星机联合SAR成像处理算法及运动补偿的研究
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摘要
双基地合成孔径雷达(BiSAR)作为传统单基地SAR的延伸,由于其自身的灵活性和对低散射截面物体的探测成像能力,大大地拓展了SAR的应用范围。具有移变(translational-variant)特性的星机联合双基地合成孔径雷达(SA-BiSAR)作为双基地合成孔径雷达应用的新方面,不仅能获取多角度目标散射信息实现对目标区域成像,而且具有系统灵活,观测范围大等优势,是当前雷达成像应用的研究热点。本文基于SA-BiSAR特点,主要进行了成像算法和运动补偿算法的研究,主要内容为:
1.讨论SA-BiSAR成像的基本问题:讨论分析了星载平台的运动轨迹,并以此为基础将星载平台和机载平台用同一个成像坐标系表示,消除了地球自转的影响,并推导了波束同步的相关公式;介绍了SA-BiSAR的成像原理并分析了空间分辨率。
2.提出了适用于平飞模式下的SA-BiSAR成像算法:分析推导了平飞移变模式下的距离历史,并在此基础上提出了改进的RD算法,针对图像出现的畸变,分析了产生的原因并提出了基于反演投影法的校正算法,最终得到了良好的成像效果。
3.提出了适用于任意模式下的SA-BiSAR时域成像算法:考虑距离历史的空域截断误差,在变尺度逆傅里叶变换算法(SIFFT)的基础上,提出基于非等间隔校正的SIFFT(NUSC-SIFFT)算法,使之适用于较大场景成像,最后利用距离分块算法得到大场景下的成像结果。
4.提出了适用于任意模式下的SA-BiSAR频域成像算法:利用距离历史的空域和时域混合展开,得到简洁的距离历史近似表达式,并利用驻定相位原理(PSP)得到信号的二维频谱的解析表达式。在聚焦过程中,通过在不同域中的相位补偿,最终得到聚焦良好且位置正确的目标成像结果。
5.分析了双基地SAR运动误差的影响,得出影响聚焦的运动误差方向,大大减少了运动误差的搜索范围。通过对比分析,提出了以图像最小自相关方差作为图像质量的评价准则,并以此为基础提出了基于图像质量的搜索算法,从而对运动误差进行估计和补偿,仿真结果充分显示了该算法的有效性和适用性。
6.提出了一种基于参数估计的运动补偿算法,通过简化误差来源,推导了速度误差对回波相位的影响,通过提取不同强点的相位信息,利用二次DCFT估计得到与速度误差有关的系数方程,通过矩阵反解求得速度误差,最终取得良好的估计精度和补偿效果。
As part of the continuing evolution of the monostatic synthetic aperture radar (SAR) system, the bistatic SAR greatly expands the application of the SAR because of its flexibility and the ability to detect the low radar cross-section object. Spaceborne-airborne bistatic SAR, as a kind of translational variant BiSAR, is one of the hotpoint in the field of SAR application, because it could not only be used to imaging, but also to revealing the scattering feature further, and improving the accuracy of the SAR image.This dissertation mainly researches imaging algorithms and motion compensation methods for translational variant SA-BiSAR. The main contributions of the dissertation are as follows:
1. Introduce the fundamental theory of SA-BiSAR imaging: first describe and analyze the track of satellite, and propose the uniform coordinate for imaging. Based on these, some formulas for beam synchroniziation are deduced. Second introduce the theory and space resolution of SA-BiSAR imaging.
2. An imaging algorithm for SA-BiSAR with parallel trajectory is proposed: First the range approximation for SA-BiSAR with parallel trajectory is deduced, some modifications are applicated to range-Doppler (RD) algorithm and well focused results are obtained, however there are some distortions. Second the courses of distortion are analysised, and a correction method named Inverse-Projection is proposed.
3. An imaging algorithm for SA-BiSAR with non-parallel trajectory in time domain is proposed: first based on the SIFFT algorithm and the analyziation of space truncation error, the non-uninformly spaced correction SIFFT (NUSC-SIFFT) algorithm is proposed, which extends the imaging range and makes the traditional SIFFT algorithm suitable for SA-BiSAR. Second based on NUSC-SIFFT, imaging different parts along range direction and obtained well focused images of large scene.
