOS). In LOS, the radio signal can travel in a straight line between the transmitter and the receiver without any obstruction. If the conditions are not met, the RSS will be significantly attenuated (i.e., NLOS). To verify the impact of environmental complexity on ILP-PSOGWO, experiments are carried out in LOS and NLOS. The experiment was carried out on Intel(R) Core(TM) [EMAIL_ADDRESS] GHz with 32 GB RAM and Python 3.7.10 using Windows 10 Professional Edition platform. The detailed parameter settings in the experimental process are shown in \[L_{1}=|L_{\alpha}-A_{1}\times D_{\alpha}|,L_{2}=|L_{\beta}-A_{2}\times D_{ \beta}|,L_{3}=|L_{\delta}-A_{3}\times D_{\delta}| \tag{6}\]1 \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline The number of target nodes & 1 \\ Experimental environment & LOS, NLOS \\ The number of reference points & 3, 5, 7, 9, 11, 13 \\ Area of localization region (m\({}^{2}\)) & 15, 20, 25, 30, 35, 40 \\ The number of iterations & 5, 10, 15, 20, 25, 30, 35 \\ The number of experiments & 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 100 \\ Test points location & (2.5, 5), (8, 7.3), (14.8, 6.2), (5.5, 9), \\  & (11.2, 7.8), (16, 5.1) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Experimental settings.