地球同步轨道SAR与中高轨道SAR成像算法研究
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摘要
星载SAR具有全天时、全天侯、高分辨、远作用距离、宽测绘带等优点，并且具有穿透一定深度的地表和植被获取大面积的遥感图像的能力。近年来，随着SAR技术的不断发展和应用领域研究的拓展，越来越多的观测任务对星载SAR的性能指标提出了更为苛刻的要求，例如地理测绘，海洋应用，情报侦察、灾害监控，这些应用不仅要求星载SAR具有高的空间分辨率，还要求其具有高的时间分辨率，能够对大面积定点区域进行长时间的频繁观测。这就在其重返周期、测绘带宽等方面对系统设计提出了新的挑战。
然而目前在轨的星载SAR系统均搭载于低轨道卫星上，轨道高度通常在500km~1000km。由于轨道高度较低的限制，其可覆盖区域小，测绘带窄，重复观测周期长等缺点也越来越明显，特别是近年来空间弹道导弹、激光武器的飞速发展，对低轨道SAR(LEO SAR)的战场生存能力提出了严峻考验，在很大程度上限制了其应用。一个有效地途径来克服LEO SAR的不足就是将轨道高度提高到中高轨道或者地球同步轨道。地球同步轨道SAR(GEO SAR)和中高轨道SAR(MEO SAR)，其可以用很小的波束角覆盖大面积区域，获得大范围、持续的对地观测能力，在地震和火山预报、灾害监控，海洋应用研究等方面具有潜在的优势。并且，由于高的轨道高度，其抗打击和摧毁能力强，有较强的战场生存能力。同时，超长的合成孔径使其具备了对动目标进行连续跟踪与高分辨率成像的潜力，是未来星载SAR对地高分辨宽测绘带探测的发展趋势之一。
GEO SAR和MEO SAR因为轨道高度高，卫星速度小，其具有与LEO SAR不同的特性。并且，其合成孔径时间长，成像几何关系复杂，“停走”假设和直线运动轨迹近似不再成立。因此，传统的SAR成像算法已经难以完成目标的精确聚焦。基于以上原因，论文分为两个部分，第一部分开展GEO SAR成像算法的研究，第二部分开展MEO SAR成像算法的研究，虽然第一部分是以GEO SAR为研究对象，但是其中的大部分结论和分析方法对于MEO SAR也是适用的。本论文所取得的主要研究成果为：
1.对GEO SAR成像中的回波信号二维频谱表达式的推导问题以求解方程获得驻相点的思路和利用级数反演获得驻相点的思路分别进行了对比研究。发现通过级数反演方法建立的二维频谱，精度高、拓展性强、易于算法实现，满足了高分辨率GEO SAR成像的需求，为之后高分辨率成像算法的研究进行了铺垫。
2.系统的研究了GEO SAR的特性和系统参数设计方法。首先建立了GEOSAR的轨道模型，对其特殊的运动特性进行了分析，重点研究了目标的多普勒特性。针对卫星姿态误差对多普勒参数的影响从而导致成像质量下降的问题，通过推导存在姿态误差情况下的多普勒参数表达式，分析了姿态误差对多普勒参数的影响，分析结果将对卫星平台控制参数精度的确定提供理论依据。在特性分析的基础上，对其各系统参数之间的关系进行了推导，详细分析了其系统参数设计方法，并针对中国的地理位置，设计了高分辨率和低分辨率的两组有效的雷达参数。
3.研究了GEO SAR子孔径成像算法。首先对其子孔径时间内的信号特点进行了分析，考虑了“停走”假设带来的误差和等效雷达速度和等效斜视角的空变性，建立了其子孔径成像模型。接着，基于该成像模型提出了两种适用于GEO SAR子孔径成像的算法。一种是改进的子孔径SPECAN算法，该算法效率高，满足实时成像要求。一种是改进的子孔径CS成像算法，其校正了空变的距离徙动，可实现较大场景的成像。这两种算法可以看做LEO SAR上的SPECAN算法和CS算法在GEO SAR上的推广，突破了卫星高度的限制。最后，经过仿真验证了这两种算法的可行性。
4.针对全孔径曲线轨迹下GEO SAR高分辨成像问题，在以级数反演法为基础的二维频谱上，提出了两种GEO SAR全孔径成像算法，即一种改进近似OMEGA-K成像算法和一种改进CS成像算法。由于GEO SAR轨道高度高，合成孔径时间长，其相对地球的运动变得更为复杂，直线轨迹模型不再适用，导致常规的基于直线轨迹模型的成像算法性能下降。因此，这两种算法根据GEO SAR平台的运动特性，对其几何构型采取高阶逼近，建立了曲线轨迹模型下的斜距方程。结合级数反演法，推导了GEO SAR回波信号二维频谱高阶近似表达式。近似OMEGA-K成像算法是一种二维频域算法，其所有的操作都由快速傅里叶变换和相位点乘完成，具有较高的效率。另外，改进的CS成像算法，采用数值拟合并结合CS变标的方法实现GEO SAR中目标的距离徙动校正，相比通过插值操作实现的距离徙动校正拥有较高的运算效率。点目标仿真结果表明所提斜距方程精度较高，所提算法能实现GEO SAR全孔径高分辨成像。
