合成孔径雷达自聚焦算法研究及其在机载干涉技术中的应用
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摘要
合成孔径雷达(Synthetic Aperture Radar,简称SAR)具有对目标场景进行全天候、全天时、远距离观测的能力，经过几十年的发展，SAR成像技术已经逐渐趋于成熟。由于SAR是相干成像系统，SAR图像和接收信号相位之间存在紧密的联系。为了获得高分辨率，高质量的SAR图像，必须利用自聚焦算法对SAR图像作进一步处理，估计其相位误差函数并进行补偿。从20世纪60年代开始，干涉合成孔径雷达（Interferometric SyntheticAperture Radar,简称InSAR）被广泛应用于对观测场景中目标高度信息的测量，并最终实现对于目标场景的三维成像。利用自聚焦算法获得高质量的SAR图像可以保证InSAR后续干涉处理的准确性。本文第一章绪论分别回顾了SAR和InSAR的发展历史，详细描述了自聚焦算法与InSAR技术的研究现状与发展趋势，最后概括了本文的主要研究内容。
第二章研究了基于多子孔径处理的SAR自聚焦算法。在传统基于多子孔径处理的SAR自聚焦算法中，基于二阶导数的子孔径相位误差函数拼接技术虽然可以正确实现对SAR图像的自聚焦处理，但是在相位拼接过程中会引起相位估计误差的严重积累，导致基于多子孔径处理自聚焦方法的实际算法性能不够理想。本章针对上述问题，结合相位梯度自聚焦(Phase Gradient Autofocus,简称PGA)算法和子孔径偏移(Map Drift,简称MD)算法，提出了一种新的基于多子孔径处理的自聚焦算法(PGA-MD)。理论分析以及实测数据处理结果对比均表明无论针对条带模式SAR图像还是聚束模式SAR图像，PGA-MD算法均可以有效提高子孔径相位误差函数的拼接精度，优化基于多子孔径处理的SAR自聚焦算法性能。
第三章研究了基于投影近似子空间跟踪(Projection Approximation Subspace Tracking,简称PAST)技术的自聚焦算法。基于特征向量法的自聚焦算法利用多个脉冲估计相位误差函数，可以获得比PGA算法更好的自聚焦效果，但必须对协方差矩阵进行特征分解(EigenvalueDecomposition,简称ED），所以该自聚焦算法运算量大、工程实现困难。本章针对特征分解过程影响算法实时处理的问题，提出了利用PAST技术估计所需特征向量，完成SAR图像自聚焦处理。通过算法性能分析和实际数据处理结果对比，证明基于PAST技术的自聚焦算法在降低原自聚焦算法计算复杂度的同时，可以获得同样优于PGA算法的自聚焦性能，是一种可满足实时处理要求的有效自聚焦算法。利用该算法替代PGA算法对子孔径相位误差函数进行估计，可以更进一步提高基于多子孔径处理SAR自聚焦算法的算法性能。
第四章主要介绍了InSAR高程测量的原理及其信号处理过程中的关键步骤。本章首先通过公式推导，对干涉相位的统计特性进行了分析和研究，然后对InSAR高程测量的信号处理流程进行了简单的介绍，利用实测干涉数据给出了部分关键步骤的处理结果。随后通过研究SAR工作的成像几何关系，推导出由干涉相位值生成数字地形高度图(Digital ElevationModel,简称DEM)的对应转换公式，完成干涉相位值到高程值的转换过程。最后，详细分析了图像中目标位移的原因，并具体推导了目标在方位向和距离向上的位移量与成像几何，目标高度之间的数学关系，提供了正确定位目标真实位置的方法。
第五章重点研究了InSAR相位解缠绕技术。二维相位解缠绕处理是InSAR数据处理的关键。本章提出了一种基于等效残差点的InSAR相位解缠绕算法。该算法首先提出了等效残差点的概念，利用质量图与残差点分布之间的关系，将残差点密集的低质量相位区域视为等效残差点，采用不同方法分别对高质量相位区域和等效残差点的内部区域进行相位解缠绕。新的相位解缠绕算法基于等效残差点正确的设置枝切线，可以阻止由于积分路径穿过残差点密集的低质量相位区域所引起的展开相位跳变现象，同时利用多像素单元共同估计的方法对残差点的内部区域进行相位展开，突破了传统相位解缠绕算法对于干涉相位梯度值的限制，并且可以有效阻止相位解缠绕误差由低质量相位区域向高质量相位区域的传递。实验结果证明，该方法可以获得比其它算法更好的相位解缠绕结果。
第六章为结束语，对全文主要工作进行了总结，并指出下一步工作的方向和研究的重点。
Based on the relative motions between the antenna and target, synthetic aperture radar (SAR)could form a larger equivalent aperture antenna to obtain high azimuth resolution imageries bysignal processing techniques. It can significant enhance the ability of the long-distanceobservation for its all weather and all time character. After the developments in the past decades,the SAR imaging technologies become mature gradually. Because SAR is a coherent imagingsystem, there is an intimate connection between the image and the phase of the received signal. Inorder to obtain high resolution and high quality SAR images, the autofocus algorithms are used toestimate and correct the phase error. The technology of the interferometric synthetic aperture radar(InSAR) was used to obtain the information of the three-dimensional terrain since late1960’s. Andthe high quality SAR image is essential to the signal processing of InSAR elevation measure.Chapter1is the introduction of the dissertation. The history of SAR and InSAR technology isoutlined, respectively. And the applications and the developments of autofocus algorithms andInSAR technology are introduced in detail. At the end of this chapter, the aim and contents of ourwork are addressed.
