## 2 Related Work
### Hybrid PSOGWO Principle
#### 2.2.2 Gwo
This is because although the PSO has a strong ability to develop new space, it lacks communication between particles and is prone to fall into local optima, resulting in unstable localization results. Although the GWO has a weak ability to develop new space, resulting in low localization precision, it can maintain high stability in localization results because of the information sharing among gray wolves. The ILP-PSOGWO significantly narrows the region where the target node exists, so it can maintain high localization precision when the number of reference point changes. #### 4.2.4 Impact of Iteration Times on Localization Precision

Figure 15a describes the relationship between the number of iterations and the localization error in LOS. With the increase in iteration times, the localization errors of three methods are significantly reduced. When the number of iterations exceeds 15, the localization errors obtained by the three methods remain unchanged. The localization errors \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Environmental**} & \multirow{2}{*}{**Localization**} & \multicolumn{6}{c}{**Test Points Location**} \\ \cline{3-8}  & & **(2.5, 5)** & **(8, 7.3)** & **(14.8, 6.2)** & **(5.5, 9)** & **(11.2, 7.8)** & **(16, 5.1)** \\ \hline \multirow{3}{*}{LOS} & PSO [24] & 0.9196 & 1.3290 & 0.9832 & 1.2939 & 1.2037 & 0.9987 \\  & GWO [25] & 1.5143 & 1.4980 & 1.0372 & 1.3258 & 1.1835 & 0.8999 \\  & EWCL [27] & 0.8675 & 1.0903 & 0.8099 & 0.9099 & 0.7936 & 0.7091 \\  & ILP-PSOGWO & 0.7186 & 0.8021 & 0.5289 & 0.6503 & 0.5910 & 0.4521 \\ \hline \multirow{3}{*}{NLOS} & PSO [24] & 2.0326 & 2.5710 & 1.7825 & 2.0627 & 2.0320 & 2.1833 \\  & GWO [25] & 2.7921 & 2.3467 & 1.9732 & 2.1362 & 2.2693 & 1.7902 \\ \cline{1-1}  & EWCL [27] & 1.1290 & 1.2293 & 0.9021 & 1.1798 & 0.8998 & 0.9098 \\ \cline{1-1}  & ILP-PSOGWO & 0.9027 & 1.0363 & 0.7936 & 0.9831 & 0.7352 & 0.5621 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The impact of target node location on localization error. Figure 14: Impact of the number of reference point on localization error. (**a**) LOS. (**b**) NLOS. of the PSO and GWO remain around 1 m, while the localization errors of ILP-PSOGWO are around 0.4 m. In addition, Figure 15a also indicates that ILP-PSOGWO achieves the optimal solution faster, which means it has strong convergence ability. This is because the hybrid PSOGWO combines the advantages of PSO and GWO, which makes it have a strong search ability and convergence ability. Figure 15b depicts the experimental results in NLOS. The environment changes lead to a significant increase in the localization errors of the three methods, which have a greater impact on the localization errors of PSO and GWO, and a smaller impact on the ILP-PSOGWO. Moreover, when the number of iterations increases to 35, the localization errors of PSO, GWO and ILP-PSOGWO are significantly reduced, which are 1.9073 m, 1.8351 m and 0.9112 m, respectively. #### 4.2.5 Stability

To verify the stability of ILP-PSOGWO, the following two aspects are evaluated in this paper: standard deviation and cumulative probability distribution. (i) Standard deviation

Standard deviation can reflect the degree of dispersion of a group of data, thus reflecting the stability of the group of data. The standard deviation \(error_{std}\) can be calculated as follows:

\[error_{std}=\sqrt{\frac{\frac{\sum\limits_{j}^{n}{(error_{j}-error_{avg})^{2}}} }{n}} \tag{23}\]

where \(n\) represents the number of experiment, \(error_{j}\) represents the localization error of the \(j\)th measurement, which can be calculated in Equation (22), and \(error_{avg}\) represents the average localization error of a group of data after the \(j\)th measurement. When the number of sample points is 7 and the area of the localization region is 17 \(\times\) 10, we conduct 5, 10, 15, 20, 25, 30, 35, 40, 45 and 50 experiments in LOS and NLOS, respectively.