5.针对MEO SAR全孔径曲线轨迹下的高分辨成像问题，提出了一种适用于MEO SAR的高阶修正双曲线距离方程，该距离方程通过引入一线性项和一四次项对双曲线距离方程进行修正，使得其能对MEO SAR真实斜距历程进行四阶精确逼近。在此基础上，采用驻相点近似的方法推导该距离方程下的二维频谱的闭合解析解，并结合级数反演法对频谱精度进行分析。为了便于成像算法的设计，对二维频谱各部分的空变性进行了分析，给出了其成像流程。这种新频谱在保持了简洁性的同时，其相位严格精确到四次项，能满足MEO SAR精确成像，适用范围更广，并且现有的MEO SAR成像算法进行少许修改就能直接利用其进行MEO SAR成像处理。仿真结果验证了所提方法的有效性。
Synthetic aperture radar (SAR) can work all day and all weather to obtain the large areaand high resolution images of the surface and of the earth through the coverage of the plants.In recent years, with the development of the technology and the expansion of the applicationsin SAR field, much tougher requirements for the growing number of observation missions areprovided on the performance index of the SAR system, such as military mapping,oceanography, intelligence reconnaissance, disaster management and so on. Most of theseapplications demand both higher spatial resolution and better temporal accessibility to getfiner imaging performance, which brings a new challenge for the system design in revisitperiod, swath width and so on.
However, all the current spaceborne SAR systems operate in low earth orbit at a heightof500km-1000km. Because of the low orbit height, the small instantaneous view field andlong revisit time show increasingly more obvious disadvantages in low earth orbit SAR (LEOSAR). Especially, with the recent rapid development of space ballistic missiles and laserweapons, a severe challenge for battlefield survivability of LEO SAR have been posed, itsapplication is largely limited. One solution to this problem is to adopt geosynchronous SAR(GEO SAR) and medium earth orbit SAR (MEO SAR). Because higher vantage points canimprove both the spatial resolution and the temporal accessibility, GEO SAR and MEO SARhave the large instantaneous view field and short revisit time, and have a lot of advantages inthe earthquake and volcano prediction, disaster management, ocean applications, and so on. Inaddition, due to the high orbit altitude, GEO SAR and MEO SAR have strong anti-strikeability and battlefield survivability. Moreover, the ultrawide synthetic aperture makes itpossible to trace the moving target and to perform high resolution imaging. Thus, the GEOSAR and MEO SAR will be one of the trends in the future’s spaceborne SAR for wide-swathand high resolution detection.