Chapter2studies a multi-subaperture autofocus algorithm. Due to the characteristics of theconventional strip-mapping mode SAR imagery, the present techniques of autofocus cannot bedirectly used to estimate the phase error functions. By using the autofocus algorithm forsubimages and the subaperture phase error combining with technology that based on the seconddifferences, we can achieve the phase error functions of the strip-map SAR imagery throughappropriately changing the construction of the original range-compressed data. However, thismethod will lead to the accumulation of estimation errors during the procedure of the subaperturephase error combining. To address these shortcomings, we present a multi-subaperture autofocusalgorithm, which combines the techniques of phase gradient autofocus (PGA) and map drift (MD).Comparison on the accuracy of this approach against the traditional algorithm is presented.Experimental results indicate that the presented PGA-MD methodology can improve the quality ofstrip-map SAR image effectively. In the spotlight mode, the subaperture-images represent exactlythe same scenario, and are highly similar after refocused by PGA. Therefore any of thesubaperture-image pairs can be used as input to MD, and the redundancy of multiplecross-correlating results serves to suppress the effects of noise and target scintillation. What’smore, it smoothly incorporates the estimation of residual range cell migration (RCM) to furtherimprove the quality of SAR image.
Chapter3proposes a novel autofocus algorithm using the projection approximation subspacetracking (PAST) approach. SAR is a coherent imaging system. The key of obtaining highresolution and high quality SAR image is the maintenance of accurate coherent phases via usingautofocus algorithms. An eigenvector method for maximum-likelihood estimation (MLE) of phaseerrors for use in an autofocus algorithm for SAR imagery by the simultaneous processing ofmultiple-pulse vectors of range-compressed data has better performance than the algorithm ofPGA. However, this method requires eigendecomposition of the sample covariance matrix，whichis a task that is computationally expensive and limits the real-time application. In order toovercome this difficulty, a novel autofocus algorithm using PAST is presented. With thismethodology, the computational cost can be reduced effectively to the level of PGA via avoidingthe procedures of covariance matrix estimation and eigendecomposition. Monte Carlo tests and real SAR data processing validate that the new approach outperforms the mostly used PGA. Theperformance of multi-subaperture autofocus algorithm, which is detail described in the previouschapter, can be further improved by utilizing the PAST based autofocus algorithm instead of PGA.
Chapter4introduces the crucial steps of InSAR technology. Analysis and research on thestatistical characteristic of interferometric phase is given by formula deducing. And then the signalprocessing of InSAR elevation measure is briefly presented. We employ the real SAR data toobtain the processing results of the partial key points of InSAR technology. This chapter alsodetailed analysis the reason of the target displacement in digital elevation model (DEM), andshows the mathematical relation between the target displacement and the SAR imaging geometryand the height of target. The simulation results validate the analysis.
