# A Hybrid Bald Eagle Search Algorithm for Time Difference of Arrival Localization
## 4 Experimental Design and Analysis
### Performance Evaluation
#### 4.2.3 Analysis of the Accuracy of TDOA Positioning Based on HBES  
The population size \(M\) is set to 100, the number of base stations \(N\) is set to 8, and the values of distance noise standard deviation \(\sigma_{r}\) is set at 0.2, 0.4, 0.6, 0.8, and 1.0 for the experiment, and the experimental scenario is shown in Figure 5. The comparison of the positioning accuracy for different distance noise standard deviations was obtained, as shown in Table 4. It can be seen that the noise immunity of PSO, SSA, and COOT is poor. When the noise standard deviation is 0.2, the RMSE is close to CRLB. As the noise standard deviation increases, the difference between RMSE and CRLB becomes larger. The CPSO, BES, and GWO have a good positioning accuracy in low noise conditions. The results of CPSO and PSO show that chaotic mapping can promote the optimization ability to some degree. Overall, the HBES algorithm has the best noise immunity and its RMSE is always close to that of CRLB.  
The effect of the number of base stations on the localization was analyzed under the condition that the standard deviation of the distance noise was 0.5 m. Experiments were conducted with 4-8 base stations involved in localization, and the comparison of the localization accuracy with different numbers of base stations was obtained, as shown in Table 5. The RMSE and CRLB of different algorithms decrease as the number of base stations increases, and HBES algorithm achieves a lower RMSE for different numbers of base stations, which is closer to the CRLB than other algorithms when the number of base stations increases from 4 to 8, the RMSE of HBES algorithm decreases by 2.34%, 4.17%, 7.8%, 8.24%, 9.06%, and 9.06% respectively compared to the BES algorithm. This indicates that the HBES algorithm can make fuller use of the redundancy of measurement values to reduce the positioning error and can perform better in high-precision positioning scenarios  
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline
**Location** & \(\sigma_{r}\)/\(m\) & **PSO** & **GWO** & **COOT** & **CPSO** & **SSA** & **BES** & **HBES** & **CRLB** \\ \hline  & 1.0 & 1.0532 & 1.0297 & 0.9966 & 1.1256 & 1.1616 & 0.8515 & 0.8396 & 0.7149 \\  & 0.8 & 0.9063 & 0.9486 & 0.8845 & 0.9002 & 1.0776 & 0.7443 & 0.6543 & 0.5719 \\ RMSE/m & 0.6 & 0.7384 & 0.7465 & 0.7840 & 0.7150 & 0.9215 & 0.6435 & 0.5869 & 0.4289 \\  & 0.4 & 0.5133 & 0.4481 & 0.5136 & 0.4563 & 0.6512 & 0.4414 & 0.3385 & 0.2861 \\  & 0.2 & 0.1698 & 0.1921 & 0.1836 & 0.1509 & 0.2463 & 0.1856 & 0.1456 & 0.1438 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Localization accuracy comparison of different distance noise standard deviation.  
Figure 5: Positioning accuracy-test simulation diagram.  
with enough base stations. In general, the difference between the positioning accuracy of HBES and other algorithms is not significant when the quantity of base stations is 4. When the quantity of base stations is increased, the RMSE of HBES is lower than that of the other algorithms. This indicates that the HBES algorithm can be used for TDOA positioning with good accuracy while the quantity of base stations is appropriate and that the HBES algorithm has good stability against noise interference and can achieve good positioning accuracy in the presence of interference.