## 4 Simulation
### Real Test
\begin{table}
\begin{tabular}{c c c c c} \hline  & Target1 & Target2 & Target3 & RMSE \\ \hline Actual position & 3.2 m & 3.6 m & 4.0 m & \\ \hline Original & 3.2 m & X & X & 3.107 \\ \hline Twice & 3.0 m & X & 4.0 m & 2.082 \\ \hline Four times & 3.1 m & 3.7 m & 4.1 m & 0.1 \\ \hline Eight times & 3.1 m & 3.65 m & 4.15 m & 0.108 \\ \hline  & \multicolumn{3}{c}{(**b**)} \\ \hline  & Target1 & Target2 & Target3 & RMSE \\ \hline Actual position & 1.8 m & 2.3 m & 2.8 m & \\ \hline Original & X & 2.4 m & X & 1.923 \\ \hline Twice & 2.0 m & 2.6 m & 3.2 m & 0.311 \\ \hline Four times & 2.0 m & 2.5 m & 2.9 m & 0.173 \\ \hline Eight times & 2.05 m & 2.55 m & 3.0 m & 0.235 \\ \hline  & Target1 & Target2 & Target3 & RMSE \\ \hline Actual position & 2.0 m & 2.5 m & 3.0 m & \\ \hline Original & 2.0 m & X & 3.2 m & 1.448 \\ \hline Twice & 2.0 m & 2.4 m & 3.2 m & 0.129 \\ \hline Four times & 2.1 m & 2.5 m & 3.3 m & 0.183 \\ \hline Eight times & 2.1 m & 2.5 m & 3.3 m & 0.183 \\ \hline  & Target1 & Target2 & Target3 & RMSE \\ \hline Actual position & 2.1 m & 2.6 m & 3.1 m & \\ \hline Original & X & 2.4 m & X & 2.165 \\ \hline Twice & X & 2.6 m & 3.0 m & 1.214 \\ \hline Four times & 2.3 m & 2.6 m & 3.0 m & 0.129 \\ \hline Eight times & 2.55 m & 2.85 m & 3.0 m & 0.303 \\ \hline  & Target1 & Target2 & Target3 & RMSE \\ \hline Actual position & 2.3 m & 2.8 m & 3.3 m & \\ \hline Original & 2.4 m & X & 3.2 m & 1.561 \\ \hline Twice & 2.4 m & X & 3.4 m & 1.561 \\ \hline Four times & 2.3 m & 2.7 m & 3.4 m & 0.082 \\ \hline Eight times & 2.3 m & 2.75 m & 3.35 m & 0.041 \\ \hline  & Target1 & Target2 & Target3 & RMSE \\ \hline Actual position & 2.5 m & 3.0 m & 3.5 m & \\ \hline Original & X & X & 3.2 m & 2.261 \\ \hline Twice & 2.4 m & 2.8 m & 3.2 m & 0.216 \\ \hline Four times & 2.5 m & 3.1 m & 3.5 m & 0.058 \\ \hline Eight times & 2.45 m & 2.75 m & 3.25 m & 0.206 \\ \hline  & Target1 & Target2 & Target3 & RMSE \\ \hline Actual position & 2.5 m & 3.0 m & 3.5 m & \\ \hline Original & X & X & 3.2 m & 2.261 \\ \hline Twice & 2.4 m & 2.8 m & 3.2 m & 0.216 \\ \hline Four times & 2.5 m & 3.1 m & 3.5 m & 0.058 \\ \hline Eight times & 2.45 m & 2.75 m & 3.25 m & 0.206 \\ \hline  & Target1 & Target2 & Target3 & RMSE \\ \hline Actual position & 2.5 m & 3.0 m & 3.5 m & \\ \hline Original & X & X & 3.6 m & 2.255 \\ \hline Twice & 2.6 m & 3.0 m & 3.6 m & 0.082 \\ \hline Four times & 2.5 m & 2.9 m & 3.5 m & 0.058 \\ \hline Eight times & 2.55 m & 3.05 m & 3.55 m & 0.05 \\ \hline \end{tabular}
\end{table} 
Table 5: _Cont._Table 6 shows the performance comparison of the algorithms with respect to the average RMSE and the average number of detected targets. The experimental results show that the proposed algorithm significantly improves the average RMSE compared to the existing method. Specifically, with twice the padding, the RMSE improved by approximately 4.3 times; with four times the padding, it improved by approximately 21.1 times; and with eight times the padding, it improved by approximately 8 times. While the existing algorithm could detect only 1 or 2 out of the 3 prepared targets, the proposed algorithm successfully detected all 3 targets in most cases, indicating a marked improvement in range resolution. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Distance between** & & **0.4 m** & & **0.5 m** \\
**Targets** & & **Average Number of** & & **Average Number of** \\  & **RMSE** & **Detected Targets** & & **Detected Targets** \\ \hline Original & 2.1653 & 1.4 & 2.1959 & 1.4 \\ \hline Twice & 0.4889 & 2.8 & 0.7819 & 2.6 \\ \hline Four times & 0.0994 & 3 & 0.1072 & 3 \\ \hline Eight times & 0.2116 & 2.9 & 0.3347 & 2.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The average RMSE for Table 5 and the average number of detected targets.