SAR解多普勒模糊与双基SAR成像算法研究
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摘要
合成孔径雷达(SAR)是一种非常重要的遥感工具,相对于光学遥感和其它微波遥感设备,具有一些独特的优点。本论文主要对SAR成像中的两个相关内容进行了深入的研究：其一为SAR多普勒中心估计中的解多普勒模糊方法,其二为双基SAR成像算法。论文内容可概括为如下六部分：
第一部分,提出了一种SAR多普勒中心估计中的解多普勒模糊的新方法。通过对SAR回波信号进行分析发现：在压缩方位时间／距离频率域内,所有目标的轨迹所占据的距离频率带宽相同而且它们所呈现的斜率也相同,而此斜率与多普勒模糊数成正比。本部分提出的解多普勒模糊的新方法正是基于上述事实的。为了测量上面提到的斜率,给出了一种简化的Radon变换。在搜索Radon变换后图像中的“能量聚集点”时,利用熵来改善算法的稳健性。这种新的解多普勒模糊方法可直接得到多普勒模糊数的可靠估计,而且解多普勒模糊与估计基带多普勒中心是相互独立的。理论分析和实验结果表明,这种新的解多普勒模糊方法对中、高对比度的场景非常有效。除此之外,此方法还具有这样一个优点：只要场景中的运动目标所引起的多普勒频移不超过一个PRF,则运动目标不会对多普勒模糊数的估计结果造成影响。
第二部分,在Neo提出的MSR(级数反演)双基二维谱的基础上,提出了两种处理双基SAR数据的OMEGA-K成像算法,即一种简易的OMEGA-K算法和一种改进的OMEGA-K算法。推导这两种OMEGA-K算法的关键步骤是推导其距离频率映射函数,而推导距离频率映射函数的关键是如何对二维谱进行线性化。对于简易OMEGA-K算法,二维谱线性化的关键是利用了一个角度近似假设,而对于改进OMEGA-K算法,二维谱线性化的关键是在双基几何模型的地平面上引入一个参考向量(值得注意的是,在本部分中还详细研究了该参考向量的最优方向,而此最优方向为这样一个方向：在此方向上的所有点目标具有相同的零方位时刻瞬时多普勒频率)。对于中等双基配置结构(即双基基线不太长的情况),两种算法的聚焦性能差别不大,均能够取得较好的成像性能,此时,简易OMEGA-K算法的运算量较小,易于编程实现。对于极端的双基配置结构(即双基基线较长或合成孔径时间较长的情况),改进的OMEGA-K算法在聚焦性能上明显优于简易OMEGA-K算法,因此极端的双基配置结构适合用改进的OMEGA-K算法进行聚焦成像。
第三部分,针对已有的MSR双基距离多普勒算法,提出了一种更新聚焦函数所需的距离导数的新方法。推导这种方法主要利用了两点：第一点是在双基SAR几何模型的地平面上引入一个参考向量,第二点是利用了级数反演原理。这种新方法的主要特点是其具有“解析性”。因此,这种新方法易于编程实现且比较精确。值得注意的是,本部分提出的这种更新成像算法所需参数的新方法还用于了其它的双基成像算法(见下面将要提到的第四部分和第六部分)。
0第四部分,针对混合星载／机载双基SAR这种特殊的配置结构,对MSR双基二维谱进行了推广,得到了一种推广的MSR(EMSR)双基二维谱。这种EMSR双基二维谱适合处理混合双基SAR数据。为了推导EMSR双基二维谱,我们首先推导了“等效平移不变方位时间”。通过分析发现,该等效平移不变方位时间可以从物理意义上解释为发射天线平移不变方位时间与接收天线平移不变方位时间的加权和,而加权因子恰好分别为发射天线和接收天线的方位调频率与双基总的方位调频率之比。在推导EMSR二维谱的过程中,我们还推导了一个重要的参数,即“等效平台速度”。利用该等效平台速度,可以把聚焦后的SAR图像的坐标校正到地面方位坐标。本部分另外一个重点是把所推导的EMSR双基二维谱应用到MSR双基距离多普勒算法中。在应用MSR双基距离多普勒算法的过程中,利用了第三部分给出的更新距离导数的新方法。对于混合星载／机载双基SAR距离多普勒算法,本部分对若干问题进行了详细讨论,比如SAR图像坐标校正问题,确定方位不变区域大小的问题。
第五部分,利用“把双基SAR系统等效为单基SAR系统”的思想,推导了一种新的双基二维谱。这种新的双基二维谱的相位包含两部分：“等效单基”相位部分与“双基变形”相位部分。推导这种新的双基二维谱的关键步骤是利用个包含“一个三次项与一个四次项”的“代数算子”来补偿“双根号”与“单根号”之差,从而在补偿后,双基SAR系统可以等效为单基SAR系统,进而得到一种新的双基二维谱。这种新双基二维谱可以看作孙进平的二维谱的推广与改进,并且,它融入了"Rocca's smile"算子的思想。这种新的双基二维谱的相位可精确到四次项,并且此二维谱适用于“一般意义”上的双基SAR结构配置(如雷达平台速度不相等,雷达平台飞行轨迹不平行,雷达平台高度不相等)。另外,本部分还从理论上分析对比了四种双基二维谱(包括本部分推导的双基二维谱、孙进平的二维谱、LBF二维谱以及ELBF二维谱)并用仿真实验比较了它们的聚焦性能。理论分析与仿真结果表明本部分推导的新双基二维谱的应用范围最广泛且精度最高。
第六部分,基于第五部分推导的等效双基二维谱,推导了一种新的双基距离多普勒算法。为了推导这种算法,首先从二维谱的“等效单基”相位中分解出“二次距离压缩”项,然后把此项与“双基变形”相位项合并从而形成一个新的“双基变形”相位项。对于新的“双基变形”相位项,由于它是空间慢变的,因此我们可以在二维频率域内以“分块”的方式(在同一块内认为“双基变形”相位项不变)把其消掉。为了解决“距离走动”相位项与“方位调制”相位项随距离变化的问题,对第三部分给出的用于MSR距离多普勒算法的距离导数更新的方法作稍微改动,使得此方法能够对三个等效参数(即等效距离、等效速度以及等效斜视角)沿着距离进行有效更新。本部分所推导的距离多普勒算法易于编程实现,因为“距离走动”与“方位调制”的表达式具有“简洁闭合”的形式(而非复杂的级数展开形式)。就成像步骤而言,本部分推导的距离多普勒算法与传统单基距离多普勒算法相比,只是多了一个“更新等效参数”的步骤,这意味着传统的单基距离多普勒算法经过较小修改后可直接用于对双基SAR数据进行成像。另外,本部分还给出了一种运动补偿的方法。此运动补偿方法是在传统的“两步补偿”法的基础上修改得到的,而修改的关键步骤是沿着参考向量进行“距离相关的运动补偿”。仿真实验的结果表明本部分给出的运动补偿方法是有效的。
Synthetic Aperture Radar (SAR) is a very important remote sensor. As compared with optical sensors and other microwave remote sensors, SAR has several unique advantages. This dissertation addresses issues of SAR imaging. The work of this dissertation mainly focuses on two aspects:The first one is a thorough study of resolving Doppler ambiguity which is an essential procedure for SAR Doppler centroid estimation, and the second one is a detailed investigation of digital processing algorithms for bistatic SAR data.