4. A 2-D spectrum imaging algorithm for SA-BiSAR based on translational variant space and time domain expansion is proposed. First, a new approximation of slant range history is obtained based on both space domain and slow time domain expansion. The expansion in space domain is applied to get the linear function of scatters’positions, which is beneficial to correct distortions. And slow time domain expansion makes it easy to use the principle of stationary phase (PSP) to obtain the 2-D spectrum expression. Second, based on the spectrum, the imaging algorithm is proposed. Because the imaging space is spanned by two vectors, which are translational variant and non-orthogonal for SA-BiSAR, so there will be some distortions, and traditional correction method is not valid any more. Then a new correction method based on eliminating coupled phase terms is proposed, and the imaging simulations show that the 2-D spectrum works well in the general configuration and the validity of correction method is proved.
5. First discusses the effects of motion measurement errors (MMEs) on Bistatic SAR images. After the theoretical derivation, we find the main factors of causing SAR images to severely defocus. Then searching in the directions of P-AVME and P-RVME, according to the quality of images, and find out the MMEs which should be compensated. So a reasonable criterion should be used to evaluate the quality of SAR images. Compare with some other criterions, the criterion named minimum auto-correlation variance of the image is analyzed and proved useful by simulation. At last, the MMEs were estimated and compensated by searching method and BP algorithm with this criterion.
6. The velocitie error will cause the defocusing of images by bring a second-order phase item. Then a compensation method based on parameters estimation is proposed, which uses the echo of different known scatterers to estimate the velocitie error and compensate the errors. The simulation results prove the validity of this method.
1.讨论SA-BiSAR成像的基本问题:讨论分析了星载平台的运动轨迹,并以此为基础将星载平台和机载平台用同一个成像坐标系表示,消除了地球自转的影响,并推导了波束同步的相关公式;介绍了SA-BiSAR的成像原理并分析了空间分辨率。
2.提出了适用于平飞模式下的SA-BiSAR成像算法:分析推导了平飞移变模式下的距离历史,并在此基础上提出了改进的RD算法,针对图像出现的畸变,分析了产生的原因并提出了基于反演投影法的校正算法,最终得到了良好的成像效果。
3.提出了适用于任意模式下的SA-BiSAR时域成像算法:考虑距离历史的空域截断误差,在变尺度逆傅里叶变换算法(SIFFT)的基础上,提出基于非等间隔校正的SIFFT(NUSC-SIFFT)算法,使之适用于较大场景成像,最后利用距离分块算法得到大场景下的成像结果。
4.提出了适用于任意模式下的SA-BiSAR频域成像算法:利用距离历史的空域和时域混合展开,得到简洁的距离历史近似表达式,并利用驻定相位原理(PSP)得到信号的二维频谱的解析表达式。在聚焦过程中,通过在不同域中的相位补偿,最终得到聚焦良好且位置正确的目标成像结果。
5.分析了双基地SAR运动误差的影响,得出影响聚焦的运动误差方向,大大减少了运动误差的搜索范围。通过对比分析,提出了以图像最小自相关方差作为图像质量的评价准则,并以此为基础提出了基于图像质量的搜索算法,从而对运动误差进行估计和补偿,仿真结果充分显示了该算法的有效性和适用性。
6.提出了一种基于参数估计的运动补偿算法,通过简化误差来源,推导了速度误差对回波相位的影响,通过提取不同强点的相位信息,利用二次DCFT估计得到与速度误差有关的系数方程,通过矩阵反解求得速度误差,最终取得良好的估计精度和补偿效果。
As part of the continuing evolution of the monostatic synthetic aperture radar (SAR) system, the bistatic SAR greatly expands the application of the SAR because of its flexibility and the ability to detect the low radar cross-section object. Spaceborne-airborne bistatic SAR, as a kind of translational variant BiSAR, is one of the hotpoint in the field of SAR application, because it could not only be used to imaging, but also to revealing the scattering feature further, and improving the accuracy of the SAR image.This dissertation mainly researches imaging algorithms and motion compensation methods for translational variant SA-BiSAR. The main contributions of the dissertation are as follows:
1. Introduce the fundamental theory of SA-BiSAR imaging: first describe and analyze the track of satellite, and propose the uniform coordinate for imaging. Based on these, some formulas for beam synchroniziation are deduced. Second introduce the theory and space resolution of SA-BiSAR imaging.
