具有移变特性的星机联合双基地SAR成像处理算法的研究
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摘要
星机联合双基地SAR(Spaceborne Airborne Bistatic SAR,SA-BiSAR)系统,是由卫星和飞机组成的一种新型双基地SAR(BiSAR)系统,不仅继承了BiSAR的诸多优点,还在扩大目标照射范围、节约数据获取成本等方面显示了独特的优势。作为一种典型的移变BiSAR系统,SA-BiSAR已经成为雷达成像应用的一个新的研究热点。本文针对SA-BiSAR系统的特点着重研究了适用于该系统的成像算法,做了如下研究工作及创新:
1、研究了SA-BiSAR系统的成像机理。首先分析了任意飞行模式的SA-BiSAR系统的几何模型,然后基于系统收发平台速度差高度差很大、卫星过顶时间短的特点建立了近似距离历史模型。最后借助模糊函数的分析手段,研究了系统的空间分辨率。
2、提出一种基于降维处理的SA-BiSAR系统成像方法。首先根据近似距离历史模型得到适用于SA-BiSAR系统的多普勒参数,再利用降维处理来实现二维聚焦。然后根据二维聚焦表达式得到目标的畸变位置与实际位置的对应关系,利用反演投影法对聚焦图像中的畸变进行校正,从而恢复出原始场景。
3、针对降维处理后的图像畸变提出了几何校正法。首先分析了聚焦图像中畸变的成因,然后引入畸变倾角并推导其表达式,从而得出畸变坐标与真实坐标的几何对应关系,最后由畸变倾角以及畸变坐标得到目标的真实坐标,完成非线性的几何校正。该方法弥补了反演投影法处理速度慢的缺点。
4、研究了目前最具代表性的求解二维频谱的模型:LBF模型和ELBF模型。由于这两种模型十分繁琐,且LBF模型不适用于SA-BiSAR系统,ELBF模型也仅限于星机速度夹角较小的情况。于是本文提出一种SA-BiSAR系统二维频谱的求解方法。该方法利用该系统的近似距离历史表达式,求得驻定相位点,从而推导出二维频谱的近似表达式。最后基于传统ωk成像算法思路对SA-BiSAR系统进行了MATLAB仿真,验证了该频域算法的有效性。
Spaceborne-Airborne Bistatic SAR (SA-BiSAR), which is a new Bistatic SAR composed by the spacecraft and aircraft, not only inherit many advantages of BiSAR, but also demonstrate some unique advantages, such as expanding the scope of target scene, saving the costs of data acquisition, and so on. As being a typical translational variant BiSAR, SA-BiSAR has become a new hotspot in radar imaging application research. In this dissertation, basing on the characteristics of SA-BiSAR, the imaging algorithm of the system has been focused on, and the main research and contributions are as follows:
1. The SA-BiSAR system is studied: Establish the general geometry and signal models of SA-BiSAR firstly, and base on these, the range history and the range cell migration (RCM) are disgussed. Then based on the characteristics of the System model, the range history has been approximated sensibly. At last, the spatial resolutions of bistatic SAR have been derived from the ambiguity function.
2. An imaging algorithm for SA-BiSAR with any flight mode is proposed. First, use the range history approximated of SA-BiSAR to derivate the Doppler parameter suitably for SA-BiSAR system, which is the key point to the focus of the imaging algorithm basing on the Dimension-reduction Focus. Then use the Inverse-Projection method to correct distortion basing on the formula of final focus expression.
3. Analysis the causes of the distortion, which appears after the Dimension-reduction Focus. Thus a geometric correction method for correction distortion is proposed. This method can quickly complete the distortion correction and compensate for the slower processing speed weaknesses of the Inverse-Projection method.
4. The LBF model and ELBF model have been detailedly studied. Being the most representative methods of solving two-dimensional spectrum for translational variant BiSAR currently, they are combined with 2-D ISFFT imaging algorithm in this dissertation, and have been compared the imaging results by MATLAB simulation. Basing on the reasonable approximation of range history, an imaging algorithm in two-dimensional frequency-domain is proposed for SA-BiSAR system. The key point of this algorithm is getting the two-dimensional spectrum basing on the inherent characteristics of SA-BiSAR system and the Expression of the range history. Then combined with the reference function multiplication (RFM), and the stolt interpolation to complete imaging method.