The main content of this dissertation is summarized as follows.
●The first part of this dissertation presents a novel method for resolving Doppler ambiguity. By analyzing the echoed SAR signal, it is found that in the compressed azimuth time and range frequency domain, all targets span the same range frequency bandwidth and exhibit the same slope which is just proportional to the Doppler ambiguity number. The aforementioned fact just makes the basis for the proposed method of Doppler ambiguity resolving. To measure the above-mentioned slope, a simplified Radon transform is utilized. The use of entropy in finding the maximum concentration of the Radon transformed image can improve the robustness of the method. The proposed method directly gives a reliable estimate of Doppler ambiguity number, and is independent of the baseband Doppler centroid estimation. Simulation and real SAR experimental results show that the proposed method works well in medium to high contrast scenes. Besides, the proposed method has another advantage that slowly-moving targets have no influence on the estimate of the Doppler ambiguity number, as long as the Doppler shift induced by these slowly-moving targets is not greater than one PRF.
●Based on Neo's method-of-series-reversion (MSR) 2-D spectrum, the second part of this dissertation proposes two OMEGA-K algorithms for focusing the bistatic data:The first OMEGA-K algorithm is an easily-implemented algorithm and the second one is an improved algorithm. The key step of deriving the two OMEGA-K algorithms is to derive their range frequency mapping function, and the key of deriving the range frequency mapping function is how to linearize the 2-D spectrum. For the easily-implemented OMEGA-K algorithm, the 2-D spectrum is linearized by adopting an angle approximation, whereas for the improved OMEGA-K algorithm, the 2-D spectrum is linearized by introducing a reference vector on the ground plane of the bistatic geometry. For the improved OMEGA-K algorithm, the optimum direction of the reference vector, along which the best performance of OMEGA-K algorithm is achieved, is also determined; this optimum direction is approximately such one along which all targets have the same instantaneous Doppler frequency as the reference target at zero azimuth time. Simulation results show that for moderate bistatic configurations (i.e., the bistatic baseline is relatively short), both the two algorithms can yield a well focused SAR image (in this case, the first OMEGA-K algorithm has a low computational load and thus is more efficient), whereas for extreme bistatic configurations (i.e., the bistatic baseline is relatively long and/or the synthetic aperture time is relatively long), the second OMEGA-K algorithm can achieve a remarkable performance improvement over the first OMEGA-K algorithm, and thus for more extreme configurations, the second OMEGA-K algorithm (i.e., the improved algorithm) is recommended to be used.