Due to its the high orbit height, whose characteristics are different from LEO SAR, theimaging geometry of GEO SAR or MEO SAR is more complicated, and the syntheticaperture time is also very long which will result in a curved synthetic aperture trajectory, thusthe “Stop-and-Go” assumption and conventional imaging methods of LEO SAR will loseeffect in GEO SAR and MEO SAR. Based on all the above reasons, this dissertation consistsof two parts，one is about the imaging methods of GEO SAR, and the other is imagingmethods of MEO SAR. Most of the conclusions and analysis methods of GEO SAR are alsoapplicable to the MEO SAR. The main research results are as follows:
1. In order to derive the expression of the two-dimensional spectrum for the echosignal, two potential thoughts are analyzed and compared. One is to solve equations to obtainthe stationary phase point and the other is to use the method of series reversion (MSR) to getthe stationary phase point. After the comparison, it is easy to find that MSR has advantages ofhigh accuracy, strong portability and easiness of realization to meet the demand of the highresolution GEO SAR imaging, paving the way for the research of the following highresolution algorithm.
2. The method for parameters design and the characteristics of the GEO SAR areresearched systematically. Firstly, the orbit model is constructed and the properties of themotion of the GEO SAR are analyzed. The Doppler property of the GEO SAR target isdiscussed in detail. The changes of the satellite attitude have significant effects on the GEOSAR imaging. By deducing the Doppler parameters expression with the satellite attitudevariety, the impact of satellite attitude changes to the GEO SAR imaging is obtained, theformula is significative for analysis of performance and preliminary design for spaceborneSAR. Based on the above analysis of the characteristics, the parameters' constraint relation isdeduced to find a parameters design method. In the end, as for the China’s geomorphiclocation, the designed parameters of low resolution and high resolution are given.
3. The subaperture imaging algorithm for GEO SAR is studied. At first, the features ofthe targets’ echo signals are analyzed. Then, a subaperture imaging model is established,which takes the “Stop-and-Go” assumption error and the space-variance of equivalent radarvelocity and the equivalent squint angle into account. Two subaperture imaging algorithms areproposed based on the imaging model. One is the improved SPECAN algorithms, which isefficient and can satisfy the demand of real time imaging. The other is improved chirp scaling(CS) algorithm, which performs range cell migration correction accurately and suits forwide-swath imaging. These two algorithms can be considered as an extension of the SPECANand the CS algorithms from LEO SAR case to the GEO SAR case, which overcome thelimitation of height. At last the effectiveness of the proposed algorithm is validated by thesimulations.
4. As for the problem of high resolution imaging of full aperture, this dissertationproposes an approximate OMEGA-K algorithm and an improved CS algorithm which arebased on the MSR based two-dimensional spectrum. Because of the higher orbit of GEO SAR,the integration time is long, and the relative motion between the satellite and the earth alsobecomes more complicated. Thus, the linear trajectory model and imaging algorithm of LEOSAR are not suitable for GEO SAR. With regard to this issue, this paper establishes the rangeequation for long synthetic aperture time by using the high order approximation based on the characters of the GEO SAR movements. Then, the two-dimensional spectrum is derived bythe method of series reversion. The approximate OMEGA-K algorithm is a two-dimensionalfrequency domain imaging algorithm, all the operations of which are composed of the fastFourier transform and the phase multiplication, so the algorithm is efficient. The improved CSalgorithm has the advantages of high accuracy and relatively low computation load, since nointerpolation is required during the whole processing steps. The range migration correction isimplemented by the chirp scaling operation and numerical approximation of the GEO SARparameters.
5. According to the problem of high resolution imaging of full aperture, a high-ordermodified hyperbolic range equation is proposed for MEO SAR. Incorporating with anadditional linear component and quartic component, quartic Taylor series expansion of it hasexactly the same value as that of the actual range history of MEO SAR. Then, thetwo-dimensional spectrum based on high-order modified hyperbolic range is analyticallyderived by using an approximate azimuth stationary phase point, based on the MSR, theaccuracy of the two-dimensional spectrum is analyzed which is exactly equal to quartic phaseterm. In order to design the imaging the space-variance of each parts of the two-dimensionalspectrum is analyzed, and the imaging flowchart is given. And current available MEO SARalgorithm can be implemented directly with little modification. Simulation results show thatthe proposed range equation and the two-dimensional spectrum are accurate which can givefine resolution imagery with the entire aperture.
