# An Efficient Ground Moving Target Imaging Method for Airborne Circular Stripmap SAR
## 6 Discussions  
The experimental results presented in Section 5 validate the proposed range model and the proposed imaging method. In Section 5.1, the qualities of the results obtained based on the original range equation, the proposed range model, the second-order and third-order Taylor-approximated range models are measured and compared. The results demonstrate that the accuracy of the proposed range model is better than that of the second-order and third-order Taylor-approximated range models, and that one can obtain a high-quality focusing result with the proposed range model. In Section 5.2, the imaging results obtained by the proposed method are analyzed. It is seen that the image qualities of the five targets are all close to the theoretical values. Therefore, the proposed imaging method can focus ground moving targets accurately.  
The computational load of the proposed imaging method is discussed as follows. According to the analyzes presented in Section 4, the major operations of the proposed method include twice 2-D Fourier transform, twice inverse 2-D Fourier transform, and a 2-D phase multiplication. Assuming that the number of azimuth samples and range samples are \(N_{a}\) and \(N_{r}\), respectively. Then, the total number of floating operations can be calculated as:  
\[20N_{r}N_{a}\log_{2}(N_{r})+20N_{r}N_{a}\log_{2}(N_{a})+6N_{r}N_{a} \tag{35}\]  
Therefore, the computational order of the proposed method is \(O\big{(}N^{2}\log_{2}N\big{)}\), where \(N\) denotes the 1-D size of the data.  
GA is a parallel stochastic algorithm, and it may not converge to the optimal result in a few cases. Now we discuss the variability and statistical significance of the results obtained by GA. Five hundred random experiments are conducted, with the target T1 being considered. The results obtained by these random experiments are analyzed, and the deviations of the obtained optimal image contrasts are plotted in Figure 8. It is found out that there are 479 out of 500 experiments converge to the optimal results. Moreover, it is also figured out that the maximum deviation, the mean deviation, and the standard deviation of the results are 0.1007, 0.0034 and 0.0178, respectively, which are all very small.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**IRW Broadening**} & \multicolumn{2}{c}{**PSLR**} & \multicolumn{2}{c}{**ISLR**} & \multicolumn{1}{c}{**Ideal ISLR**} \\  & & **(dB)** & **(dB)** & **(dB)** & **(dB)** \\ \hline \multirow{2}{*}{T1} & Azimuth & 0.81\% & \(-\)13.21 & \(-\)10.02 & \(-\)10.01 \\ \cline{2-6}  & Range & 0.00\% & \(-\)13.16 & \(-\)9.79 & \(-\)9.86 \\ \hline \multirow{2}{*}{T2} & Azimuth & 0.00\% & \(-\)13.22 & \(-\)9.90 & \(-\)9.96 \\ \cline{2-6}  & Range & 0.00\% & \(-\)13.22 & \(-\)9.80 & \(-\)9.86 \\ \hline \multirow{2}{*}{T3} & Azimuth & 0.00\% & \(-\)13.26 & \(-\)9.98 & \(-\)10.00 \\ \cline{2-6}  & Range & 0.00\% & \(-\)13.27 & \(-\)9.88 & \(-\)9.86 \\ \hline \multirow{2}{*}{T4} & Azimuth & 0.00\% & \(-\)13.25 & \(-\)9.95 & \(-\)9.96 \\ \cline{2-6}  & Range & 0.00\% & \(-\)13.22 & \(-\)9.80 & \(-\)9.86 \\ \hline \multirow{2}{*}{T5} & Azimuth & 0.00\% & \(-\)13.18 & \(-\)9.89 & \(-\)9.94 \\ \cline{2-6}  & Range & 0.00\% & \(-\)13.27 & \(-\)9.90 & \(-\)9.86 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Measured image quality parameters.