●The third part of this dissertation gives an analytical method to update the range derivatives for the MSR-based range Doppler algorithm (RDA). The proposed method mainly exploits two points:The first one is the introduction of a reference vector on the ground plane of the bistatic geometry, and the second one is the use of the principle of series reversion. The proposed method is accurate and easy to implement, since it is analytical. Note that the proposed method of updating the required parameters along range is also applied to other bistatic processing algorithms (see the fourth and sixth parts of this dissertation which will be mentioned in the following).
●Based on Neo's MSR 2-D spectrum, the fourth part of this dissertation derives an extended MSR (EMSR) 2-D spectrum for bistatic data processing. The EMSR 2-D spectrum is suitable for handling a special bistatic configuration, called the hybrid spaceborne/airborne bistatic SAR configuration. The key step of the derivation of the EMSR spectrum is to derive an equivalent translational invariance azimuth time (TIAT) for the bistatic geometry. It is found that the equivalent TIAT of the bistatic geometry can be physically interpreted to be a weighted sum of the transmitter TIAT and the receiver TIAT, and the weighting factors are just the ratios of the azimuth FM rate of the transmitter platform and the receiver platform to the overall azimuth FM rate, respectively. In the EMSR spectrum, an important parameter called the equivalent platform velocity, which is used to register the azimuth coordinate of the focused SAR image to the ground coordinate, is also derived. Then, we apply this newly derived EMSR spectrum to the MSR-based RDA. In developing the modified RDA, the new method for updating the required range derivatives for the MSR-based RDA which is given in the third part of this dissertation, is adapted to the newly derived EMSR spectrum. Besides, in this part, we also investigate several issues related to the modified RDA, including the SAR image registration and the determination of the azimuth-invariance region size.
●Based on the way of transforming the bistatic system into an equivalent one, the fifth part of this dissertation derives a new 2-D spectrum for bistatic SAR processing. For the newly derived 2-D spectrum, two phase terms are identified, the first one being an equivalent monostatic (EM) contribution and the second one corresponding to a bistatic deformation (BD) contribution. The key step of formulation of the 2-D spectrum is to compensate the difference between the double square-root (DSR) range equation and an equivalent single square-root (SSR) range equation by using an algebraic operator which consists of a third-order term plus a fourth-order term, so that the bistatic system can be transformed into an equivalent monostatic one. The new 2-D spectrum can be regarded as an extension of Sun's spectrum, and it also incorporates the concept of Rocca's smile operator. The new 2-D spectrum is exactly accurate up to the fourth-order phase term and it can handle a general bistatic SAR configuration with nonparallel flight tracks, unequal radar velocities and different heights of the transmitter and receiver. Besides, in this part, we also compare four bistatic 2-D spectra, i.e., the spectrum derived in this part, Sun's spectrum, LBF spectrum and the extended LBF (ELBF) spectrum. Theoretical analyses and simulation results show that the spectrum proposed in this part applies to a more general bistatic configuration and can achieve a better focusing performance than the other three spectra.
●Based on the new bistatic 2-D spectrum derived in the fifth part of this dissertation, a bistatic RDA is developed in the sixth part of this dissertation. In developing the RDA, the secondary-range-compression (SRC) term was first factored out from the EM term and then was incorporated into the BD term so that a new BD term is formed. To handle the problem of the space dependence of the new BD term, we can divide the whole scene into segments and then remove the new BD term using phase multiplies blockwise in the 2-D frequency domain, due to its slowly-varying property in space. To address the problem of the range dependence of the RCM term and the azimuth modulation term, the new method which is proposed for the MSR-based RDA in the third part of this dissertation is adapted, so that after adaptation, this method can effectively update the three equivalent parameters (i.e., the equivalent range, the equivalent velocity and the equivalent squint angle) along range. The proposed RDA is efficient and easy to implement, since the expressions of the RCM term and azimuth modulation both have a concise and closed form (rather than a Taylor expansion version). The proposed RDA almost has the same processing steps as the conventional monostatic RDA except for an extra procedure of updating the required equivalent parameters, which means that the conventional monostatic RDA can be readily applied to process the bistatic SAR data with minor modification. Besides, in this part, based on the conventional two-step method, we also present a motion compensation (MOCO) method for the proposed RDA. The key step of the proposed MOCO method is to perform range-dependent MOCO along the reference vector. Simulation results show that the proposed MOCO method is effective.
