# A Hybrid Bald Eagle Search Algorithm for Time Difference of Arrival Localization
## 2 Background and Related Work
These methods initialize a large number of random points in the observation range and evaluate the merits of the random points by constructing an adaptation function between the random points and the measurements. Then, the position of random points is updated according to the formula of the swarm intelligence optimization algorithm to find the best degree of adaption position. Therefore, this method avoids matrix inversion, overcoming the disadvantage of least-squares-like algorithms that require the placement of multiple observation stations. However, the swarm intelligence algorithm has a slow convergence rate and tends to fall into a local optimum. Therefore, other strategies are needed to optimize the swarm intelligence algorithm and enhance its optimization capability. The application of improved particle swarm algorithms, and genetic algorithms in TDOA localization is described in the literature [27; 28]. They both improve the original algorithm to enhance the algorithm's search accuracy, such as introducing chaotic mapping to initialize the population quality to improve the global search capability of the particle swarm algorithm, and using adaptive crossover rate and variation rate to optimize the local search capability of the genetic algorithm. The reported approaches have improved the performance of the swarm intelligence algorithms to some extent, and they have been used to solve some practical problems. On the other hand, some swarm intelligence algorithms still suffer from slow convergence speed and low accuracy in finding the optimal individual. In addition, the use of swarm intelligence algorithms for TDOA localization only takes into account factors such as algorithm accuracy and stability, two-dimensional scenarios, and specific deployment of base stations. These methods are not closely related to practical application. According to the NFL (no free lunch) theory [29], The results of each swarm intelligence algorithm are uncertain when solving different optimization problems, and there is no swarm intelligent algorithm that can optimize all engineering problems. In addition, different swarm intelligent optimization algorithms require different numbers of control parameters, and numerous control parameters not only increase the complexity of the algorithm but also increase the workload of adjusting parameters. Therefore, it is vital and significant to find a more suitable swarm intelligence algorithm to solve the TDOA localization problem. All these defects are considered via proposing an effective method combining HBES to improve the accuracy of the TDOA localization. A localization model combining the TDOA localization and HBES algorithm is designed. The search strategy of the BES algorithm is improved by using many strategies such as chaotic mapping, Levy flight, and opposition-based learning, which can avoid the algorithm falling into a local optimum. The effect of population size and the number of iterations on the algorithm results is analyzed. In two-dimensional (2D) and three-dimensional (3D) scenarios, we analyze the random deployment of base stations, noise effects, and the impact of base station numbers on TDOA localization to better solve practical problems.