1、研究了SA-BiSAR系统的成像机理。首先分析了任意飞行模式的SA-BiSAR系统的几何模型,然后基于系统收发平台速度差高度差很大、卫星过顶时间短的特点建立了近似距离历史模型。最后借助模糊函数的分析手段,研究了系统的空间分辨率。
2、提出一种基于降维处理的SA-BiSAR系统成像方法。首先根据近似距离历史模型得到适用于SA-BiSAR系统的多普勒参数,再利用降维处理来实现二维聚焦。然后根据二维聚焦表达式得到目标的畸变位置与实际位置的对应关系,利用反演投影法对聚焦图像中的畸变进行校正,从而恢复出原始场景。
3、针对降维处理后的图像畸变提出了几何校正法。首先分析了聚焦图像中畸变的成因,然后引入畸变倾角并推导其表达式,从而得出畸变坐标与真实坐标的几何对应关系,最后由畸变倾角以及畸变坐标得到目标的真实坐标,完成非线性的几何校正。该方法弥补了反演投影法处理速度慢的缺点。
4、研究了目前最具代表性的求解二维频谱的模型:LBF模型和ELBF模型。由于这两种模型十分繁琐,且LBF模型不适用于SA-BiSAR系统,ELBF模型也仅限于星机速度夹角较小的情况。于是本文提出一种SA-BiSAR系统二维频谱的求解方法。该方法利用该系统的近似距离历史表达式,求得驻定相位点,从而推导出二维频谱的近似表达式。最后基于传统ωk成像算法思路对SA-BiSAR系统进行了MATLAB仿真,验证了该频域算法的有效性。
Spaceborne-Airborne Bistatic SAR (SA-BiSAR), which is a new Bistatic SAR composed by the spacecraft and aircraft, not only inherit many advantages of BiSAR, but also demonstrate some unique advantages, such as expanding the scope of target scene, saving the costs of data acquisition, and so on. As being a typical translational variant BiSAR, SA-BiSAR has become a new hotspot in radar imaging application research. In this dissertation, basing on the characteristics of SA-BiSAR, the imaging algorithm of the system has been focused on, and the main research and contributions are as follows:
1. The SA-BiSAR system is studied: Establish the general geometry and signal models of SA-BiSAR firstly, and base on these, the range history and the range cell migration (RCM) are disgussed. Then based on the characteristics of the System model, the range history has been approximated sensibly. At last, the spatial resolutions of bistatic SAR have been derived from the ambiguity function.
2. An imaging algorithm for SA-BiSAR with any flight mode is proposed. First, use the range history approximated of SA-BiSAR to derivate the Doppler parameter suitably for SA-BiSAR system, which is the key point to the focus of the imaging algorithm basing on the Dimension-reduction Focus. Then use the Inverse-Projection method to correct distortion basing on the formula of final focus expression.
3. Analysis the causes of the distortion, which appears after the Dimension-reduction Focus. Thus a geometric correction method for correction distortion is proposed. This method can quickly complete the distortion correction and compensate for the slower processing speed weaknesses of the Inverse-Projection method.
4. The LBF model and ELBF model have been detailedly studied. Being the most representative methods of solving two-dimensional spectrum for translational variant BiSAR currently, they are combined with 2-D ISFFT imaging algorithm in this dissertation, and have been compared the imaging results by MATLAB simulation. Basing on the reasonable approximation of range history, an imaging algorithm in two-dimensional frequency-domain is proposed for SA-BiSAR system. The key point of this algorithm is getting the two-dimensional spectrum basing on the inherent characteristics of SA-BiSAR system and the Expression of the range history. Then combined with the reference function multiplication (RFM), and the stolt interpolation to complete imaging method.
引文
[1]向敬成,张明友:“雷达系统”, [c]电子工业出版社,2001年5月;
[2] Ian G. Cumming, Frank H. Wong. Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation.合成孔径雷达成像-算法与实现。北京:电子工业出版社,2007,10
[3]汤子跃,张守融.双站SAR系统原理.北京:科学出版社,2003,2-7
[4] 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, pp.630-632.
[5] Yew. Lam. Neo, Frank. H. Wong, and Ian. G. Cumming,“Processing of azimuth-invariant bistatic SAR data using the range Doppler algorithm,”IEEE Trans. Geosci. Remote Sens., vol. 46, no. 1, pp. 14–21, Jan. 2008.
[6] 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 Page(s):2140-2143.
[7] O. Loffeld, and A. Hein. SAR processing by‘inverse scaled Fourier transformation’. In Proc. EUSAR, Germany, 1996, pp.143-146.
[8]刘喆，杨建宇，张晓玲，“星机双基地SAR二维频谱解析解求解方法研究”[J],《电子与信息学报》,v 30, n 9, 2008年9月, p 2073-2076.
