多发多收干涉合成孔径雷达高程测量关键技术研究
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摘要
干涉合成孔径雷达(InSAR)是一种全天时、全天候的微波遥感技术,能够提供高分辨率、高精度的地表数字高程图。在地质、地理和地球物理等许多学科有着广泛的应用。传统的单基线InSAR只能提供一个干涉相位,其相位展开的精度和可靠性较低,且难以应对大坡度、非连续以及高程重叠(Layover)等复杂地形。而多频和多基线InSAR这一类具有多个观测通道的模式由于能够提供多个独立干涉相位,大大提高了相位展开的可靠性和精度,并能够解决复杂地形条件下的高程测量问题。因此,多通道InSAR已成为目前国内、外的研究热点。近年来兴起的MIMO雷达技术能够在不增加真实观测通道的条件下通过多发多收形成更多的虚拟观测通道,为进一步提高多通道InSAR模式的高程测量性能提供了一条新的技术途径。本论文的研究工作将围绕多发多收干涉合成孔径雷达高程测量的关键技术展开,主要的研究工作包括以下几个方面:
1)分析了多基线InSAR联合像素矢量的协方差矩阵特征谱随回波相干性和SAR图像配准误差的变化情况。分析结果指出:在去相关效应不可忽略和各SAR图像间的配准误差各不相等且不为整数的时候,联合像素矢量协方差矩阵的信号子空间将占据整个特征空间。此时,基于信号子空间向噪声子空间投影的联合子空间投影方法将会出现干涉信息损失,从而导致高程估计的稳健性和精度下降。针对这一问题,提出了一种基于联合像素矢量协方差矩阵拟合的多基线InSAR回波数据联合处理方法。该方法能够避免由于信号子空间占据整个特征空间而引起的干涉信息损失,具有更好的高程估计精度和稳健性。同时,该方法通过相关系数加权的方法抑制了采样协方差矩阵各元素中的误差项对高程估计的影响,保证了其在有限样本数条件下的可靠性。
2)根据常规多发多收(MIMO)雷达中常用的两种信号分集方式,提出了基于频率编码和波形编码的两种MIMO InSAR高程测量模式,能以较小的代价换取高程测量性能的大幅提高。首先,由于MIMO技术带来了更多的独立观测通道,因此MIMO InSAR模式的高程估计精度将高于传统的多频或多基线InSAR模式。本论文分别推导了上述两种MIMO InSAR模式下的高程估计的克拉美罗界,证明了MIMO InSAR模式对高程估计精度的改善。同时,独立观测通道数量的增加也提高了系统的高程估计稳健性。通过组合不同的工作频率和观测基线,频率编码MIMO InSAR模式能够有效的扩展系统的高程估计模糊间隔,在系统各工作频率和各基线之间均不具有互质关系的条件下,该模式仍然能够得到稳健的高程估计结果;而通过虚拟阵列扩展,波形编码MIMO InSAR模式能够辨识数量多于真实观测阵元的Layover单元,极大地提高了InSAR系统在复杂地形条件下的高程测量能力。
3)针对波形编码MIMO InSAR模式存在的调制波形正交性不足、缺乏高精度和大场景成像的算法等问题,提出了基于时间编码和空间编码的两种MIMO InSAR模式。时间编码模式通过各观测阵元交替发射信号的方式,等效形成多发多收的各观测通道,并且通过引入波束扫描技术,以牺牲方位向分辨率为代价实现宽域观测。而空间编码模式则通过将各观测阵元发射波束主瓣脚印在地面同一观测条带中彼此分离的方式等效形成了多发多收的各观测通道,并通过在接收端使用子天线阵空域滤波来实现无多普勒模糊的宽域观测。在以上两种模式下,各观测阵元发射信号回波间的可分离性不再依赖各发射信号间的正交性,可以利用线性调频信号作为各阵元的发射信号,从而可以利用各种基于线性调频信号的成熟算法完成高精度、大场景成像处理。
4)针对MIMO雷达中由于回波数据维数的大幅增加而引起传统参数估计算法的运算量也随之大幅增加的问题,提出了一种基于ESPRIT算法和Kalman滤波的高精度、低复杂度的MIMO雷达波达方向估计方法。该方法将MIMO雷达经匹配滤波后形成的虚拟阵列分解为多个构形相同但空间位置不同的虚拟子阵,利用这些虚拟子阵间的旋转不变性得到了同一目标波达方向的多个估计值,并利用Kalman滤波对同一目标波达方向的多个估计值进行融合处理进一步提高了估计的高精度。该方法只需要对若干个维数较小的协方差矩阵进行特征分解且不需要进行谱峰搜索,故其运算量远小于传统的参数估计算法。同时,该方法对阵列构形没有要求,能够适用于MIMO模式下非均匀线阵以及二维阵列的波达方向估计问题。由于阵列波达方向估计与InSAR高程估计之间的相似性,本论文将该方法的基本思想应用于MIMO InSAR的高程估计问题,提出了一种低复杂度的MIMO InSAR高程估计算法,并且解决了由于MIMO InSAR虚拟观测阵元空间超稀疏分布而带来的近场阵列问题。不过,受到InSAR回波信号特有的乘性噪声的影响,在应用于高程估计时该方法的估计精度会因模型失配而出现一定程度的下降,本论文推导了乘性噪声背景下该方法的高程估计均方误差公式,对乘性噪声的影响进行了定量的分析。
Synthetic aperture radar Interferometry (InSAR) is a powerful remote sensing technique, which has been exploited for the generation of digital elevation model with high resolutions and has found many applications in the earth system science study. The accuracy and robustness of interferometric phase unwrapping of the traditionally single baseline InSAR suffers severely from the interferometric phase noises. And it is difficult for the single baseline InSAR to deal with the highly sloping, discontinuous and Layover scene. Recently, the multi-baseline/multi-frequency InSAR system, which would be referred as multi-channel InSAR in the following, has been widely investigated for its abilities to restore a unique solution to the terrain height and resolve the terrain mapping problem of the highly sloping, discontinuous and Layover scene. The newly emergent MIMO radar concept, depending on its ability to virtually extend the sensor array, provides a feasible way to improve the performance of multi-channel InSAR without extending the number of real sensors or frequencies. This dissertation would mainly focuses on the application of MIMO radar concept to the multi-channel InSAR. The research of this dissertation is summarized below:
