星载高轨合成孔径雷达成像球面地表效应分析

Analysis of the Spherical Earth Surface Effect in Spaceborne High-Orbit Synthetic Aperture Radar Imaging

  • 摘要: 星载高轨合成孔径雷达(Synthetic Aperture Radar, SAR)具有短时重访周期和大范围测绘能力,在军事和民用中都具有独特的优势。然而,高轨SAR的成像几何也更加复杂,较长的合成孔径时间使得轨道的弯曲效应不可忽视,宽大的波束覆盖范围也导致平面地表假设不再适用,因此必须考虑球面地表效应对成像的影响。本文从简单的直线轨迹和更具有现实意义的曲线轨迹两方面对成像出现的几何失真和散焦进行分析。首先,假设雷达短时间内做直线运动,由“距离-多普勒”关系得到成像平面与弯曲地表的位置映射关系,并通过回波历程分析得到直线轨迹时聚焦良好。然后,在曲线轨迹情况下,同样根据“距离-多普勒”关系解决了高轨SAR由于球面地表效应导致的几何失真问题。另外,基于对球面地表真实目标和成像域内像素点的距离历程分析,得到回波的二次相位误差,该误差导致雷达运行在弯曲轨道时成像出现散焦,而且由于该误差相位与成像场景宽度呈正相关,散焦会随着合成孔径时间的增长以及成像场景的扩大而愈加明显,具有显著空变性。接着,通过对相位误差进一步分析得到有效成像半径。最后,利用仿真实验对球面地表与成像平面的映射关系和成像散焦特性进行了验证。本文解决了由于地表弯曲效应带来的成像几何失真问题,得到了雷达运行在曲线轨迹时造成成像出现散焦的二次相位误差,为后续的基于该误差相位的补偿成像算法研究提供了便利。

     

    Abstract: ‍ Spaceborne high-orbit Synthetic Aperture Radar (SAR), with its short revisit period and large range mapping capability, has attracted widespread attention worldwide owing to its unique advantages in both military and civilian applications. However, the imaging geometry of high-orbit SAR is more complex. Under the same resolution condition, the synthetic aperture time of high-orbit SAR is much longer than that of low-Earth-orbit SAR. In this case, the assumption that the radar moves in a straight line is no longer applicable, and the longer synthetic aperture time makes the orbital bending effect more obvious. Additionally, general SAR imaging algorithms are based on the assumption of flat ground, while high-orbit SAR has wide beam coverage. The drop of the surface height in the beam irradiation area cannot be ignored, which makes the plane surface hypothesis no longer applicable, and the influence of the spherical earth surface effect on the imaging must be considered. To analyze the influence of the spherical surface effect on high-orbit SAR imaging, the geometric distortion and defocusing in imaging are studied in detail from two aspects: simple linear trajectory and more realistic curved trajectory. First, assuming that the radar moved in a straight line in a short time, the position mapping relationship between the imaging plane and the curved surface was obtained by detailed analysis of the range-Doppler relationship between the real target point on the surface of the earth and the pixels in the two-dimensional imaging domain, and the echo of the two was reversely deduced based on the mapping relationship. When imaging the SAR in straight track by echo analysis, the focusing was clear and defocusing did not occur. Then, in the case of a curved trajectory, the geometric distortion caused by the spherical surface effect of high-orbit SAR was also solved by the range-Doppler relationship. Additionally, based on the analysis of the distance history of the real target on the spherical surface and the corresponding pixels in the plane found based on the mapping relationship, it was found that additional defocusing would occur in the imaging under the case of curved trajectory. For this defocusing phenomenon, the Taylor expansion of the two distance-histories was performed in this study. By comparing the Taylor series of the two processes, the quadratic phase error of the two echoes was obtained, and the error phase was positively correlated with the width of the imaging scene. The defocusing would become more obvious with the increase of synthetic aperture time and the expansion of the imaging scene, with significant spatial variability. The effective focusing radius is given by the phase error. Finally, the mapping relationship between the spherical surface and the imaging plane and the imaging defocusing characteristics are verified by simulation experiments. In this study, the imaging geometry distortion caused by the surface bending effect is solved, and the secondary phase error of the radar echo when the radar is running on the curved track is obtained, which causes imaging defocusing. This study provides convenience for the subsequent research of compensation imaging algorithms based on the phase error, which solves the defocusing problem caused by the curved orbit and spherical surface of the Earth.

     

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