雷达成像的电磁场仿真与超分辨成像算法研究
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摘要
雷达成像技术是一种在军事和国防现代化建设中极为重要并且得到广泛应用的高尖端技术。长期以来对雷达成像技术的研究注重于如何获得更高的分辨率,而基于对雷达成像物理本质的认识进而对目标进行识别的研究开展得还相对较少。在雷达成像中,直接在雷达天线近场对目标进行成像和在雷达天线远场获取雷达回波信号通过合成孔径技术得到的雷达图像(目标处于合成的等效大天线的近场)的效果是不相同的,两者在成像机理和成像本质上有很大的区别,但对于这一问题的研究目前还很少。
本文首先建立基于时域有限差分方法(FDTD)的雷达成像的全电磁场仿真模型,并基于模型的近场仿真数据,使用时域相关法(TDC)、后向投影法(BP)和相移偏移法(PSM)三种近场成像算法进行处理,发现虽然PSM成像算法在远场时可以等效为加权BP成像算法,但在近场成像中,两者差别很大,不存在这样的等效关系。论文从信号频谱与空间频谱之间的投影关系对此作出了解释,并且从空间谱的角度分析了PSM算法“添零”操作的物理意义。
为研究直接近场成像与在远场合成孔径处理后得到“等效近场成像”之间的区别问题,论文通过建立电偶极子的辐射模型,从电磁场的角度对雷达近场成像和雷达远场成像进行了分析和比较,从辐射波形和雷达散射回波源自物体表面感应电流(由一系列电耦极子组成)、磁流(由一系列磁耦极子组成)二次辐射的角度出发,分析了雷达回波的幅度、相位、频率等在近场成像和远场成像中的差别,基于物理机理的认识总结了雷达近场和远场
成像的特点。超分辨成像是一种在不提高雷达信号带宽前提下,在较小的观测角度范围内实现通常要靠大的信号带宽和大的观测角度才能获得高分辨率雷达图像的成像技术。本文研究了MUSIC和ESPRIT超分辨成像算法,对两种算法的性能进行了统计分析,并证明了采用“空间平滑技术”的二维MUSIC成像算法和一维MUSIC算法的等价性。论文从统计学的角度,利用自相关矩阵的理论特征值和特征向量,从理论上推导了二维MUSIC成像算法的性能估计公式;利用空间倒谱的统计特性,推导了二维MUSIC算法的唯一性条件,分析了在特定情况下导致二维MUSIC失效的原因以及影响二维MUSIC算法性能的各个参数。论文还对一维ESPRIT算法应用于ISAR方位向时的性能及影响因素进行了分析,并采用RD算法、二维MUSIC算法和二维ESPRIT算法对FDTD成像模型的远场仿真数据进行成像处理,分别对RD成像结果、二维MUSIC的成像结果和二维ESPRIT的成像结果进行了分析,并从分辨率、计算量以及算法稳定性等角度对三种成像算法进行了比较。
Radar imaging is one of extremely important and widely used technologies in military and national defense modernization. For a long time, much more attentions have been focused on how to obtain higher resolution, but fewer researches have been done on physical understanding the nature of radar imaging. In fact this understanding could help us identify target better. In radar imaging, they are obvious difference between radar images generated by processing radar echoes directly collected in the near-field of the radar antenna and radar images generated by synethetically processing the collected radar echoes in far-field of antenna, although the imaged targets are indeed in the near-field of the equivalent synthesized large antenna. However fewer studies have been conducted on investigating the similarities and dissimilarities from the point of view of imaging mechanism.
In this dissertation, we firstly developed a full-wave electromagnetic field radar imaging simulator based on FDTD (Finite Difference Time Domain) method, and by using the model, we simulated near-field radar echoes, and then performed imaging processing on the echo data by using TDC (Time Domain Correlation), BP (Back Projection) and PSM (Phase Shift Migration) imaging algorithms. Through simulation we found that although the PSM algorithm is equivalent to the weighted BP algorithm in the far-field case, but they are not equivalent in the near-field case. We explained the difference based on the relation between the signal spectrum and the projected spatial spectrum, and we further explained the physical meaning of“Zero-padding”operation in the PSM algorithm from the perspective of spatial spectrum projection.
For investigating the difference between direct near-field imaging and the“equivalent near-field imaging”obtained by synthesizing the far-field data in azimuthal direction, by establishing the radiation model of electric dipole, we compared the radar imaging in these two cases from electromagnetic point of view through analyzing radar waveform, the induced electric currents and magnetic currents and the re-radiation of the induced currents focusing on the amplitude, phase and frequency aspects. Based on physical mechanism understanding we summarized the characteristics of near-field imaging and equivalent near-field imaging.
Super-resolution imaging is a kind of technique used in radar for obtaining much higher resolution even with a small range of observation angle and small signal bandwidth, but usually it is achieved with large observation angle range and large bandwidth. In this dissertation we studied two super-resolution algorithms, i.e. MUSIC (Multiple Slgnal Classification) and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) algorithms and statistically analyzed their performance. In MUSIC study, we show that two-dimensional MUSIC (2D-MUSIC) algorithm by using spatial smoothing technique is equivalent to one-dimensional algorithm. Based on statistical viewing point and applying eigenvalues and eigenvectors of the auto-correlation matrix, we derived theoretically the equation for describing the performance estimation of 2D-MUSIC algorithm. By using the statistic characteristics of spatial spectrum, we derived the uniqueness conditions for 2D-MUSIC algorithm, and analyzed the reasons resulting in malfunction and the different parameters influencing the performance of 2D-MUSIC. We analyzed the performance of 1D-ESPRIT applied in azimuthal direction for ISAR and some parameters affecting it. At the same time, we applied RD, 2D-MUSIC, and 2D-ESPRIT algorithms to processing the simulated electromagnetic far-field signals generated by FDTD simulator, and compared these three algorithms from aspects of resolution, calculation burden, and algorithm stability, explained why 2D-ESPRIT can get higher resolution than 2D-MUSIC does.
