## 5 Conclusions  
In this paper, for the node localization problem in HWSNs, we compared the localization accuracy and localization time consumption of 15 common meta-heuristic algorithms and found that the comprehensive performance of SSA is the best. Thus, a multi-strategy improved sparrow search algorithm is proposed to address the problems of SSA. To improve the global exploration capability of SSA, the golden sine strategy was introduced into the producer's position update method. Meanwhile, to accelerate the convergence speed of SSA, the idea of individual optimality of particle swarm was introduced to the location update method of the investigator. To prevent SSA from falling into local optimality, Gaussian perturbation was applied to the globally optimal sparrow individuals. A total of 23 benchmark functions and 5 meta-heuristics were chosen to evaluate ISSA's optimization performance. In terms of the average value and standard deviation of the search results, ISSA achieved first place or was tied for first place on a total of 20 benchmark functions. Except for F14, the convergence speed of ISSA is not weaker than the rest of the comparison algorithms. In addition, the Wilcoxon rank sum test and the average value were combined in order to evaluate the performance of the algorithms. From a statistical point of view, the number of benchmark functions in which ISSA outperforms PSO, Gold-SA, HHO, GTO, and SSA is 14, 10, 13, 6, and 13, respectively.  
Finally, ISSA was used to solve the problem of solving unknown node coordinates for HWSNs coordinate calculation. Simulation experiments showed that the localization accuracy obtained using ISSA to compute node coordinates is the best among the 15 meta  
Figure 6: Effect of parameter variation on positioning accuracy: (a) change in number of nodes; (b) change of anchor node ratio.  
heuristic algorithms and LS, and it reduces the localization error by 14.19% compared with LS. Changing the internal parameters of HWSNs, it can be found that increasing the number of nodes and increasing the proportion of anchor nodes can improve the accuracy of the localization algorithm. However, when the number of nodes reaches 160 and the proportion of anchor nodes reaches 25%, the enhancement effect will be significantly weakened.  
Unfortunately, applying the proposed ISSA to the node localization of HWSNs improves the localization accuracy but also increases the time required for localization. In our future work, we will further optimize the search mechanism of ISSA to reduce the search time during node localization. In addition, we will also focus on the distance estimation of the first stage of the HWSNs localization problem to further improve the localization accuracy.  
Conceptualization, H.Z. and J.Y.; formal analysis, J.Y.; investigation, W.W. and Y.F.; methodology, H.Z.; software, T.Q.; supervision, W.W.; validation, H.Z., W.W. and Y.F.; writing--original draft, H.Z.; writing--review and editing, H.Z., J.Y. and Z.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the NNSF of China (No. 61640014, No. 61963009), the Industrial Project of Guizhou province (No. Qiankehe Zhicheng [2022]Yiban017, [2019] 2152), the Innovation Group of the Guizhou Education Department (No. Qianjiaohe KY [2021]012), the Science and Technology Fund of Guizhou Province (No. Qiankehejichu [2020]1Y266), the CASE Library of IOT (KCALK201708), and the IOT platform of the Guiyang National High technology industry development zone (No. 2015).  
Not applicable.  
Data Availability StatementData are contained within the article. The data presented in this study can be requested from the authors.  
The authors declare no conflict of interest.