第一部分,提出了一种SAR多普勒中心估计中的解多普勒模糊的新方法。通过对SAR回波信号进行分析发现：在压缩方位时间／距离频率域内,所有目标的轨迹所占据的距离频率带宽相同而且它们所呈现的斜率也相同,而此斜率与多普勒模糊数成正比。本部分提出的解多普勒模糊的新方法正是基于上述事实的。为了测量上面提到的斜率,给出了一种简化的Radon变换。在搜索Radon变换后图像中的“能量聚集点”时,利用熵来改善算法的稳健性。这种新的解多普勒模糊方法可直接得到多普勒模糊数的可靠估计,而且解多普勒模糊与估计基带多普勒中心是相互独立的。理论分析和实验结果表明,这种新的解多普勒模糊方法对中、高对比度的场景非常有效。除此之外,此方法还具有这样一个优点：只要场景中的运动目标所引起的多普勒频移不超过一个PRF,则运动目标不会对多普勒模糊数的估计结果造成影响。
第二部分,在Neo提出的MSR(级数反演)双基二维谱的基础上,提出了两种处理双基SAR数据的OMEGA-K成像算法,即一种简易的OMEGA-K算法和一种改进的OMEGA-K算法。推导这两种OMEGA-K算法的关键步骤是推导其距离频率映射函数,而推导距离频率映射函数的关键是如何对二维谱进行线性化。对于简易OMEGA-K算法,二维谱线性化的关键是利用了一个角度近似假设,而对于改进OMEGA-K算法,二维谱线性化的关键是在双基几何模型的地平面上引入一个参考向量(值得注意的是,在本部分中还详细研究了该参考向量的最优方向,而此最优方向为这样一个方向：在此方向上的所有点目标具有相同的零方位时刻瞬时多普勒频率)。对于中等双基配置结构(即双基基线不太长的情况),两种算法的聚焦性能差别不大,均能够取得较好的成像性能,此时,简易OMEGA-K算法的运算量较小,易于编程实现。对于极端的双基配置结构(即双基基线较长或合成孔径时间较长的情况),改进的OMEGA-K算法在聚焦性能上明显优于简易OMEGA-K算法,因此极端的双基配置结构适合用改进的OMEGA-K算法进行聚焦成像。
第三部分,针对已有的MSR双基距离多普勒算法,提出了一种更新聚焦函数所需的距离导数的新方法。推导这种方法主要利用了两点：第一点是在双基SAR几何模型的地平面上引入一个参考向量,第二点是利用了级数反演原理。这种新方法的主要特点是其具有“解析性”。因此,这种新方法易于编程实现且比较精确。值得注意的是,本部分提出的这种更新成像算法所需参数的新方法还用于了其它的双基成像算法(见下面将要提到的第四部分和第六部分)。
0第四部分,针对混合星载／机载双基SAR这种特殊的配置结构,对MSR双基二维谱进行了推广,得到了一种推广的MSR(EMSR)双基二维谱。这种EMSR双基二维谱适合处理混合双基SAR数据。为了推导EMSR双基二维谱,我们首先推导了“等效平移不变方位时间”。通过分析发现,该等效平移不变方位时间可以从物理意义上解释为发射天线平移不变方位时间与接收天线平移不变方位时间的加权和,而加权因子恰好分别为发射天线和接收天线的方位调频率与双基总的方位调频率之比。在推导EMSR二维谱的过程中,我们还推导了一个重要的参数,即“等效平台速度”。利用该等效平台速度,可以把聚焦后的SAR图像的坐标校正到地面方位坐标。本部分另外一个重点是把所推导的EMSR双基二维谱应用到MSR双基距离多普勒算法中。在应用MSR双基距离多普勒算法的过程中,利用了第三部分给出的更新距离导数的新方法。对于混合星载／机载双基SAR距离多普勒算法,本部分对若干问题进行了详细讨论,比如SAR图像坐标校正问题,确定方位不变区域大小的问题。
第五部分,利用“把双基SAR系统等效为单基SAR系统”的思想,推导了一种新的双基二维谱。这种新的双基二维谱的相位包含两部分：“等效单基”相位部分与“双基变形”相位部分。推导这种新的双基二维谱的关键步骤是利用个包含“一个三次项与一个四次项”的“代数算子”来补偿“双根号”与“单根号”之差,从而在补偿后,双基SAR系统可以等效为单基SAR系统,进而得到一种新的双基二维谱。这种新双基二维谱可以看作孙进平的二维谱的推广与改进,并且,它融入了"Rocca's smile"算子的思想。这种新的双基二维谱的相位可精确到四次项,并且此二维谱适用于“一般意义”上的双基SAR结构配置(如雷达平台速度不相等,雷达平台飞行轨迹不平行,雷达平台高度不相等)。另外,本部分还从理论上分析对比了四种双基二维谱(包括本部分推导的双基二维谱、孙进平的二维谱、LBF二维谱以及ELBF二维谱)并用仿真实验比较了它们的聚焦性能。理论分析与仿真结果表明本部分推导的新双基二维谱的应用范围最广泛且精度最高。
第六部分,基于第五部分推导的等效双基二维谱,推导了一种新的双基距离多普勒算法。为了推导这种算法,首先从二维谱的“等效单基”相位中分解出“二次距离压缩”项,然后把此项与“双基变形”相位项合并从而形成一个新的“双基变形”相位项。对于新的“双基变形”相位项,由于它是空间慢变的,因此我们可以在二维频率域内以“分块”的方式(在同一块内认为“双基变形”相位项不变)把其消掉。为了解决“距离走动”相位项与“方位调制”相位项随距离变化的问题,对第三部分给出的用于MSR距离多普勒算法的距离导数更新的方法作稍微改动,使得此方法能够对三个等效参数(即等效距离、等效速度以及等效斜视角)沿着距离进行有效更新。本部分所推导的距离多普勒算法易于编程实现,因为“距离走动”与“方位调制”的表达式具有“简洁闭合”的形式(而非复杂的级数展开形式)。就成像步骤而言,本部分推导的距离多普勒算法与传统单基距离多普勒算法相比,只是多了一个“更新等效参数”的步骤,这意味着传统的单基距离多普勒算法经过较小修改后可直接用于对双基SAR数据进行成像。另外,本部分还给出了一种运动补偿的方法。此运动补偿方法是在传统的“两步补偿”法的基础上修改得到的,而修改的关键步骤是沿着参考向量进行“距离相关的运动补偿”。仿真实验的结果表明本部分给出的运动补偿方法是有效的。
Synthetic Aperture Radar (SAR) is a very important remote sensor. As compared with optical sensors and other microwave remote sensors, SAR has several unique advantages. This dissertation addresses issues of SAR imaging. The work of this dissertation mainly focuses on two aspects:The first one is a thorough study of resolving Doppler ambiguity which is an essential procedure for SAR Doppler centroid estimation, and the second one is a detailed investigation of digital processing algorithms for bistatic SAR data.