2. An imaging algorithm for SA-BiSAR with parallel trajectory is proposed: First the range approximation for SA-BiSAR with parallel trajectory is deduced, some modifications are applicated to range-Doppler (RD) algorithm and well focused results are obtained, however there are some distortions. Second the courses of distortion are analysised, and a correction method named Inverse-Projection is proposed.
3. An imaging algorithm for SA-BiSAR with non-parallel trajectory in time domain is proposed: first based on the SIFFT algorithm and the analyziation of space truncation error, the non-uninformly spaced correction SIFFT (NUSC-SIFFT) algorithm is proposed, which extends the imaging range and makes the traditional SIFFT algorithm suitable for SA-BiSAR. Second based on NUSC-SIFFT, imaging different parts along range direction and obtained well focused images of large scene.
4. A 2-D spectrum imaging algorithm for SA-BiSAR based on translational variant space and time domain expansion is proposed. First, a new approximation of slant range history is obtained based on both space domain and slow time domain expansion. The expansion in space domain is applied to get the linear function of scatters’positions, which is beneficial to correct distortions. And slow time domain expansion makes it easy to use the principle of stationary phase (PSP) to obtain the 2-D spectrum expression. Second, based on the spectrum, the imaging algorithm is proposed. Because the imaging space is spanned by two vectors, which are translational variant and non-orthogonal for SA-BiSAR, so there will be some distortions, and traditional correction method is not valid any more. Then a new correction method based on eliminating coupled phase terms is proposed, and the imaging simulations show that the 2-D spectrum works well in the general configuration and the validity of correction method is proved.
5. First discusses the effects of motion measurement errors (MMEs) on Bistatic SAR images. After the theoretical derivation, we find the main factors of causing SAR images to severely defocus. Then searching in the directions of P-AVME and P-RVME, according to the quality of images, and find out the MMEs which should be compensated. So a reasonable criterion should be used to evaluate the quality of SAR images. Compare with some other criterions, the criterion named minimum auto-correlation variance of the image is analyzed and proved useful by simulation. At last, the MMEs were estimated and compensated by searching method and BP algorithm with this criterion.
6. The velocitie error will cause the defocusing of images by bring a second-order phase item. Then a compensation method based on parameters estimation is proposed, which uses the echo of different known scatterers to estimate the velocitie error and compensate the errors. The simulation results prove the validity of this method.
引文
[1]汤子跃,张守融.双站合成孔径雷达系统原理.北京:科学出版社, 2003
[2] Merrill I. Skolnik.雷达手册.北京:电子工业出版社,2003
[3]皮亦鸣等.合成孔径雷达成像原理.成都:电子科技大学出版社.2007
[4]袁孝康.星载合成孔径雷达导论.北京::国防工业出版社, 2003
[5]魏钟铨.合成孔径雷达卫星.北京:科学出版社, 2001
[6]张明友,吕幼新.信号与系统分析.成都:电子科技大学出版社,2000
[7]张贤达.现代信号处理.北京:清华大学出版社,2002
[8] Steven J. Leon. Linear algebra with applications.北京:机械工业出版社,2007
[9] Ian G. Cumming,Frank H. Wong.合成孔径雷达成像-算法与实现.北京:电子工业出版社, 2007
[10]张明友,吕明.信号检测与估计.北京:电子工业出版社, 2005
[11]向敬成,张明友.雷达系统.北京:电子工业出版社,2001
[12]保铮,邢孟道,王彤.雷达成像技术.北京:电子工业出版社,2006;
[13]师君.新型SAR技术与成像机理研究:[博士学位论文].电子科技大学,2009
[14] Shi jun; Zhang Xiaoling; Yang Jianyu; Translational variant bistatic SAR signal space-time feature and processing method, Geoscience and Remote Sensing Symposium, 2007. IGARSS 2007. IEEE International, 23-28 July 2007, 2140– 2143
[15] Shi Jun; Xiaoling Zhang; Jianyu Yang; Principle and Methods on Bistatic SAR Signal Processing via Time Correlation Geoscience and Remote Sensing, IEEE Transactions on Volume 46, Issue 10, Part 2, Oct. 2008, 3163– 3178
[16] Otmar Loffeld, Holger Nies, Valerij Peters, Stefan Knedlik. Models and useful relations for bistatic SAR processing. IEEE Trans.on Geosci. Remote Sensing. Oct. 2004, 42(10): 2031-2038.