[9] 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
[10] Koba Natroshvili,Otmar Loffeld, Amaya Medrano Ortiz, and Stefan Knedlik.“Focusing of General Bistatic SAR Configuration DataWith 2-Dinverse Scaled FFT”. IEEE Transactions on Geoscience and Remote Sensing, vol.44, No.10, October 2006.
[11] Shi Jun; Xiaoling Zhang; Jianyu Yang; Principle and Methods on Bistatic SAR SignalProcessing via Time Correlation Geoscience and Remote Sensing, IEEE Transactions on Volume 46, Issue 10, Part 2, Oct. 2008 Page(s):3163– 3178
[12]皮亦鸣,杨建宇等,合成孔径雷达成像原理,成都:电子科技大学出版社,2007
[13] Otmar Loffeld, Nies H, Peters V, et al. Models and useful relations for bistatic SAR processing. IEEE Transactions on Geoscience and Remote Sensing, 2004, 42(10):2031-2038
[14]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,2008
[15]保铮等,雷达成像技术。北京:电子工业出版社,2005.
[16] U. Gebhardt, O. Loffeld, H. Nies, K. Natroshvili, S. Knedlik;“Bistatic Space Borne / Airborne Experiment:Geometrical Modeling and Simulation”, IEEE, vol.42, July 2006 Page(s):1832-1835.
[17]袁孝康.星载合成孔径雷达导论.北京:国防工业出版社, 2003
[18] Shi jun; Zhang Xiaoling; Yang Jianyu,“Translational variant bistatic SAR signal space-time feature and processing method”, Geosciences and Remote Sensing Symposium, 2007. IGARSS 2007. IEEE International, 23-28 July 2007, pp. 2140– 2143, (2007)
[19]刘永坦.雷达成像技术.哈尔滨:哈尔滨工业大学出版社,1999年
[20] Krieger G, Fiedler H, Houman D, et al. Analysis of system concepts for bi- and multi-static SAR missions. IEEE International Geoscience and Remote Sensing Symposium, 2003, vol.2, pp.770-772.
[21] S.samo, Whinnery, Van Duzer, The Bistatic Radar equation for Randomly Distributed Targets, fields and waves in communication Electronics. New York: Wiley, 1965 Sec.3.12 and 3.13.
[22] Tsao, T., Slamani, M., Varshney, P., Weiner, D., Schwarzlander, H. Ambiguity function for a bistatic radar. IEEE Transactions on Aerospace and Electronic Systems, 33,3(1997), 1041-1051.
[23]邵甜鸽,双基地SAR空间分辨特性的研究:[硕士学位论文].电子科技大学,2007.
[24] Tao Zeng; Cherniakov, M.; Teng Long, Generalized approach to resolution analysis in BSAR. Aerospace and Electronic Systems, IEEE Transactions on;Volume 41, Issue 2, April 2005 Page(s):461-474.
[25] Cherniakov, M, Ambiguity function for bistatic SAR and its application in SS-BSAR performance analysis. Presented at the Intermational Conference RADAR-2003, Adelaide, Australia, 2003.
[26] Auterman J L. Phase stability requirements for a bistatic SAR. Proc. of IEEE National Radar Conference, Atlanta, USA, 1984:48-52
[27] Fiedler H, Krieger G, Jochim F, et al. Analysis of bistatic configurations for spaceborne SAR interferometry. Proc. of European Conference on Synthetic Aperture Radar(EUSAR), Cologne, Germany, 2002:29-32
[28] Lee P F, James K. The RADARSAT-2/3 topographic mission. International Geoscience and Remote Sensing Symposium(IGARSS), Sydney, Australia, 2001:499-501
[29] Wendler M, Krieger G, Horn R. Results of a bistatic airborne SAR experiment. Proc. of International Radar Symposium, Dresden, Germany, 2003:247-253
[30] Hsu Y S, Loreti D C. Spaceborne bistatic radar - an overview. IEE Proc. Radar Sonar Navigation, 1986, 133(7):642-648
[31] 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
[32] 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
[33] Ul-Ann Q, Loffeld O, Nies H, et al. Optimizing the Individual Azimuth Contribution of Transmitter and Receiver Phase terms in Loffeld's Bistatic Formula (LBF) for Bistatic SAR Processing. International Geoscience and Remote Sensing Symposimu(IGARSS), 2008: 455-458
[34] Neo Y L. A two-dimensional spectrum for bistatic SAR processing using series reversion. IEEE Geoscience and Remote Sensing Letters, 2007, 4(1):93-96
[35] Neo Y L, Wong F H, Cumming I G. A comparison of point target spectra derived for bistatic SAR processing. IEEE Transactions on Geoscience and Remote Sensing, 2008, 46(9):2481-2492
[36]刘喆，星机联合双基地SAR成像理论的研究:[博士学位论文].电子科技大学,2009.