The main content of this dissertation is summarized as follows.
●The first part of this dissertation presents a novel method for resolving Doppler ambiguity. By analyzing the echoed SAR signal, it is found that in the compressed azimuth time and range frequency domain, all targets span the same range frequency bandwidth and exhibit the same slope which is just proportional to the Doppler ambiguity number. The aforementioned fact just makes the basis for the proposed method of Doppler ambiguity resolving. To measure the above-mentioned slope, a simplified Radon transform is utilized. The use of entropy in finding the maximum concentration of the Radon transformed image can improve the robustness of the method. The proposed method directly gives a reliable estimate of Doppler ambiguity number, and is independent of the baseband Doppler centroid estimation. Simulation and real SAR experimental results show that the proposed method works well in medium to high contrast scenes. Besides, the proposed method has another advantage that slowly-moving targets have no influence on the estimate of the Doppler ambiguity number, as long as the Doppler shift induced by these slowly-moving targets is not greater than one PRF.
●Based on Neo's method-of-series-reversion (MSR) 2-D spectrum, the second part of this dissertation proposes two OMEGA-K algorithms for focusing the bistatic data:The first OMEGA-K algorithm is an easily-implemented algorithm and the second one is an improved algorithm. The key step of deriving the two OMEGA-K algorithms is to derive their range frequency mapping function, and the key of deriving the range frequency mapping function is how to linearize the 2-D spectrum. For the easily-implemented OMEGA-K algorithm, the 2-D spectrum is linearized by adopting an angle approximation, whereas for the improved OMEGA-K algorithm, the 2-D spectrum is linearized by introducing a reference vector on the ground plane of the bistatic geometry. For the improved OMEGA-K algorithm, the optimum direction of the reference vector, along which the best performance of OMEGA-K algorithm is achieved, is also determined; this optimum direction is approximately such one along which all targets have the same instantaneous Doppler frequency as the reference target at zero azimuth time. Simulation results show that for moderate bistatic configurations (i.e., the bistatic baseline is relatively short), both the two algorithms can yield a well focused SAR image (in this case, the first OMEGA-K algorithm has a low computational load and thus is more efficient), whereas for extreme bistatic configurations (i.e., the bistatic baseline is relatively long and/or the synthetic aperture time is relatively long), the second OMEGA-K algorithm can achieve a remarkable performance improvement over the first OMEGA-K algorithm, and thus for more extreme configurations, the second OMEGA-K algorithm (i.e., the improved algorithm) is recommended to be used.