[17] O. Loffeld, and A. Hein. SAR processing by‘inverse scaled Fourier transformation’. In Proc. EUSAR, Germany, 1996, 143-146.
[18] O. Loffeld, F. Schneider, and A. Hein. Focusing SAR images by inverse scaled Fourier transformation. In Proc. Int . Conf. Signal Process. Commun. Las Palmas, Spain, 1998, vol.2, 630-632.
[19] Zeng, Tao,Cherniakov, Mikhail; Long, Teng.Generalized approach to resolution analysis in BSAR. IEEE Transactions on Aerospace and Electronic Systems, v 41, n 2, April, 2005, pp 461-474;
[20] Jordan, R.The Seasat-A synthetic aperture radar system. IEEE Journal of Oceanic Engineering, Volume 5, Issue 2, April 1980, 154– 164;
[21] Way, J. Smith, E.A..The evolution of synthetic aperture radar systems and their progression to the EOS SAR. IEEE Transactions on Geoscience and Remote Sensing, Volume 29, Issue 6, Nov. 1991,962– 985;
[22]邓彦.机载双基地SAR成像算法及相关技术研究:[硕士学位论文].电子科技大学, 2006
[23] Minh N.Do, Martin Vetterli. The Contourlet Transform: An Efficient Directional Multiresolution Image Representation. IEEE Trans. On Image Processing, Dec.2006,14(12): 2091-2105
[24]龚镇强.双基地SAR成像处理算法研究:[硕士学位论文].电子科技大学, 2007
[25] Gong Zhenqiang, Zhang Xiaoling, Tian Zhong. Automobile-Based Bistatic SAR processing and experimental results. Proc, IGARSS 2007, Barcelona, Spain, July, 2007
[26] Y. Neo, F. Wong, and I. G. Cumming. A two-dimensional spectrum for bistatic SAR processing using series reversion. IEEE Geosci. Remote Sens. Lett., 2007, 4(1): 93–96,.
[27] Yew Lam Neo, Frank H. Wong, Ian G. Cumming. Processing of Azimuth-Invariant Bistatic SAR Data Using the Range Doppler Algorithm. IEEE Trans.on Geosci. Remote Sensing. Jan. 2008, 46(1): 14-20.
[28] Koba Matroshvili, Otmar Loffeld. Focusing of General Bistatic SAR Configuration Data With 2-D Inverse Scaled FFT. IEEE Trans.on Geosci. Remote Sensing. Oct.2006, 44(10):2718-2726.
[29]王宏禹.非平稳随机信号分析与处理.北京,国防工业出版社. 1999
[30] Roger F, Jean-Claude S, Jean-Marc G, Philippe D, Didier M. Impact of Ambiguities in Multistatic SAR. IGARSS '2004
[31] Zhe Liu, Jianyu Yang, Xiaoling Zhang, Yiming Pi. Study on Spaceborne/Airborne Hybrid Bistatic SAR Image Formation in Frequency Domain[J]. IEEE Geoscience and Remote Sensing Letters, October, 2008, 5(4):578-582.
[32] Zhe Liu,Jianyu Yang,Xiaoling Zhang Yiming Pi. Spaceborne/Airborne Hybrid Bistatic SAR Frequency Domain Imaging Processing Algorithm[J]. Chinese Journal of Electronics, July, 2008, 17(3): 487-491.
[33] Zhe Liu, Jianyu Yang, Xiaoling Zhang, Yiming Pi. Frequency Domain Imaging Algorithm forSpaceborneAirborne Hybrid Bistatic SAR[C]. IEEE International Geoscience and Remote Sensing Symposium, IGARSS 2007, 2008, p 842-845.
[34] Zhe Liu, Jianyu Yang, Xiaoling Zhang, Yiming Pi .An Approximated Analytical Solution for Two-Dimensional Spectrum of Spaceborne/Airborne Hybrid Bistatic SAR[C]. ICCCAS’2007.
[35] Zhe Liu, Yanhai Shang, Jianyu Yang. Imaging Performance Analysis of Space-Air Non-Cooperative BSAR [C], International Conference on Radar’2006.
