# A Hybrid Bald Eagle Search Algorithm for Time Difference of Arrival Localization
## 1 Introduction  
The composition of wireless sensor networks (WSNs) includes numerous sensor nodes with signal processing, communication, and other functions to the fore area to be monitored. These nodes then connect, sense, and process information through wireless communication technology to form a multi-hop self-organizing network [1, 2, 3, 4, 5], which has the characteristics of low networking cost, self-organizing ability, and environmental adaptability. A wireless sensor node usually consists of sensing units, processing units, transceivers, and power units. Its function can be summarized as three keywords: communication, perception, and calculation. WSNs have great applications in military, medical, transportation, and environmental monitoring [6].  
Location information is an integral part of data sensing in most applications of the WSNs, such as monitoring the extent of the enemy's area during military activities, determining the exact location of the fire source during forest fires, and quickly identifying the affected area during earthquake disasters [7, 8]. Knowledge of the node location information can improve the efficiency of routing protocols and enable automatic configuration of the network topology to improve coverage quality [9]. We can obtain the location informationof nodes by deploying some nodes with a global positioning system (GPS) or BeiDou navigation satellite system (BDS) modules in the WSN. The greater the number of nodes with known locations, the more accurate the user can be in determining the location of the information source, but these devices are energy-intensive, large, and costly, and are not suitable for deployment in all nodes. Therefore, it is necessary to research a precise and effective localization algorithm for WSNs.  
The main contributions of this paper are as follows:  
* Aiming at the shortcomings of TDOA localization algorithm in WSNs, which is susceptible to interference from non-visual range errors and poor localization results, a hybrid bald eagle search algorithm (HBES) is proposed to replace the mathematical analysis method to estimate the unknown node coordinates. It avoids the inverse and the derivative of the matrix in the mathematical analysis method, which can lead to unsolvable solutions.
* To enhance the optimization capability of the bald eagle search algorithm (BES), we propose to use chaotic mapping, [PERSON]'s flight and backward learning strategies to improve the population quality, and hybrid sine and cosine algorithms to improve the performance of the bald eagle algorithm.
* A localization model combining the TDOA algorithm and HBES algorithm is developed, and experiments are conducted to analyze the performance of the algorithm and the localization effect.  
The rest of this article is arranged as follows. In Section 2, we introduce some existing positioning technologies in WSNs. In Section 3, we describe our model for TDOA localization in detail. In Section 4, we make a comparison between our algorithm and other swarm intelligence algorithms for assessing the performance of the proposed algorithm, and we use the localization algorithm in localization experiments to analyze the actual performance of the proposed algorithm. Section 5 concludes the paper and predicts trends in applications.