●The third part of this dissertation gives an analytical method to update the range derivatives for the MSR-based range Doppler algorithm (RDA). The proposed method mainly exploits two points:The first one is the introduction of a reference vector on the ground plane of the bistatic geometry, and the second one is the use of the principle of series reversion. The proposed method is accurate and easy to implement, since it is analytical. Note that the proposed method of updating the required parameters along range is also applied to other bistatic processing algorithms (see the fourth and sixth parts of this dissertation which will be mentioned in the following).
●Based on Neo's MSR 2-D spectrum, the fourth part of this dissertation derives an extended MSR (EMSR) 2-D spectrum for bistatic data processing. The EMSR 2-D spectrum is suitable for handling a special bistatic configuration, called the hybrid spaceborne/airborne bistatic SAR configuration. The key step of the derivation of the EMSR spectrum is to derive an equivalent translational invariance azimuth time (TIAT) for the bistatic geometry. It is found that the equivalent TIAT of the bistatic geometry can be physically interpreted to be a weighted sum of the transmitter TIAT and the receiver TIAT, and the weighting factors are just the ratios of the azimuth FM rate of the transmitter platform and the receiver platform to the overall azimuth FM rate, respectively. In the EMSR spectrum, an important parameter called the equivalent platform velocity, which is used to register the azimuth coordinate of the focused SAR image to the ground coordinate, is also derived. Then, we apply this newly derived EMSR spectrum to the MSR-based RDA. In developing the modified RDA, the new method for updating the required range derivatives for the MSR-based RDA which is given in the third part of this dissertation, is adapted to the newly derived EMSR spectrum. Besides, in this part, we also investigate several issues related to the modified RDA, including the SAR image registration and the determination of the azimuth-invariance region size.
●Based on the way of transforming the bistatic system into an equivalent one, the fifth part of this dissertation derives a new 2-D spectrum for bistatic SAR processing. For the newly derived 2-D spectrum, two phase terms are identified, the first one being an equivalent monostatic (EM) contribution and the second one corresponding to a bistatic deformation (BD) contribution. The key step of formulation of the 2-D spectrum is to compensate the difference between the double square-root (DSR) range equation and an equivalent single square-root (SSR) range equation by using an algebraic operator which consists of a third-order term plus a fourth-order term, so that the bistatic system can be transformed into an equivalent monostatic one. The new 2-D spectrum can be regarded as an extension of Sun's spectrum, and it also incorporates the concept of Rocca's smile operator. The new 2-D spectrum is exactly accurate up to the fourth-order phase term and it can handle a general bistatic SAR configuration with nonparallel flight tracks, unequal radar velocities and different heights of the transmitter and receiver. Besides, in this part, we also compare four bistatic 2-D spectra, i.e., the spectrum derived in this part, Sun's spectrum, LBF spectrum and the extended LBF (ELBF) spectrum. Theoretical analyses and simulation results show that the spectrum proposed in this part applies to a more general bistatic configuration and can achieve a better focusing performance than the other three spectra.
●Based on the new bistatic 2-D spectrum derived in the fifth part of this dissertation, a bistatic RDA is developed in the sixth part of this dissertation. In developing the RDA, the secondary-range-compression (SRC) term was first factored out from the EM term and then was incorporated into the BD term so that a new BD term is formed. To handle the problem of the space dependence of the new BD term, we can divide the whole scene into segments and then remove the new BD term using phase multiplies blockwise in the 2-D frequency domain, due to its slowly-varying property in space. To address the problem of the range dependence of the RCM term and the azimuth modulation term, the new method which is proposed for the MSR-based RDA in the third part of this dissertation is adapted, so that after adaptation, this method can effectively update the three equivalent parameters (i.e., the equivalent range, the equivalent velocity and the equivalent squint angle) along range. The proposed RDA is efficient and easy to implement, since the expressions of the RCM term and azimuth modulation both have a concise and closed form (rather than a Taylor expansion version). The proposed RDA almost has the same processing steps as the conventional monostatic RDA except for an extra procedure of updating the required equivalent parameters, which means that the conventional monostatic RDA can be readily applied to process the bistatic SAR data with minor modification. Besides, in this part, based on the conventional two-step method, we also present a motion compensation (MOCO) method for the proposed RDA. The key step of the proposed MOCO method is to perform range-dependent MOCO along the reference vector. Simulation results show that the proposed MOCO method is effective.
引文
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[1]Cumming I.G. and Wong F.H. Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation. Norwood, MA:Artech House,2005.
[2]D'Aria D., Monti Guarnieri A., and Rocca F. Focusing bistatic synthetic aperture radar using dip move out. IEEE Trans. Geosci. Remote Sens., vol.42, no.7, pp. 1362-1376, Jul.2004.
[3]Hanle E. Survey of bistatic and multistatic radar. IEE Proceedings, vol.133, pp. 587-595,1986.
[4]Neo Y. L. Digital processing algorithms for bistatic synthetic aperture radar data. Ph.D. dissertation, Dept. Electr. Comput. Eng., Univ. British Columbia, Vancouver, BC, Canada, May 2007.