然而目前在轨的星载SAR系统均搭载于低轨道卫星上，轨道高度通常在500km~1000km。由于轨道高度较低的限制，其可覆盖区域小，测绘带窄，重复观测周期长等缺点也越来越明显，特别是近年来空间弹道导弹、激光武器的飞速发展，对低轨道SAR(LEO SAR)的战场生存能力提出了严峻考验，在很大程度上限制了其应用。一个有效地途径来克服LEO SAR的不足就是将轨道高度提高到中高轨道或者地球同步轨道。地球同步轨道SAR(GEO SAR)和中高轨道SAR(MEO SAR)，其可以用很小的波束角覆盖大面积区域，获得大范围、持续的对地观测能力，在地震和火山预报、灾害监控，海洋应用研究等方面具有潜在的优势。并且，由于高的轨道高度，其抗打击和摧毁能力强，有较强的战场生存能力。同时，超长的合成孔径使其具备了对动目标进行连续跟踪与高分辨率成像的潜力，是未来星载SAR对地高分辨宽测绘带探测的发展趋势之一。
GEO SAR和MEO SAR因为轨道高度高，卫星速度小，其具有与LEO SAR不同的特性。并且，其合成孔径时间长，成像几何关系复杂，“停走”假设和直线运动轨迹近似不再成立。因此，传统的SAR成像算法已经难以完成目标的精确聚焦。基于以上原因，论文分为两个部分，第一部分开展GEO SAR成像算法的研究，第二部分开展MEO SAR成像算法的研究，虽然第一部分是以GEO SAR为研究对象，但是其中的大部分结论和分析方法对于MEO SAR也是适用的。本论文所取得的主要研究成果为：
1.对GEO SAR成像中的回波信号二维频谱表达式的推导问题以求解方程获得驻相点的思路和利用级数反演获得驻相点的思路分别进行了对比研究。发现通过级数反演方法建立的二维频谱，精度高、拓展性强、易于算法实现，满足了高分辨率GEO SAR成像的需求，为之后高分辨率成像算法的研究进行了铺垫。
2.系统的研究了GEO SAR的特性和系统参数设计方法。首先建立了GEOSAR的轨道模型，对其特殊的运动特性进行了分析，重点研究了目标的多普勒特性。针对卫星姿态误差对多普勒参数的影响从而导致成像质量下降的问题，通过推导存在姿态误差情况下的多普勒参数表达式，分析了姿态误差对多普勒参数的影响，分析结果将对卫星平台控制参数精度的确定提供理论依据。在特性分析的基础上，对其各系统参数之间的关系进行了推导，详细分析了其系统参数设计方法，并针对中国的地理位置，设计了高分辨率和低分辨率的两组有效的雷达参数。
3.研究了GEO SAR子孔径成像算法。首先对其子孔径时间内的信号特点进行了分析，考虑了“停走”假设带来的误差和等效雷达速度和等效斜视角的空变性，建立了其子孔径成像模型。接着，基于该成像模型提出了两种适用于GEO SAR子孔径成像的算法。一种是改进的子孔径SPECAN算法，该算法效率高，满足实时成像要求。一种是改进的子孔径CS成像算法，其校正了空变的距离徙动，可实现较大场景的成像。这两种算法可以看做LEO SAR上的SPECAN算法和CS算法在GEO SAR上的推广，突破了卫星高度的限制。最后，经过仿真验证了这两种算法的可行性。
4.针对全孔径曲线轨迹下GEO SAR高分辨成像问题，在以级数反演法为基础的二维频谱上，提出了两种GEO SAR全孔径成像算法，即一种改进近似OMEGA-K成像算法和一种改进CS成像算法。由于GEO SAR轨道高度高，合成孔径时间长，其相对地球的运动变得更为复杂，直线轨迹模型不再适用，导致常规的基于直线轨迹模型的成像算法性能下降。因此，这两种算法根据GEO SAR平台的运动特性，对其几何构型采取高阶逼近，建立了曲线轨迹模型下的斜距方程。结合级数反演法，推导了GEO SAR回波信号二维频谱高阶近似表达式。近似OMEGA-K成像算法是一种二维频域算法，其所有的操作都由快速傅里叶变换和相位点乘完成，具有较高的效率。另外，改进的CS成像算法，采用数值拟合并结合CS变标的方法实现GEO SAR中目标的距离徙动校正，相比通过插值操作实现的距离徙动校正拥有较高的运算效率。点目标仿真结果表明所提斜距方程精度较高，所提算法能实现GEO SAR全孔径高分辨成像。
5.针对MEO SAR全孔径曲线轨迹下的高分辨成像问题，提出了一种适用于MEO SAR的高阶修正双曲线距离方程，该距离方程通过引入一线性项和一四次项对双曲线距离方程进行修正，使得其能对MEO SAR真实斜距历程进行四阶精确逼近。在此基础上，采用驻相点近似的方法推导该距离方程下的二维频谱的闭合解析解，并结合级数反演法对频谱精度进行分析。为了便于成像算法的设计，对二维频谱各部分的空变性进行了分析，给出了其成像流程。这种新频谱在保持了简洁性的同时，其相位严格精确到四次项，能满足MEO SAR精确成像，适用范围更广，并且现有的MEO SAR成像算法进行少许修改就能直接利用其进行MEO SAR成像处理。仿真结果验证了所提方法的有效性。