[36] Yang Yue; Zhang Xiaoling; Zuo Zijin . An imaging method and the correction of distortion for Spaceborne-airborne Bistatic SAR. 2008 China-Japan-Korea Post Graduate Research Conference on Electronics & Communications. CD-Rom
[37] Zijin Zuo , Xiaoling Zhang , Yang Yue. The comparison of two imaging algorithms for Spaceborne-airborne Bistatic SAR. 2008 China-Korea-Japan Graduates Workshop on Electronic Information. CD-Rom
[38] Yang Yue, XiaoLing Zhang, ZiJin Zuo. An imaging method and the correction of distortion for Spaceborne-airborne Bistatic SAR. IEEE International Geosciences and Remote Sensing Symposium, 2009. IV625-IV628
[39] Yang Yue, XiaoLing Zhang, Shijun; "Motion Compensation Method for Translational Variant Bistatic SAR using Auto-correlation Variance" IET RADAR CONFERENCE 2009. 42-43
[40] Auterman J L. Phase stability requirements for a bistatic SAR. IEEE National Radar Conference, 1984, 48-52.
[41] Lorti D C, Bowman J J. Will tactical aircraft use bistatic radar. Microwave Systems News, vol.8, no.9, Sept. 1978, 49-52, 54.
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[45] Wang R, Loffeld O, Ul-Ann Q, et al. A bistatic point target reference spectrum for general bistatic SAR processing. IEEE Geoscience and Remote Sensing Letters, 2008, 5(3): 517-521
[46] Ul-Ann Q, Loffeld O, Nies H, et al. A point target reference spectrum based on Loffeld’s Bistatic Formula (LBF) for hybrid configurations. Proc. of International Conference on Emerging Technologies, Pakistan, 2008:74-77
[2] Merrill I. Skolnik.雷达手册.北京:电子工业出版社,2003
[3]皮亦鸣等.合成孔径雷达成像原理.成都:电子科技大学出版社.2007
[4]袁孝康.星载合成孔径雷达导论.北京::国防工业出版社, 2003
[5]魏钟铨.合成孔径雷达卫星.北京:科学出版社, 2001
[6]张明友,吕幼新.信号与系统分析.成都:电子科技大学出版社,2000
[7]张贤达.现代信号处理.北京:清华大学出版社,2002
[8] Steven J. Leon. Linear algebra with applications.北京:机械工业出版社,2007
[9] Ian G. Cumming,Frank H. Wong.合成孔径雷达成像-算法与实现.北京:电子工业出版社, 2007
[10]张明友,吕明.信号检测与估计.北京:电子工业出版社, 2005
[11]向敬成,张明友.雷达系统.北京:电子工业出版社,2001
[12]保铮,邢孟道,王彤.雷达成像技术.北京:电子工业出版社,2006;
[13]师君.新型SAR技术与成像机理研究:[博士学位论文].电子科技大学,2009
[14] Shi jun; Zhang Xiaoling; Yang Jianyu; Translational variant bistatic SAR signal space-time feature and processing method, Geoscience and Remote Sensing Symposium, 2007. IGARSS 2007. IEEE International, 23-28 July 2007, 2140– 2143
[15] Shi Jun; Xiaoling Zhang; Jianyu Yang; Principle and Methods on Bistatic SAR Signal Processing via Time Correlation Geoscience and Remote Sensing, IEEE Transactions on Volume 46, Issue 10, Part 2, Oct. 2008, 3163– 3178
[16] Otmar Loffeld, Holger Nies, Valerij Peters, Stefan Knedlik. Models and useful relations for bistatic SAR processing. IEEE Trans.on Geosci. Remote Sensing. Oct. 2004, 42(10): 2031-2038.
[17] O. Loffeld, and A. Hein. SAR processing by‘inverse scaled Fourier transformation’. In Proc. EUSAR, Germany, 1996, 143-146.
[18] O. Loffeld, F. Schneider, and A. Hein. Focusing SAR images by inverse scaled Fourier transformation. In Proc. Int . Conf. Signal Process. Commun. Las Palmas, Spain, 1998, vol.2, 630-632.