Chapter5focuses on the phase unwrapping. We investigate the Goldstein branch-cut phaseunwrapping method and the least squares estimation technique. And then a two-dimensional phaseunwrapping approach using equivalent residues is proposed for InSAR. In this proposed algorithm,the relationship between quality map and residues is used to find out the low quality unreliableregions, which are residues dense distribution and regarded as equivalent residues. Then, differentphase unwrapping strategies are taken for different quality regions. With this methodology,integration path crossing of unreliable regions, which may produce a phase error that propagatesto all the pixels in integration path, is prevented because that the unreliable regions are treated asequivalent residues. Each pixel inside equivalent residues is unwrapped based on its unwrappedneighbors, which breaks the limit of the absolute value of phase gradient between two adjacentpixels. Simulated and real SAR data processing validate the new approach.
Chapter6summarizes the major contents in this thesis and points out the direction and thefocus of next research work in the future.
第二章研究了基于多子孔径处理的SAR自聚焦算法。在传统基于多子孔径处理的SAR自聚焦算法中，基于二阶导数的子孔径相位误差函数拼接技术虽然可以正确实现对SAR图像的自聚焦处理，但是在相位拼接过程中会引起相位估计误差的严重积累，导致基于多子孔径处理自聚焦方法的实际算法性能不够理想。本章针对上述问题，结合相位梯度自聚焦(Phase Gradient Autofocus,简称PGA)算法和子孔径偏移(Map Drift,简称MD)算法，提出了一种新的基于多子孔径处理的自聚焦算法(PGA-MD)。理论分析以及实测数据处理结果对比均表明无论针对条带模式SAR图像还是聚束模式SAR图像，PGA-MD算法均可以有效提高子孔径相位误差函数的拼接精度，优化基于多子孔径处理的SAR自聚焦算法性能。
第三章研究了基于投影近似子空间跟踪(Projection Approximation Subspace Tracking,简称PAST)技术的自聚焦算法。基于特征向量法的自聚焦算法利用多个脉冲估计相位误差函数，可以获得比PGA算法更好的自聚焦效果，但必须对协方差矩阵进行特征分解(EigenvalueDecomposition,简称ED），所以该自聚焦算法运算量大、工程实现困难。本章针对特征分解过程影响算法实时处理的问题，提出了利用PAST技术估计所需特征向量，完成SAR图像自聚焦处理。通过算法性能分析和实际数据处理结果对比，证明基于PAST技术的自聚焦算法在降低原自聚焦算法计算复杂度的同时，可以获得同样优于PGA算法的自聚焦性能，是一种可满足实时处理要求的有效自聚焦算法。利用该算法替代PGA算法对子孔径相位误差函数进行估计，可以更进一步提高基于多子孔径处理SAR自聚焦算法的算法性能。
第四章主要介绍了InSAR高程测量的原理及其信号处理过程中的关键步骤。本章首先通过公式推导，对干涉相位的统计特性进行了分析和研究，然后对InSAR高程测量的信号处理流程进行了简单的介绍，利用实测干涉数据给出了部分关键步骤的处理结果。随后通过研究SAR工作的成像几何关系，推导出由干涉相位值生成数字地形高度图(Digital ElevationModel,简称DEM)的对应转换公式，完成干涉相位值到高程值的转换过程。最后，详细分析了图像中目标位移的原因，并具体推导了目标在方位向和距离向上的位移量与成像几何，目标高度之间的数学关系，提供了正确定位目标真实位置的方法。
第五章重点研究了InSAR相位解缠绕技术。二维相位解缠绕处理是InSAR数据处理的关键。本章提出了一种基于等效残差点的InSAR相位解缠绕算法。该算法首先提出了等效残差点的概念，利用质量图与残差点分布之间的关系，将残差点密集的低质量相位区域视为等效残差点，采用不同方法分别对高质量相位区域和等效残差点的内部区域进行相位解缠绕。新的相位解缠绕算法基于等效残差点正确的设置枝切线，可以阻止由于积分路径穿过残差点密集的低质量相位区域所引起的展开相位跳变现象，同时利用多像素单元共同估计的方法对残差点的内部区域进行相位展开，突破了传统相位解缠绕算法对于干涉相位梯度值的限制，并且可以有效阻止相位解缠绕误差由低质量相位区域向高质量相位区域的传递。实验结果证明，该方法可以获得比其它算法更好的相位解缠绕结果。
第六章为结束语，对全文主要工作进行了总结，并指出下一步工作的方向和研究的重点。
Based on the relative motions between the antenna and target, synthetic aperture radar (SAR)could form a larger equivalent aperture antenna to obtain high azimuth resolution imageries bysignal processing techniques. It can significant enhance the ability of the long-distanceobservation for its all weather and all time character. After the developments in the past decades,the SAR imaging technologies become mature gradually. Because SAR is a coherent imagingsystem, there is an intimate connection between the image and the phase of the received signal. Inorder to obtain high resolution and high quality SAR images, the autofocus algorithms are used toestimate and correct the phase error. The technology of the interferometric synthetic aperture radar(InSAR) was used to obtain the information of the three-dimensional terrain since late1960’s. Andthe high quality SAR image is essential to the signal processing of InSAR elevation measure.Chapter1is the introduction of the dissertation. The history of SAR and InSAR technology isoutlined, respectively. And the applications and the developments of autofocus algorithms andInSAR technology are introduced in detail. At the end of this chapter, the aim and contents of ourwork are addressed.