[37]武俊杰,双基地斜视合成孔径雷达成像技术研究:[硕士学位论文].电子科技大学,2007.
[38]钱钟卿,具有空变特性的移变双基地SAR成像算法研究:[硕士学位论文].电子科技大学,2009.
[39] Gong Zhenqiang, Zhang Xiaoling, Tian Zhong,“Automobile-Based Bistatic SAR processing and experimental results”, Proc, IGARSS 2007, Barcelona, Spain, July, 2007
[40] 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, v 5, n 4, October, 2008, p 578-582.
[41] Zhe Liu,Jianyu Yang,Xiaoling Zhang Yiming Pi. Spaceborne/Airborne Hybrid Bistatic SAR Frequency Domain Imaging Processing Algorithm[J]. Chinese Journal of Electronics, v 17, n 3, July, 2008, p 487-491.
[42]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
[43] Zhe Liu, Jianyu Yang, Xiaoling Zhang, Yiming Pi. Frequency Domain Imaging Algorithm for SpaceborneAirborne Hybrid Bistatic SAR[C]. IEEE International Geoscience and Remote Sensing Symposium, IGARSS 2007, 2008, p 842-845.
[44] 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.
[45]师君,新型合成孔径雷达原理与成像技术研究:[博士学位论文].电子科技大学,2009.
[46] Zhe Liu, Yanhai Shang, Jianyu Yang. Imaging Performance Analysis of Space-Air Non-Cooperative BSAR [C], International Conference on Radar’2006.
[47]魏钟铨.合成孔径雷达卫星.北京:科学出版社, 2001.
[2] Ian G. Cumming, Frank H. Wong. Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation.合成孔径雷达成像-算法与实现。北京:电子工业出版社,2007,10
[3]汤子跃,张守融.双站SAR系统原理.北京:科学出版社,2003,2-7
[4] 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, pp.630-632.
[5] Yew. Lam. Neo, Frank. H. Wong, and Ian. G. Cumming,“Processing of azimuth-invariant bistatic SAR data using the range Doppler algorithm,”IEEE Trans. Geosci. Remote Sens., vol. 46, no. 1, pp. 14–21, Jan. 2008.
[6] 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 Page(s):2140-2143.
[7] O. Loffeld, and A. Hein. SAR processing by‘inverse scaled Fourier transformation’. In Proc. EUSAR, Germany, 1996, pp.143-146.
[8]刘喆，杨建宇，张晓玲，“星机双基地SAR二维频谱解析解求解方法研究”[J],《电子与信息学报》,v 30, n 9, 2008年9月, p 2073-2076.
[9] 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
[10] Koba Natroshvili,Otmar Loffeld, Amaya Medrano Ortiz, and Stefan Knedlik.“Focusing of General Bistatic SAR Configuration DataWith 2-Dinverse Scaled FFT”. IEEE Transactions on Geoscience and Remote Sensing, vol.44, No.10, October 2006.
[11] Shi Jun; Xiaoling Zhang; Jianyu Yang; Principle and Methods on Bistatic SAR SignalProcessing via Time Correlation Geoscience and Remote Sensing, IEEE Transactions on Volume 46, Issue 10, Part 2, Oct. 2008 Page(s):3163– 3178
[12]皮亦鸣,杨建宇等,合成孔径雷达成像原理,成都:电子科技大学出版社,2007
[13] Otmar Loffeld, Nies H, Peters V, et al. Models and useful relations for bistatic SAR processing. IEEE Transactions on Geoscience and Remote Sensing, 2004, 42(10):2031-2038
[14]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,2008
[15]保铮等,雷达成像技术。北京:电子工业出版社,2005.
[16] U. Gebhardt, O. Loffeld, H. Nies, K. Natroshvili, S. Knedlik;“Bistatic Space Borne / Airborne Experiment:Geometrical Modeling and Simulation”, IEEE, vol.42, July 2006 Page(s):1832-1835.
[17]袁孝康.星载合成孔径雷达导论.北京:国防工业出版社, 2003
[18] Shi jun; Zhang Xiaoling; Yang Jianyu,“Translational variant bistatic SAR signal space-time feature and processing method”, Geosciences and Remote Sensing Symposium, 2007. IGARSS 2007. IEEE International, 23-28 July 2007, pp. 2140– 2143, (2007)
[19]刘永坦.雷达成像技术.哈尔滨:哈尔滨工业大学出版社,1999年
[20] Krieger G, Fiedler H, Houman D, et al. Analysis of system concepts for bi- and multi-static SAR missions. IEEE International Geoscience and Remote Sensing Symposium, 2003, vol.2, pp.770-772.
