# A Hybrid Bald Eagle Search Algorithm for Time Difference of Arrival Localization
## 2 Background and Related Work  
The positioning of the WSNs is usually done by two kinds of nodes. The first is the anchor node with known position data. The other is the target node without location information [10; 11; 12]. The two-dimensional or three-dimensional coordinates of the target node is calculated by combining the coordinates with the communication of the anchor node using localization algorithms. Range-based localization methods require distance information to be obtained first, and then the unknown node coordinates are solved by using localization algorithms. Range-based methods include TDOA, time of arrival (TOA), received signal strength indication (RSSI), etc. The coordinates are then located using methods such as least-squares and trilateration methods. Range-free localization methods generally use connectivity information between unknown nodes and landmarks to obtain estimated distances and then use localization algorithms to estimate unknown node coordinates. Range-free methods include Distance Vector HOP algorithms, centroid localization algorithms, and Approximate Point-in-Triangulation Test (APIT) localization algorithms [13; 14]. Both types of algorithms have their own applications and need to be selected according to the actual situation. The swarm intelligence algorithm is a kind of metaheuristic algorithm. The concept of \"swarm intelligence\" was proposed by [PERSON] and [PERSON] for the first time in 1989 in Swarm Intelligence [15]. Researchers have proposed many swarm intelligence algorithms to solve practical optimization problems by observing the unique behaviors and survival modes of birds, animals, and other biological groups formed in the evolution process and imitating the behaviors of biological groups. The ant colony algorithm [16; 17; 18] proposed in 1991 and the particle swarm optimization algorithm [19] proposed in 1994 were among the earlier swarm intelligence optimization algorithms. Given the advantages of distributed computing, parallel search, and robustness in solving optimization problems, swarm intelligence has been used to solve the problems such as routing, coverage, and localization in sensor networks. TDOA [20; 21] localization methods have the characteristics of simple models and high localization accuracy and are applied in the localization scenario of the WSN localization. The Taylor-series estimation method [22] is one of the general methods of classic TDOA localization, but it is very prone to non-convergence of the algorithm when the initial value is poorly chosen. In addition, two-step least-squares algorithms, weighted least-squares algorithms and constrained least-squares algorithms [23; 24] are also common algorithms for solving localization problems. These algorithms do not need iterative arithmetic, are computationally small, fast and can approximate the Cramer-Rao Lower Bound (CRLB) when the noise is small, and is the more established of the commonly used algorithms. However, there is a matrix inversion process in the least-squares algorithm, and more observatories must be used to satisfy the operational conditions in order to keep the operations free of matrix singularities. The emergence of swarm intelligence optimization algorithms, which simulate the nature of organisms searching for food, has a wide range of applications for solving optimal solutions to complex functions and provides new ideas for the TDOA localization problem. [PERSON] et al. [25] put forward using Particle Swarm Optimization (PSO) algorithm to solve the TDOA localization problem, which does not need original values for localization and can attain better localization precision than the least-squares method. [PERSON] [26] et al. proposed the use of the Salp Swarm algorithm to solve the passive time difference localization problem. The Salp Swarm algorithm has fewer control parameters and a simple model, which is also applicable to TDOA localization. Swarm intelligent optimization algorithms omit the complex computational process.