本文首先建立基于时域有限差分方法(FDTD)的雷达成像的全电磁场仿真模型,并基于模型的近场仿真数据,使用时域相关法(TDC)、后向投影法(BP)和相移偏移法(PSM)三种近场成像算法进行处理,发现虽然PSM成像算法在远场时可以等效为加权BP成像算法,但在近场成像中,两者差别很大,不存在这样的等效关系。论文从信号频谱与空间频谱之间的投影关系对此作出了解释,并且从空间谱的角度分析了PSM算法“添零”操作的物理意义。
为研究直接近场成像与在远场合成孔径处理后得到“等效近场成像”之间的区别问题,论文通过建立电偶极子的辐射模型,从电磁场的角度对雷达近场成像和雷达远场成像进行了分析和比较,从辐射波形和雷达散射回波源自物体表面感应电流(由一系列电耦极子组成)、磁流(由一系列磁耦极子组成)二次辐射的角度出发,分析了雷达回波的幅度、相位、频率等在近场成像和远场成像中的差别,基于物理机理的认识总结了雷达近场和远场
成像的特点。超分辨成像是一种在不提高雷达信号带宽前提下,在较小的观测角度范围内实现通常要靠大的信号带宽和大的观测角度才能获得高分辨率雷达图像的成像技术。本文研究了MUSIC和ESPRIT超分辨成像算法,对两种算法的性能进行了统计分析,并证明了采用“空间平滑技术”的二维MUSIC成像算法和一维MUSIC算法的等价性。论文从统计学的角度,利用自相关矩阵的理论特征值和特征向量,从理论上推导了二维MUSIC成像算法的性能估计公式;利用空间倒谱的统计特性,推导了二维MUSIC算法的唯一性条件,分析了在特定情况下导致二维MUSIC失效的原因以及影响二维MUSIC算法性能的各个参数。论文还对一维ESPRIT算法应用于ISAR方位向时的性能及影响因素进行了分析,并采用RD算法、二维MUSIC算法和二维ESPRIT算法对FDTD成像模型的远场仿真数据进行成像处理,分别对RD成像结果、二维MUSIC的成像结果和二维ESPRIT的成像结果进行了分析,并从分辨率、计算量以及算法稳定性等角度对三种成像算法进行了比较。
Radar imaging is one of extremely important and widely used technologies in military and national defense modernization. For a long time, much more attentions have been focused on how to obtain higher resolution, but fewer researches have been done on physical understanding the nature of radar imaging. In fact this understanding could help us identify target better. In radar imaging, they are obvious difference between radar images generated by processing radar echoes directly collected in the near-field of the radar antenna and radar images generated by synethetically processing the collected radar echoes in far-field of antenna, although the imaged targets are indeed in the near-field of the equivalent synthesized large antenna. However fewer studies have been conducted on investigating the similarities and dissimilarities from the point of view of imaging mechanism.
In this dissertation, we firstly developed a full-wave electromagnetic field radar imaging simulator based on FDTD (Finite Difference Time Domain) method, and by using the model, we simulated near-field radar echoes, and then performed imaging processing on the echo data by using TDC (Time Domain Correlation), BP (Back Projection) and PSM (Phase Shift Migration) imaging algorithms. Through simulation we found that although the PSM algorithm is equivalent to the weighted BP algorithm in the far-field case, but they are not equivalent in the near-field case. We explained the difference based on the relation between the signal spectrum and the projected spatial spectrum, and we further explained the physical meaning of“Zero-padding”operation in the PSM algorithm from the perspective of spatial spectrum projection.
For investigating the difference between direct near-field imaging and the“equivalent near-field imaging”obtained by synthesizing the far-field data in azimuthal direction, by establishing the radiation model of electric dipole, we compared the radar imaging in these two cases from electromagnetic point of view through analyzing radar waveform, the induced electric currents and magnetic currents and the re-radiation of the induced currents focusing on the amplitude, phase and frequency aspects. Based on physical mechanism understanding we summarized the characteristics of near-field imaging and equivalent near-field imaging.
Super-resolution imaging is a kind of technique used in radar for obtaining much higher resolution even with a small range of observation angle and small signal bandwidth, but usually it is achieved with large observation angle range and large bandwidth. In this dissertation we studied two super-resolution algorithms, i.e. MUSIC (Multiple Slgnal Classification) and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) algorithms and statistically analyzed their performance. In MUSIC study, we show that two-dimensional MUSIC (2D-MUSIC) algorithm by using spatial smoothing technique is equivalent to one-dimensional algorithm. Based on statistical viewing point and applying eigenvalues and eigenvectors of the auto-correlation matrix, we derived theoretically the equation for describing the performance estimation of 2D-MUSIC algorithm. By using the statistic characteristics of spatial spectrum, we derived the uniqueness conditions for 2D-MUSIC algorithm, and analyzed the reasons resulting in malfunction and the different parameters influencing the performance of 2D-MUSIC. We analyzed the performance of 1D-ESPRIT applied in azimuthal direction for ISAR and some parameters affecting it. At the same time, we applied RD, 2D-MUSIC, and 2D-ESPRIT algorithms to processing the simulated electromagnetic far-field signals generated by FDTD simulator, and compared these three algorithms from aspects of resolution, calculation burden, and algorithm stability, explained why 2D-ESPRIT can get higher resolution than 2D-MUSIC does.
引文
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