1. A new joint processing method is proposed, which carries out the height estimation through the joint covariance matrix fitting. The eigen-spectrum of the joint pixel vector is analyzed firstly, which shows that the joint noise subspace would exist only under some specific conditions. The original joint processing method based on joint subspace projection would suffer from the loss of interferometric information since, in this case, the absent joint noise subspace would be replace by the eigen-subspace which also contains some interferometric information. However, through the joint covariance matrix fitting, all the interferometric information embedded in the joint pixel vector would be exploited for the height estimation. Further more, the sample joint covariance matrix is tapered by the coherence matrix, which improves the robustness of the proposed method in the case of limited samples available.
2. Two MIMO InSAR modes are proposed, which are based on the frequency diversity and the waveform diversity, respectively. The data models for these two modes are presented. And the performance of these two modes are analyzed theoretically, which indicates that MIMO InSAR is able to identify the laid over ground patches more than its real sensors and provided a more accurate estimation of the terrain profile than that of its SIMO counterpart. Hence, MIMO InSAR would exhibit a better identifiability in the areas of complex terrain profile such as mountains, buildings and other complex man made objects, especially when the number of real sensors is small.
3. Since the orthogonality of the available orthogonal waveforms at present could not satisfy the requirement of the available SAR imaging technique, two substitutive MIMO InSAR modes based on spatial/temporal encoding are proposed, which remain the advantages of the waveform diversity based MIMO InSAR mode. Under the temporal encoding mode, the MIMO channels are obtained through transmitting signals alternately from the sensors. And the ScanSAR technique is employed to enlarge the swath width under such mode. While, under the spatial encoding mode, the MIMO channels are obtained through spreading the footprints of the mainlobes of the transmitting beams along the observing strip. And the antenna of each sensor is divided into multiple sub-antennae along the azimuth direction for the spatial filtering on receive, which makes it possible to avoid doppler ambiguity without increasing the PRF. The orthogonality of the transmitting signals is no more necessary under these two modes. Thus, the linear frequency modulated signal could be employed as the transmitting signal of every sensor, which would make it possible to complete the imaging processing via the ordinary SAR imaging algorithms.
