## 10 Experimental Analysis
### Evaluation of Accuracy of Localization
Figure 4: RMSE performance of different algorithms vs. \(p\) for first simulation case. Figure 5: Plot of the obtained RMSE curves in relation to the measurement noise for second simulation case. Based on the results in Figure 5 we observe that even in this case the proposed ICDEBOA algorithm is able to attain the CRLB accuracy and show better performance with regard to other algorithms taken for simulation. In this case, the DE and BOA algorithm show a slight degradation in performance, compared to the previous case, which is observed in the bigger discrepancy from the CRLB. Again, the CWLS method has the worst performance among all algorithms. In Figure 6 the results of the third simulation case, which considers a random placement of target in the area \(150\times 150\) m\({}^{2}\) in each simulation iteration, are depicted as a function RMSE of \(p\). Based on the results of the third simulation scenario depicted in Figure 6, we observe that the ICDEBOA algorithm is able to reach the CRLB accuracy, while outperforming CWLS, DE and BOA algorithms. In this case, it is notable that there is a higher discrepancy between the CRLB and the DE, BOA, and CWLS algorithms' RMSE performance curves. As in previous cases, the CWLS showed the lowest accuracy, with the curve high above the CRLB. If we compare the results in Figure 4 through Figure 6 and analyze the obtained RMSE values under different conditions, we find that the considered algorithms had the performance closest to the CRLB in the first simulation case when we placed the target in the area surrounded by transmitters. Alternatively, we observe the biggest descrepency from the CRLB in the case when the target is not surrounded by transmitters, as shown in Figure 5. In addition, it is observed that the proposed ICDEBOA algorithm holds the CRLB accuracy for the entire considered range of \(p\) in all of the scenarios that have been considered for simulation. Further investigation into the localization performance of different approaches is conducted by considering the localization error of considered algorithm trough the cumulative distribution functions (CDFs) when the measurement noise is \(\sigma^{2}=10\) m\({}^{2}\). The localization error (LE) is introduced for CDF analysis as the Euclidean norm of the actual and estimated positions discrepancy, and it is computed as  
\[LE=\left\|\hat{\mathbf{x}}^{(n)}-\mathbf{x}\right\|_{2^{\prime}}\forall n\in \{1,\ldots,N_{m}\} \tag{69}\]  
Figure 6: The results obtained for the third simulation case depicted in the form of RMSE performance of different algorithms vs. \(p\). The CDFs of the localization error for the considered algorithms for the passive target positioned as in the first simulation scenario are presented in Figure 7 as a function of LE. Based on the results shown in Figure 7, we can observe that the proposed ICDEBOA algorithm provides localization accuracy of less than 2.5 m for the 90% CDF percentile, while the BOA, DE, and CWLS algorithms achieve \(LE\)s of less than 2.74 m, 2.66 m, and 3.12 m, respectively, for the same case. So, we can say that the ICDEBOA algorithm improves LE by 9.6% compared to BOA, by 6.4% compared to DE, and by 24% compared to the CWLS method, proving that it has improved performance. Lastly, we look at how the accuracy of the localization changes as the number of transmitters involved in localization increases. Consider \(N^{l}\) transmitters that are uniformly dispersed on a circle of a radius \(R=80\sqrt{2}\), such that the coordinate of each transmitter can be obtained as  
\[\mathbf{x}_{i}^{t}= \begin{bmatrix}R\cos 2\pi/N^{l}_{i}\\ R\sin 2\pi/N^{l}_{i}\end{bmatrix} ,\quad i\in\left\{1,2,\ldots,N^{l}\right\} \tag{70}\]  
where we fix the target inside the circle formed by transmitters near the center at the coordinates \(x= \begin{bmatrix}20&30\end{bmatrix}