Synthetic aperture radar (SAR) can work all day and all weather to obtain the large areaand high resolution images of the surface and of the earth through the coverage of the plants.In recent years, with the development of the technology and the expansion of the applicationsin SAR field, much tougher requirements for the growing number of observation missions areprovided on the performance index of the SAR system, such as military mapping,oceanography, intelligence reconnaissance, disaster management and so on. Most of theseapplications demand both higher spatial resolution and better temporal accessibility to getfiner imaging performance, which brings a new challenge for the system design in revisitperiod, swath width and so on.
However, all the current spaceborne SAR systems operate in low earth orbit at a heightof500km-1000km. Because of the low orbit height, the small instantaneous view field andlong revisit time show increasingly more obvious disadvantages in low earth orbit SAR (LEOSAR). Especially, with the recent rapid development of space ballistic missiles and laserweapons, a severe challenge for battlefield survivability of LEO SAR have been posed, itsapplication is largely limited. One solution to this problem is to adopt geosynchronous SAR(GEO SAR) and medium earth orbit SAR (MEO SAR). Because higher vantage points canimprove both the spatial resolution and the temporal accessibility, GEO SAR and MEO SARhave the large instantaneous view field and short revisit time, and have a lot of advantages inthe earthquake and volcano prediction, disaster management, ocean applications, and so on. Inaddition, due to the high orbit altitude, GEO SAR and MEO SAR have strong anti-strikeability and battlefield survivability. Moreover, the ultrawide synthetic aperture makes itpossible to trace the moving target and to perform high resolution imaging. Thus, the GEOSAR and MEO SAR will be one of the trends in the future’s spaceborne SAR for wide-swathand high resolution detection.