4. A computationally efficient method employing ESPRIT and Kalman filtering is proposed for the direction finding of MIMO radar. The property that the virtual array of MIMO radar is equivalent to multiple virtual subarrays with the same geometry but different displacements is exploited to provide multiple direction estimates for each target. And the multiple estimates of each target are fused through Kalman filtering to improve the accuracy of direction estimation. This method has no specific requirement on the geometry configuration of the MIMO array and can resolve the parameter estimation problem of array in the near-field, which make it applicable to the height estimation problem of MIMO InSAR. Therefore, computationally efficient method is presented for the height estimation of MIMO InSAR based on the basic concept of the method mentioned above. Furthermore, the impact of multiplicative noise on this method is analyzed theoretically when it is applied to the height estimation problem of MIMO InSAR.
1)分析了多基线InSAR联合像素矢量的协方差矩阵特征谱随回波相干性和SAR图像配准误差的变化情况。分析结果指出:在去相关效应不可忽略和各SAR图像间的配准误差各不相等且不为整数的时候,联合像素矢量协方差矩阵的信号子空间将占据整个特征空间。此时,基于信号子空间向噪声子空间投影的联合子空间投影方法将会出现干涉信息损失,从而导致高程估计的稳健性和精度下降。针对这一问题,提出了一种基于联合像素矢量协方差矩阵拟合的多基线InSAR回波数据联合处理方法。该方法能够避免由于信号子空间占据整个特征空间而引起的干涉信息损失,具有更好的高程估计精度和稳健性。同时,该方法通过相关系数加权的方法抑制了采样协方差矩阵各元素中的误差项对高程估计的影响,保证了其在有限样本数条件下的可靠性。
2)根据常规多发多收(MIMO)雷达中常用的两种信号分集方式,提出了基于频率编码和波形编码的两种MIMO InSAR高程测量模式,能以较小的代价换取高程测量性能的大幅提高。首先,由于MIMO技术带来了更多的独立观测通道,因此MIMO InSAR模式的高程估计精度将高于传统的多频或多基线InSAR模式。本论文分别推导了上述两种MIMO InSAR模式下的高程估计的克拉美罗界,证明了MIMO InSAR模式对高程估计精度的改善。同时,独立观测通道数量的增加也提高了系统的高程估计稳健性。通过组合不同的工作频率和观测基线,频率编码MIMO InSAR模式能够有效的扩展系统的高程估计模糊间隔,在系统各工作频率和各基线之间均不具有互质关系的条件下,该模式仍然能够得到稳健的高程估计结果;而通过虚拟阵列扩展,波形编码MIMO InSAR模式能够辨识数量多于真实观测阵元的Layover单元,极大地提高了InSAR系统在复杂地形条件下的高程测量能力。
3)针对波形编码MIMO InSAR模式存在的调制波形正交性不足、缺乏高精度和大场景成像的算法等问题,提出了基于时间编码和空间编码的两种MIMO InSAR模式。时间编码模式通过各观测阵元交替发射信号的方式,等效形成多发多收的各观测通道,并且通过引入波束扫描技术,以牺牲方位向分辨率为代价实现宽域观测。而空间编码模式则通过将各观测阵元发射波束主瓣脚印在地面同一观测条带中彼此分离的方式等效形成了多发多收的各观测通道,并通过在接收端使用子天线阵空域滤波来实现无多普勒模糊的宽域观测。在以上两种模式下,各观测阵元发射信号回波间的可分离性不再依赖各发射信号间的正交性,可以利用线性调频信号作为各阵元的发射信号,从而可以利用各种基于线性调频信号的成熟算法完成高精度、大场景成像处理。
4)针对MIMO雷达中由于回波数据维数的大幅增加而引起传统参数估计算法的运算量也随之大幅增加的问题,提出了一种基于ESPRIT算法和Kalman滤波的高精度、低复杂度的MIMO雷达波达方向估计方法。该方法将MIMO雷达经匹配滤波后形成的虚拟阵列分解为多个构形相同但空间位置不同的虚拟子阵,利用这些虚拟子阵间的旋转不变性得到了同一目标波达方向的多个估计值,并利用Kalman滤波对同一目标波达方向的多个估计值进行融合处理进一步提高了估计的高精度。该方法只需要对若干个维数较小的协方差矩阵进行特征分解且不需要进行谱峰搜索,故其运算量远小于传统的参数估计算法。同时,该方法对阵列构形没有要求,能够适用于MIMO模式下非均匀线阵以及二维阵列的波达方向估计问题。由于阵列波达方向估计与InSAR高程估计之间的相似性,本论文将该方法的基本思想应用于MIMO InSAR的高程估计问题,提出了一种低复杂度的MIMO InSAR高程估计算法,并且解决了由于MIMO InSAR虚拟观测阵元空间超稀疏分布而带来的近场阵列问题。不过,受到InSAR回波信号特有的乘性噪声的影响,在应用于高程估计时该方法的估计精度会因模型失配而出现一定程度的下降,本论文推导了乘性噪声背景下该方法的高程估计均方误差公式,对乘性噪声的影响进行了定量的分析。
Synthetic aperture radar Interferometry (InSAR) is a powerful remote sensing technique, which has been exploited for the generation of digital elevation model with high resolutions and has found many applications in the earth system science study. The accuracy and robustness of interferometric phase unwrapping of the traditionally single baseline InSAR suffers severely from the interferometric phase noises. And it is difficult for the single baseline InSAR to deal with the highly sloping, discontinuous and Layover scene. Recently, the multi-baseline/multi-frequency InSAR system, which would be referred as multi-channel InSAR in the following, has been widely investigated for its abilities to restore a unique solution to the terrain height and resolve the terrain mapping problem of the highly sloping, discontinuous and Layover scene. The newly emergent MIMO radar concept, depending on its ability to virtually extend the sensor array, provides a feasible way to improve the performance of multi-channel InSAR without extending the number of real sensors or frequencies. This dissertation would mainly focuses on the application of MIMO radar concept to the multi-channel InSAR. The research of this dissertation is summarized below:
1. A new joint processing method is proposed, which carries out the height estimation through the joint covariance matrix fitting. The eigen-spectrum of the joint pixel vector is analyzed firstly, which shows that the joint noise subspace would exist only under some specific conditions. The original joint processing method based on joint subspace projection would suffer from the loss of interferometric information since, in this case, the absent joint noise subspace would be replace by the eigen-subspace which also contains some interferometric information. However, through the joint covariance matrix fitting, all the interferometric information embedded in the joint pixel vector would be exploited for the height estimation. Further more, the sample joint covariance matrix is tapered by the coherence matrix, which improves the robustness of the proposed method in the case of limited samples available.
2. Two MIMO InSAR modes are proposed, which are based on the frequency diversity and the waveform diversity, respectively. The data models for these two modes are presented. And the performance of these two modes are analyzed theoretically, which indicates that MIMO InSAR is able to identify the laid over ground patches more than its real sensors and provided a more accurate estimation of the terrain profile than that of its SIMO counterpart. Hence, MIMO InSAR would exhibit a better identifiability in the areas of complex terrain profile such as mountains, buildings and other complex man made objects, especially when the number of real sensors is small.
3. Since the orthogonality of the available orthogonal waveforms at present could not satisfy the requirement of the available SAR imaging technique, two substitutive MIMO InSAR modes based on spatial/temporal encoding are proposed, which remain the advantages of the waveform diversity based MIMO InSAR mode. Under the temporal encoding mode, the MIMO channels are obtained through transmitting signals alternately from the sensors. And the ScanSAR technique is employed to enlarge the swath width under such mode. While, under the spatial encoding mode, the MIMO channels are obtained through spreading the footprints of the mainlobes of the transmitting beams along the observing strip. And the antenna of each sensor is divided into multiple sub-antennae along the azimuth direction for the spatial filtering on receive, which makes it possible to avoid doppler ambiguity without increasing the PRF. The orthogonality of the transmitting signals is no more necessary under these two modes. Thus, the linear frequency modulated signal could be employed as the transmitting signal of every sensor, which would make it possible to complete the imaging processing via the ordinary SAR imaging algorithms.
4. A computationally efficient method employing ESPRIT and Kalman filtering is proposed for the direction finding of MIMO radar. The property that the virtual array of MIMO radar is equivalent to multiple virtual subarrays with the same geometry but different displacements is exploited to provide multiple direction estimates for each target. And the multiple estimates of each target are fused through Kalman filtering to improve the accuracy of direction estimation. This method has no specific requirement on the geometry configuration of the MIMO array and can resolve the parameter estimation problem of array in the near-field, which make it applicable to the height estimation problem of MIMO InSAR. Therefore, computationally efficient method is presented for the height estimation of MIMO InSAR based on the basic concept of the method mentioned above. Furthermore, the impact of multiplicative noise on this method is analyzed theoretically when it is applied to the height estimation problem of MIMO InSAR.
引文
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