# Microwave Staring Correlated Imaging Based on Unsteady Aerostat Platform
## 4 Simulation
### Verification of the Proposed Model  
In this subsection, simulations are taken to compare the imaging performance of different imaging models. The proposed imaging model based on unsteady aerostat platform (UPIM) will be compared with the imaging model for stationary platform (SPIM) and imaging model which only uses the  
Figure 4: Target image. Figure 5: The motion trajectory of each component. (**a**) the translational component along the \(X_{t}\); (**b**) the translational component along the \(Y_{t}\); (**c**) the translational component along the \(Z_{t}\); (**d**) the rotation of yaw; (**e**) the rotation of pitch; (**f**) the rotation of roll. discrete POS data (DPDIM). SPIM ignores the motion of antenna array and assumes that the position vector of antenna and the beam coverage do not change during the imaging process. When calculating the radiation field, SPIM uses the first recorded POS data as the position and the attitude angles of the array, i.e., \(\mathbf{r}^{n}\left(t_{l}\right)=\mathbf{r}^{n}\left(t_{1,pos}\right)\left(l=1,2, \cdots,L\right)\). DPDIM does not fit the discrete POS data and uses the closest POS data for each pulse. The normalized mean square error (NMSE) is used to quantity the reconstruction performance, with the definition as: \(NMSE=\left\|\mathbf{\hat{x}}-\mathbf{x}\right\|_{2}/\left\|\mathbf{x}\right\| _{2}\), where \(\mathbf{\hat{x}}\) and \(\mathbf{x}\) denote the reconstructed and true value of target. The imaging results are depicted in Figure 6. As shown in Figure 6a, Comparably, the image reconstructed by UPIM is focused with quite a few spurious scatters, whose better imaging performance benefits from the fact that the UPIM has the minimal motion estimation error. In Figure 6b, apart from strong scatters, the image reconstructed by DPDIM has many spurious scatters. In Figure 6c, the reconstructed image by SPIM is defocused and blurry, and the target is hard to recognize. The point spread functions (PSF) of UPIM, DPIM, and SPIM are illustrated in Figure 7 and the \(X\)-axis and \(Y\)-axis profiles of the PSF are shown in Figure 8. It can be seen from Figure 7, the number and the level of the side lobes is minimum for UPIM while the other two methods both have more side lobes and higher level of side lobes. Figure 8 shows that these methods have almost the same width of the main lobe in \(X\)-axis profile and the \(Y\)-axis profile. The above simulation results demonstrate that UPIM indeed reduces the number and the level of side lobes caused by platform instability, but it does not improve the imaging resolution of MSCI. For the three imaging models mentioned above, Figure 9 shows the fitting effect on the translational motion trajectory of the aerostat platform along the \(X_{t}\). It can be seen that the proposed UPIM model has the best fitting effect that the estimated translational trajectory is almost the same with the real one with the most minimum motion estimation error, which obviously benefits a better imaging performance in UPIM. To verify the effectiveness of the proposed method with the translation amplitude increasing, the relationship between the imaging quality and the translation amplitude for three imaging models is presented in Figure 10. The amplitude of three-dimensional translations gradually increased by the step of 0.5 times the original amplitude shown in Figure 5, while the rotation amplitudes keep constant. The coordinate of the horizontal axis in Figure 10 represents the multiple of the original translation amplitude. As seen from Figure 10, the imaging performance of UPIM is still better than the other imaging models when the amplitude of translation increases. Figure 8: The profile of the point spread function of UPIM, DPIM, and SPIM. (**a**) the \(X\)-axis profile of the point spread function; (**b**) the \(Y\)-axis profile of the point spread function. Figure 9: The estimated and the real trajectory of the translation along the \(X_{t}\). (**a**) UPIM; (**b**) DPDIM; (**c**) SPIM.