Due to its the high orbit height, whose characteristics are different from LEO SAR, theimaging geometry of GEO SAR or MEO SAR is more complicated, and the syntheticaperture time is also very long which will result in a curved synthetic aperture trajectory, thusthe “Stop-and-Go” assumption and conventional imaging methods of LEO SAR will loseeffect in GEO SAR and MEO SAR. Based on all the above reasons, this dissertation consistsof two parts，one is about the imaging methods of GEO SAR, and the other is imagingmethods of MEO SAR. Most of the conclusions and analysis methods of GEO SAR are alsoapplicable to the MEO SAR. The main research results are as follows:
1. In order to derive the expression of the two-dimensional spectrum for the echosignal, two potential thoughts are analyzed and compared. One is to solve equations to obtainthe stationary phase point and the other is to use the method of series reversion (MSR) to getthe stationary phase point. After the comparison, it is easy to find that MSR has advantages ofhigh accuracy, strong portability and easiness of realization to meet the demand of the highresolution GEO SAR imaging, paving the way for the research of the following highresolution algorithm.
2. The method for parameters design and the characteristics of the GEO SAR areresearched systematically. Firstly, the orbit model is constructed and the properties of themotion of the GEO SAR are analyzed. The Doppler property of the GEO SAR target isdiscussed in detail. The changes of the satellite attitude have significant effects on the GEOSAR imaging. By deducing the Doppler parameters expression with the satellite attitudevariety, the impact of satellite attitude changes to the GEO SAR imaging is obtained, theformula is significative for analysis of performance and preliminary design for spaceborneSAR. Based on the above analysis of the characteristics, the parameters' constraint relation isdeduced to find a parameters design method. In the end, as for the China’s geomorphiclocation, the designed parameters of low resolution and high resolution are given.
3. The subaperture imaging algorithm for GEO SAR is studied. At first, the features ofthe targets’ echo signals are analyzed. Then, a subaperture imaging model is established,which takes the “Stop-and-Go” assumption error and the space-variance of equivalent radarvelocity and the equivalent squint angle into account. Two subaperture imaging algorithms areproposed based on the imaging model. One is the improved SPECAN algorithms, which isefficient and can satisfy the demand of real time imaging. The other is improved chirp scaling(CS) algorithm, which performs range cell migration correction accurately and suits forwide-swath imaging. These two algorithms can be considered as an extension of the SPECANand the CS algorithms from LEO SAR case to the GEO SAR case, which overcome thelimitation of height. At last the effectiveness of the proposed algorithm is validated by thesimulations.
4. As for the problem of high resolution imaging of full aperture, this dissertationproposes an approximate OMEGA-K algorithm and an improved CS algorithm which arebased on the MSR based two-dimensional spectrum. Because of the higher orbit of GEO SAR,the integration time is long, and the relative motion between the satellite and the earth alsobecomes more complicated. Thus, the linear trajectory model and imaging algorithm of LEOSAR are not suitable for GEO SAR. With regard to this issue, this paper establishes the rangeequation for long synthetic aperture time by using the high order approximation based on the characters of the GEO SAR movements. Then, the two-dimensional spectrum is derived bythe method of series reversion. The approximate OMEGA-K algorithm is a two-dimensionalfrequency domain imaging algorithm, all the operations of which are composed of the fastFourier transform and the phase multiplication, so the algorithm is efficient. The improved CSalgorithm has the advantages of high accuracy and relatively low computation load, since nointerpolation is required during the whole processing steps. The range migration correction isimplemented by the chirp scaling operation and numerical approximation of the GEO SARparameters.
5. According to the problem of high resolution imaging of full aperture, a high-ordermodified hyperbolic range equation is proposed for MEO SAR. Incorporating with anadditional linear component and quartic component, quartic Taylor series expansion of it hasexactly the same value as that of the actual range history of MEO SAR. Then, thetwo-dimensional spectrum based on high-order modified hyperbolic range is analyticallyderived by using an approximate azimuth stationary phase point, based on the MSR, theaccuracy of the two-dimensional spectrum is analyzed which is exactly equal to quartic phaseterm. In order to design the imaging the space-variance of each parts of the two-dimensionalspectrum is analyzed, and the imaging flowchart is given. And current available MEO SARalgorithm can be implemented directly with little modification. Simulation results show thatthe proposed range equation and the two-dimensional spectrum are accurate which can givefine resolution imagery with the entire aperture.
引文
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