[21] S.samo, Whinnery, Van Duzer, The Bistatic Radar equation for Randomly Distributed Targets, fields and waves in communication Electronics. New York: Wiley, 1965 Sec.3.12 and 3.13.
[22] Tsao, T., Slamani, M., Varshney, P., Weiner, D., Schwarzlander, H. Ambiguity function for a bistatic radar. IEEE Transactions on Aerospace and Electronic Systems, 33,3(1997), 1041-1051.
[23]邵甜鸽,双基地SAR空间分辨特性的研究:[硕士学位论文].电子科技大学,2007.
[24] Tao Zeng; Cherniakov, M.; Teng Long, Generalized approach to resolution analysis in BSAR. Aerospace and Electronic Systems, IEEE Transactions on;Volume 41, Issue 2, April 2005 Page(s):461-474.
[25] Cherniakov, M, Ambiguity function for bistatic SAR and its application in SS-BSAR performance analysis. Presented at the Intermational Conference RADAR-2003, Adelaide, Australia, 2003.
[26] Auterman J L. Phase stability requirements for a bistatic SAR. Proc. of IEEE National Radar Conference, Atlanta, USA, 1984:48-52
[27] Fiedler H, Krieger G, Jochim F, et al. Analysis of bistatic configurations for spaceborne SAR interferometry. Proc. of European Conference on Synthetic Aperture Radar(EUSAR), Cologne, Germany, 2002:29-32
[28] Lee P F, James K. The RADARSAT-2/3 topographic mission. International Geoscience and Remote Sensing Symposium(IGARSS), Sydney, Australia, 2001:499-501
[29] Wendler M, Krieger G, Horn R. Results of a bistatic airborne SAR experiment. Proc. of International Radar Symposium, Dresden, Germany, 2003:247-253
[30] Hsu Y S, Loreti D C. Spaceborne bistatic radar - an overview. IEE Proc. Radar Sonar Navigation, 1986, 133(7):642-648
[31] 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
[32] 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
[33] Ul-Ann Q, Loffeld O, Nies H, et al. Optimizing the Individual Azimuth Contribution of Transmitter and Receiver Phase terms in Loffeld's Bistatic Formula (LBF) for Bistatic SAR Processing. International Geoscience and Remote Sensing Symposimu(IGARSS), 2008: 455-458
[34] Neo Y L. A two-dimensional spectrum for bistatic SAR processing using series reversion. IEEE Geoscience and Remote Sensing Letters, 2007, 4(1):93-96
[35] Neo Y L, Wong F H, Cumming I G. A comparison of point target spectra derived for bistatic SAR processing. IEEE Transactions on Geoscience and Remote Sensing, 2008, 46(9):2481-2492
[36]刘喆，星机联合双基地SAR成像理论的研究:[博士学位论文].电子科技大学,2009.
[37]武俊杰,双基地斜视合成孔径雷达成像技术研究:[硕士学位论文].电子科技大学,2007.
[38]钱钟卿,具有空变特性的移变双基地SAR成像算法研究:[硕士学位论文].电子科技大学,2009.
[39] Gong Zhenqiang, Zhang Xiaoling, Tian Zhong,“Automobile-Based Bistatic SAR processing and experimental results”, Proc, IGARSS 2007, Barcelona, Spain, July, 2007
[40] 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, v 5, n 4, October, 2008, p 578-582.
[41] Zhe Liu,Jianyu Yang,Xiaoling Zhang Yiming Pi. Spaceborne/Airborne Hybrid Bistatic SAR Frequency Domain Imaging Processing Algorithm[J]. Chinese Journal of Electronics, v 17, n 3, July, 2008, p 487-491.
[42]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
[43] Zhe Liu, Jianyu Yang, Xiaoling Zhang, Yiming Pi. Frequency Domain Imaging Algorithm for SpaceborneAirborne Hybrid Bistatic SAR[C]. IEEE International Geoscience and Remote Sensing Symposium, IGARSS 2007, 2008, p 842-845.
[44] 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.
[45]师君,新型合成孔径雷达原理与成像技术研究:[博士学位论文].电子科技大学,2009.
[46] Zhe Liu, Yanhai Shang, Jianyu Yang. Imaging Performance Analysis of Space-Air Non-Cooperative BSAR [C], International Conference on Radar’2006.
[47]魏钟铨.合成孔径雷达卫星.北京:科学出版社, 2001.