[5]Dubois-Fernandez P., Ruault du Plessis O., Wendler M., Horn R., Krieger G., Vaizan B., Cantalloube H., Heuz D., and Gabler B. The ONERA-DLR Bistatic Experiment: Design of the Experiment and Preliminary Results. In Proc. Advanced SAR Workshop, Canadian Space Agency, Saint-Hubert, Quebec, June 25-27,2003.
[6]Rodriguez-Cassola M., Baumgartner S. V., Krieger G., and Moreira A. Bistatic Terra SAR-X/F-SAR Spaceborne-Airborne SAR Experiment:Description, Data Processing, and Results. IEEE Trans. Geosci. Remote Sens., vol.48, no.2, pp. 781-794, Feb.2010.
[7]Baumgartner S. V, Rodriguez-Cassola M., Nottensteiner A., Horn R., Schwerdt M., Scheiber R., Steinbrecher U., Metzig R., Limbach M., Mittermayer J., Krieger G., and Moreira A. Bistatic experiment using TerraSAR-X and DLR's new F-SAR system. In Proc. EUSAR, Friedrichshafen, Germany,2008.
[8]Belcher D. P. and Baker C. J. High resolution processing of hybrid strip-map/spotlight mode SAR. IEE Proc. Radar, Sonar & Navigation. Vol.143, no. 6, pp.366-374, December 1996.
[9]Mittermayer J., Lord R., and Boerner E. Sliding spotlight SAR processing for TerraSAR-X using a new formulation of the extended chirp scaling algorithm. In IGARSS 2003, Toulouse, France, July 2003, pp.1462-1464.
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[41]孙进平,白霞,毛士艺.双基地合成孔径雷达的扩展ETF成像算法.电子学报.2007年12月,vol.35(12).2394-2398.
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[1]Cumming I.G. and Wong F.H. Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation. Norwood, MA:Artech House,2004.
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[1]Neo Y. L., Wong F. H., and Cumming I. G. A two-dimensional spectrum for bistatic SAR processing using series reversion. IEEE Geosci. Remote Sens. Lett., vol.4, no. 1, pp.93-96, Jan.2007.
[2]Neo Y. L., Wong F. H., and Cumming I. G. 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.
[3]Liu B., Wang T., and Bao Z. An Analytical Method of Updating the Range Derivatives and a Simple Image Registration Method for the MSR-based Range Doppler Algorithm. IEEE Geosci. Remote Sens. Lett., vol.7, no.4, pp.831-835, Oct.2010.已网络发表(2010年10月正式出版)
[4]Cumming I. G. and Wong F. H., Digital Processing of Synthetic Aperture Radar Data Algorithms and Implementation. Norwood, MA:Artech House,2005.
[1]Rodriguez-Cassola M., Baumgartner S. V., Krieger G., and Moreira A. Bistatic TerraSAR-X/F-SAR Spaceborne-Airborne SAR Experiment:Description, Data Processing, and Results. IEEE Trans. Geosci. Remote Sens., vol.48, no.2, pp. 781-794, Feb.2010.
[2]Wang R., Loffeld 0., Nies H., and Ender J. H. G. Focusing Spaceborne/Airborne Hybrid Bistatic SAR Data Using Wavenumber-Domain Algorithm. IEEE Trans. Geosci. Remote Sens., vol.47, no.7, pp.2275-2283, Aug.2009.
[3]Baumgartner S. V., Rodriguez-Cassola M., Nottensteiner A., Horn R., Schwerdt M., Scheiber R., Steinbrecher U., Metzig R., Limbach M., Mittermayer J., Krieger G., and Moreira A.. Bistatic experiment using TerraSAR-X and DLR's new F-SAR system. In Proc. EUSAR, Friedrichshafen, Germany,2008.
[4]Neo Y. L., Wong F. H., and Cumming I. G. A two-dimensional spectrum for bistatic SAR processing using series reversion. IEEE Geosci. Remote Sens. Lett., vol.4, no. 1,pp.93-96, Jan.2007.
[5]Neo Y. L., Wong F. H., and Cumming I. G. 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]Liu B., Wang T., and Bao Z.. An Analytical Method of Updating the Range Derivatives and a Simple Image Registration Method for the MSR-based Range Doppler Algorithm. IEEE Geosci. Remote Sens. Lett.,vol.7, no.4, pp.831-835, Oct.2010.已网络发表(2010年10月正式出版)
[7]Wong F. H., Cumming I. G., and Neo Y. L.. Focusing Bistatic SAR Data Using the Nonlinear Chirp Scaling Algorithm. IEEE Trans. Geosci. Remote Sens., vol.46, no. 9, pp.2493-2505, Sep.2008.
