## 10 Experimental Analysis
### Evaluation of Accuracy of Localization  
This section presents the results of the numerical simulations of localization performance comparison between the ICDEBOA alg., proposed in this work, and the widely applied CWLS, DE, and BOA methods on the considered TDOA based passive target localization problem. The goal of this section is to verify the proposed improvements introduced in ICDEBOA algorithm and its efficiency on the considered localization problem. In order to measure the localization efficiency, the algorithms are evaluated through RMSE performance and compared to the derived CRLB, as it represents the lower bound on the variance of any unbiased estimator. To measure the localization accuracy, the RMSE is employed, which can be calculated as  
\[RMSE=\sqrt{\frac{1}{N_{m}}\sum_{n=1}^{N}\left\|\hat{\mathbf{x}}^{(n)}-\mathbf{ x}\right\|_{2}^{2}}, \tag{68}\]  
where \(\mathbf{x}\) is the location of target which is known, \(\hat{\mathbf{x}}^{(n)}\) is the estimate of the target position and \(N_{m}=1000\) denotes how much Monte Carlo simulation iterations are made for fixed \(\sigma^{2}\). It has been shown that some algorithms are sensitive to relative target-transmitter-receiver positions in the localization process, which leads to the singularity and bad solutions. To analyze how this relative position affects the localization performance of the considered algorithms, we consider three characteristic cases in the simulation. Thus, in the first four simulations, the transmitters are fixed to locations \(\mathbf{x_{1}^{t}}=\left[100\quad 100\right]^{\mathsf{T}}\) m, \(\mathbf{x_{2}^{t}}=\left[100\quad-100\right]^{\mathsf{T}}\) m, \(\mathbf{x_{3}^{t}}=\left[-100\quad 100\right]^{\mathsf{T}}\)m, and \(\mathbf{x_{4}^{t}}=\left[-100\quad-100\right]^{\mathsf{T}}\)m, and as stated in Section 3, we place the receiver in the center of the introduced coordinate system. The arrangement of transmitters forms a convex polygon, and we firstly consider how the placement of the target near the centroid of the figure formed by transmitter locations, at \(\mathbf{x}=\left[20\quad 30\right]^{\mathsf{T}}\), affect the localization. Then, in the second simulation the position of the target is moved outside the convex figure formed by transmitters at \(\mathbf{x}=\left[120\quad 130\right]^{\mathsf{T}}\). Finally, we consider the case when we assign the target a random location in the area \(150\times 150\)m\({}^{2}\) in each run of the simulation. The results of the first simulation scenario are depicted in the Figure 4 as the functional relationship between the measurement noise \(p=10\log\bigl{(}\sigma^{2}\bigr{)}\) and RMSE performance and compared to the CRLB. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Algorithm** & **10D** & **30D** & **50D** & **100D** & **Mean Ranking** & **Rank** \\ \hline ICDEBOA & 1.23 & 1.77 & 1.67 & 1.75 & 1.60 & 1 \\ HPSOBOA & 3.50 & 2.60 & 2.97 & 2.65 & 2.93 & 2 \\ jDE & 3.07 & 3.10 & 3.00 & 3.10 & 3.07 & 3 \\ BOA & 3.37 & 3.60 & 3.50 & 3.57 & 3.51 & 4 \\ SHADE & 3.83 & 3.93 & 3.87 & 3.93 & 3.89 & 5 \\ Friedman \(p\)-value & \(2.90\times 10^{-10}\) & \(4.50\times 10^{-7}\) & \(1.01\times 10^{-6}\) & \(5.34\times 10^{-7}\) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of the performance comparison using Friedman test with significance \(\alpha=0.05\) on CEC2014 test problems. From the Figure 4 it can be concluded that the proposed ICDEBOA algorithm attains the CRLB and outperforms other considered methods on a whole considered range of measurement noise \(p\). The performance of DE and BOA algorithms is slightly above the CRLB, while the CWLS algorithm showed the worse performance, especially when \(p>30\) dB. Figure 5 presents the results of the second scenario, where we place the target in the position outside of polygon formed by transmitter locations. Here, the RMSE performances of considered algorithms are plotted as a function of the measurement noise, and compared to the CRLB.