[19] Zeng, Tao,Cherniakov, Mikhail; Long, Teng.Generalized approach to resolution analysis in BSAR. IEEE Transactions on Aerospace and Electronic Systems, v 41, n 2, April, 2005, pp 461-474;
[20] Jordan, R.The Seasat-A synthetic aperture radar system. IEEE Journal of Oceanic Engineering, Volume 5, Issue 2, April 1980, 154– 164;
[21] Way, J. Smith, E.A..The evolution of synthetic aperture radar systems and their progression to the EOS SAR. IEEE Transactions on Geoscience and Remote Sensing, Volume 29, Issue 6, Nov. 1991,962– 985;
[22]邓彦.机载双基地SAR成像算法及相关技术研究:[硕士学位论文].电子科技大学, 2006
[23] Minh N.Do, Martin Vetterli. The Contourlet Transform: An Efficient Directional Multiresolution Image Representation. IEEE Trans. On Image Processing, Dec.2006,14(12): 2091-2105
[24]龚镇强.双基地SAR成像处理算法研究:[硕士学位论文].电子科技大学, 2007
[25] Gong Zhenqiang, Zhang Xiaoling, Tian Zhong. Automobile-Based Bistatic SAR processing and experimental results. Proc, IGARSS 2007, Barcelona, Spain, July, 2007
[26] Y. Neo, F. Wong, and I. G. Cumming. A two-dimensional spectrum for bistatic SAR processing using series reversion. IEEE Geosci. Remote Sens. Lett., 2007, 4(1): 93–96,.
[27] Yew Lam Neo, Frank H. Wong, Ian G. Cumming. Processing of Azimuth-Invariant Bistatic SAR Data Using the Range Doppler Algorithm. IEEE Trans.on Geosci. Remote Sensing. Jan. 2008, 46(1): 14-20.
[28] Koba Matroshvili, Otmar Loffeld. Focusing of General Bistatic SAR Configuration Data With 2-D Inverse Scaled FFT. IEEE Trans.on Geosci. Remote Sensing. Oct.2006, 44(10):2718-2726.
[29]王宏禹.非平稳随机信号分析与处理.北京,国防工业出版社. 1999
[30] Roger F, Jean-Claude S, Jean-Marc G, Philippe D, Didier M. Impact of Ambiguities in Multistatic SAR. IGARSS '2004
[31] Zhe Liu, Jianyu Yang, Xiaoling Zhang, Yiming Pi. Study on Spaceborne/Airborne Hybrid Bistatic SAR Image Formation in Frequency Domain[J]. IEEE Geoscience and Remote Sensing Letters, October, 2008, 5(4):578-582.
[32] Zhe Liu,Jianyu Yang,Xiaoling Zhang Yiming Pi. Spaceborne/Airborne Hybrid Bistatic SAR Frequency Domain Imaging Processing Algorithm[J]. Chinese Journal of Electronics, July, 2008, 17(3): 487-491.
[33] Zhe Liu, Jianyu Yang, Xiaoling Zhang, Yiming Pi. Frequency Domain Imaging Algorithm forSpaceborneAirborne Hybrid Bistatic SAR[C]. IEEE International Geoscience and Remote Sensing Symposium, IGARSS 2007, 2008, p 842-845.
[34] Zhe Liu, Jianyu Yang, Xiaoling Zhang, Yiming Pi .An Approximated Analytical Solution for Two-Dimensional Spectrum of Spaceborne/Airborne Hybrid Bistatic SAR[C]. ICCCAS’2007.
[35] Zhe Liu, Yanhai Shang, Jianyu Yang. Imaging Performance Analysis of Space-Air Non-Cooperative BSAR [C], International Conference on Radar’2006.
[36] Yang Yue; Zhang Xiaoling; Zuo Zijin . An imaging method and the correction of distortion for Spaceborne-airborne Bistatic SAR. 2008 China-Japan-Korea Post Graduate Research Conference on Electronics & Communications. CD-Rom
[37] Zijin Zuo , Xiaoling Zhang , Yang Yue. The comparison of two imaging algorithms for Spaceborne-airborne Bistatic SAR. 2008 China-Korea-Japan Graduates Workshop on Electronic Information. CD-Rom
[38] Yang Yue, XiaoLing Zhang, ZiJin Zuo. An imaging method and the correction of distortion for Spaceborne-airborne Bistatic SAR. IEEE International Geosciences and Remote Sensing Symposium, 2009. IV625-IV628
[39] Yang Yue, XiaoLing Zhang, Shijun; "Motion Compensation Method for Translational Variant Bistatic SAR using Auto-correlation Variance" IET RADAR CONFERENCE 2009. 42-43
[40] Auterman J L. Phase stability requirements for a bistatic SAR. IEEE National Radar Conference, 1984, 48-52.
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