[1]D'Aria D., Monti Guarnieri A., and Rocca F.. Focusing bistatic synthetic aperture radar using dip move out. IEEE Trans. Geosci. Remote Sens., vol.42, no.7, pp. 1362-1376, Jul.2004.
[2]Bamler R., Meyer F., and Liebhart W.. Processing of bistatic SAR data from quasi-stationary configurations. IEEE Trans. Geosci. Remote Sens., vol.45, no.11, pp.3350-3358, Nov.2007.
[3]Hale D.. Dip-moveout by Fourier transform. Geophysics, vol.49, no.14, pp.741-757,Jun.1984.
[4]Loffeld O., Nies H., Peters V., and Knedlik S.. Models and useful relations for bistatic SAR processing. IEEE Trans. Geosci. Remote Sens., vol.42, no.10, pp. 2031-2038, Oct.2004.
[5]Wang R., Loffeld O., Ul-Ann Q., Nies H., and Medrano Ortiz A., and Samarah A. A bistatic point target reference spectrum for general bistatic SAR processing. IEEE Geosci. Remote Sens. Lett., vol.5, no.3, pp.517-521, Jul.2008.
[6]Natroshvili K., Loffeld O., Nies H., and Ortiz A. M.. First steps to bistatic focusing. In Proc. IGARSS, Seoul, Korea, Jul.2003, pp.1072-1076.
[7]Natroshvili K., Loffeld O., and Nies H.. Focusing of arbitrary bistatic SAR configurations. In Proc. EUSAR, Dresden, Germany, May 2006. CD-ROM.
[8]Rodriguez-CassolaM., Krieger G., and Wendler M.. Azimuth-invariant, bistatic airborne SAR processing strategies based on monostatic algorithms. In Proc. IGARSS, Seoul Korea, Aug.2005, pp.1047-1050.
[9]Wang R., Loffeld O., Nies H., and Ender J. H. G. Focusing Spaceborne/Airborne Hybrid Bistatic SAR Data Using Wavenumber-Domain Algorithm. IEEE Trans. Geosci. Remote Sens., vol.47, no.7, pp.2275-2283, Aug.2009.
[10]Wang R., Loffeld O., Nies H., Knedlik S., and Ender J. H. G. Chirp-Scaling Algorithm for Bistatic SAR Data in the Constant-Offset Configuration. IEEE Trans. Geosci. Remote Sens., vol.47, no.3, pp.952-964, Mar.2009.
[11]孙进平,白霞,毛士艺.双基地合成孔径雷达的扩展ETF成像算法.电子学报.2007年12月,vol.35(12).2394-2398.
[12]Zhang Z., Xing M., Ding J., and Bao Z.. Focusing parallel bistatic SAR data using the analytic transfer function in the wavenumber domain. IEEE Trans. Geosci. Remote Sens., vol.45, no.11, pp.3633-3645, Nov.2007.
[13]Cumming I.G. and Wong F.H.. Digital Processing of Synthetic Aperture Radar Data:Algorithms and Implementation. Norwood, MA:Artech House,2005.
[14]Neo Y. L., Wong F. H., and Cumming I. G. A two-dimensional spectrum for bistatic SAR processing using series reversion. IEEE Geosci. Remote Sens. Lett., vol.4, no.1, pp.93-96, Jan.2007.
[1]Wang R., Loffeld O., Nies H., and Ender J. H. G. Focusing Spaceborne/Airborne Hybrid Bistatic SAR Data Using Wavenumber-Domain Algorithm. IEEE Trans. Geosci. Remote Sens., vol.47, no.7, pp.2275-2283, Aug.2009.
[2]Cumming I.G. and Wong F. H.. Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation. Norwood, MA:Artech House,2005.
[3]Liu B., Wang T., and Bao Z.. An Analytical Method of Updating the Range Derivatives and a Simple Image Registration Method for the MSR-based Range Doppler Algorithm. IEEE Geosci. Remote Sens. Lett., vol.7, no.4, pp.831-835, Oct.2010.已网络发表(2010年10月正式出版)
[4]Fornaro G., Franceschetti G, and Perna S.. Trajectory deviations in airborne SAR: Analysis and compensation. IEEE Trans. Geosci. Remote Sens., vol.35, no.7, pp. 997-1009, Jul.1999.
[5]Moreira A. and Huang Y. H.. Airborne SAR processing of highly squinted data using a chirp scaling approach with integrated motion compensation. IEEE Trans. Geosci. Remote Sens., vol.32, no.10, pp.1029-1040, Sep.1994.
[6]Wang R., Loffeld O., Nies H., Knedlik S., and Ender J. H. G. Chirp-Scaling Algorithm for Bistatic SAR Data in the Constant-Offset Configuration. IEEE Trans. Geosci. Remote Sens., vol.47, no.3, pp.952-964, Mar.2009.