Chapter2studies a multi-subaperture autofocus algorithm. Due to the characteristics of theconventional strip-mapping mode SAR imagery, the present techniques of autofocus cannot bedirectly used to estimate the phase error functions. By using the autofocus algorithm forsubimages and the subaperture phase error combining with technology that based on the seconddifferences, we can achieve the phase error functions of the strip-map SAR imagery throughappropriately changing the construction of the original range-compressed data. However, thismethod will lead to the accumulation of estimation errors during the procedure of the subaperturephase error combining. To address these shortcomings, we present a multi-subaperture autofocusalgorithm, which combines the techniques of phase gradient autofocus (PGA) and map drift (MD).Comparison on the accuracy of this approach against the traditional algorithm is presented.Experimental results indicate that the presented PGA-MD methodology can improve the quality ofstrip-map SAR image effectively. In the spotlight mode, the subaperture-images represent exactlythe same scenario, and are highly similar after refocused by PGA. Therefore any of thesubaperture-image pairs can be used as input to MD, and the redundancy of multiplecross-correlating results serves to suppress the effects of noise and target scintillation. What’smore, it smoothly incorporates the estimation of residual range cell migration (RCM) to furtherimprove the quality of SAR image.
Chapter3proposes a novel autofocus algorithm using the projection approximation subspacetracking (PAST) approach. SAR is a coherent imaging system. The key of obtaining highresolution and high quality SAR image is the maintenance of accurate coherent phases via usingautofocus algorithms. An eigenvector method for maximum-likelihood estimation (MLE) of phaseerrors for use in an autofocus algorithm for SAR imagery by the simultaneous processing ofmultiple-pulse vectors of range-compressed data has better performance than the algorithm ofPGA. However, this method requires eigendecomposition of the sample covariance matrix，whichis a task that is computationally expensive and limits the real-time application. In order toovercome this difficulty, a novel autofocus algorithm using PAST is presented. With thismethodology, the computational cost can be reduced effectively to the level of PGA via avoidingthe procedures of covariance matrix estimation and eigendecomposition. Monte Carlo tests and real SAR data processing validate that the new approach outperforms the mostly used PGA. Theperformance of multi-subaperture autofocus algorithm, which is detail described in the previouschapter, can be further improved by utilizing the PAST based autofocus algorithm instead of PGA.
Chapter4introduces the crucial steps of InSAR technology. Analysis and research on thestatistical characteristic of interferometric phase is given by formula deducing. And then the signalprocessing of InSAR elevation measure is briefly presented. We employ the real SAR data toobtain the processing results of the partial key points of InSAR technology. This chapter alsodetailed analysis the reason of the target displacement in digital elevation model (DEM), andshows the mathematical relation between the target displacement and the SAR imaging geometryand the height of target. The simulation results validate the analysis.
Chapter5focuses on the phase unwrapping. We investigate the Goldstein branch-cut phaseunwrapping method and the least squares estimation technique. And then a two-dimensional phaseunwrapping approach using equivalent residues is proposed for InSAR. In this proposed algorithm,the relationship between quality map and residues is used to find out the low quality unreliableregions, which are residues dense distribution and regarded as equivalent residues. Then, differentphase unwrapping strategies are taken for different quality regions. With this methodology,integration path crossing of unreliable regions, which may produce a phase error that propagatesto all the pixels in integration path, is prevented because that the unreliable regions are treated asequivalent residues. Each pixel inside equivalent residues is unwrapped based on its unwrappedneighbors, which breaks the limit of the absolute value of phase gradient between two adjacentpixels. Simulated and real SAR data processing validate the new approach.
Chapter6summarizes the major contents in this thesis and points out the direction and thefocus of next research work in the future.
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