# A Hybrid Bald Eagle Search Algorithm for Time Difference of Arrival Localization
## 5 Conclusions  
The purpose of the research in this article is to further address the problem of poor TDOA localization accuracy by using swarm intelligence algorithms. To achieve this goal,  
Figure 8: 3D-scene positioning diagram: (**a**) 3D five-base stations; (**b**) 3D six-base stations; (**c**) 3D seven-base stations; (**d**) 3D eight-base stations.  
Figure 9: Error statistics of base stations in 3D scenes. (**a**) The average error of the algorithm in the experiment in different base stations; (**b**) the standard deviation of the algorithm in the experiment in different base stations.  
we proposed an improved BES method named HBES algorithm and applied HBES to the TDOA problem with higher accuracy and precision than that of other similar algorithms. In the basic BES algorithm, chaotic mappings are introduced to initialize the population. A Levy flight strategy is incorporated to expand the global search capability of the algorithm, and an opposition-based learning strategy is added to increase the ability of the algorithm to step out of local optima, which can promote the optimization-seeking accuracy and convergence speed of BES.  
In order to verify the performance of HBES, firstly, we performed an experimental simulation with other advanced swarm intelligence algorithms in 23 test functions for finding the optimum. At last, in the two-dimensional and three-dimensional scenarios, we respectively analyzed the impacts of some aspects, such as noise effects, number of base stations, number of algorithm iterations, and population size on the TDOA localization. As a general conclusion, the HBES metaheuristic algorithm has better convergence accuracy and faster convergence speed in the test function experiments and shows the best performance, solution quality, and robustness in dealing with the node localization problem.  
In this paper, the TDOA localization problem was not yet identified in the real scenarios. Therefore, in order to improve the practicality of this research, further research will be carried out on TDOA localization in indoor, underwater, and underground scenarios. Since many of the challenges from the research area of WSNs belong to the NP-hard optimization group and the swarm intelligence metaheuristic is proven to be a robust solution method for such problems, we will apply HBES to other problems in WSNs, such as deployment, coverage, and routing. Moreover, there are many opportunities for improvement in swarm intelligence research. We also plan to explore the existing population intelligence algorithms for improvement research to make swarm intelligence work better in the field of WSNs.  
Conceptualization, W.L. and J.Y.; formal analysis, W.L., T.Q. and Y.F.; investigation, F.L.; methodology, W.L. and W.W.; software, W.L.; supervision, J.Z. and J.Y.; validation, W.L.; writing--original draft, W.L.; writing--review and editing, J.Y. and J.Z.; data curation, J.Z.; funding acquisition, J.Z., W.W., T.Q., Y.F., F.L. and J.Y.; project administration, J.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by NNSF of China (No. 61640014, No. 61963009), Industrial Project of Guizhou province (No. Qiankehe Zhicheng [2022])?iban017, [2019]2152), Innovation group of Guizhou Education Department (No. Qianjiaohe KY[2021]012), Science and Technology Fund of Guizhou Province (No. Qiankehejichu [2020]1Y266), CASE Library of IoT (KCALK201708), and the platform regarding the IoT of Guiyang National High Technology Industry Development Zone (No. 2015).  
Not applicable.  
The authors declare no conflict of interest.