欠采样环境下的参数估计及阵列校正方法研究
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摘要
论文主要研究时间(频率)、空间欠采样条件下的参数估计与阵列校正方法。当到达传感器端的多个信号占据较宽的频带时，直接对信号进行Nyquist采样其硬件实现复杂度相当大，且后端用于信号处理的DSP和其它硬件设备很难满足如此高的数据吞吐，因此欠采样是目前宽频带信号频率估计中的首选技术。无模糊测向要求阵列中阵元的间距要小于所估计的最高频率信号波长的一半，这样势必会加大低频信号在不同阵元间的互耦，大大降低各信号波达方向(DOA)估计的精度，在这种情况下，增大阵元间距，即对信号进行空间欠采样可降低不同频率信号在阵元间的互耦，有效增大阵列的孔径，提高信号DOA的估计精度。阵列误差估计、校正也是本文的研究重点，论文最后两章结合分布式小卫星这一特殊应用背景提出了两种高速运动、超大稀疏阵列的校正方法，获得了一些有益的结论。论文各章节具体研究内容安排如下：
1．第二章提出了一种基于延迟和旋转不变子空间(ESPRIT)方法的欠采样频率估计算法。欠采样所引入的模糊可以通过延迟相位差和提出的解模糊算法来加以消除。为进一步降低算法运算复杂度，文中使用传播算子思想(PM)简化了提出的算法，并且弥补了已有基于PM进行参数估计时存在信号空间维数损失的缺陷，使之具有更好的参数估计性能。然而分析发现，已有的欠采样频率估计算法频率估计精度严重依赖于延迟线精度和有、无延迟采样通道一致性，因此在本章中也给出了一种基于双模数转换器(ADC)的欠采样频率估计算法，该方法克服了已有方法的不足，并且所提出的欠采样频率估计算法可以通过给单路ADC在不同时刻配以不同的采样时钟而实现，这可在一定程度上减小包括ADC在内的硬件设备量，具有一定的意义。
2．第三章结合前章提出的频率欠采样频率估计方法给出了一种近场源频率、DOA和距离的联合估计算法。本章采用类似状态空间的方法对阵列接收的近场源信号进行建模，然后通过一定的运算直接获得各近场源三个参数的闭式解。已有的近场源参数估计算法都假定信源频率已知，在频率未知时失效，并且已有的大部分近场源参数估计算法需要复杂的搜索运算，参数间需要配对。相比之下，
本章虽然进行的是频率、DOA和距离三维参数的估计，但算法中没有复杂的搜索运算，并且所估计的参数自动配对，有一定的优越性。
3．第四章提出了一种时空欠采样条件下基于矢量传感器(VS)阵列的横平面电磁波(TEM)信号频率、DOA和极化的估计算法。为了降低对宽频带信号高速采样的压力，本章仍然采用频率欠采样的方法。同时，为了降低不同频率信号在
采样环境下的参数估计及阵列校正方法研究
VS间的互祸，文中对信号采用了空间欠采样的方法。不同于已有的空间欠采
样解模糊方法要求阵列的排布遵循一定的法则，本章VS的应用可大大放宽布
阵约束，使得传感器排布更加随意。同时，VS的稀疏排布减小了不同频率信
号在传感器间的互祸，增大了阵列孔径，提高了算法对信号DOA的估计精度。
最后的计算机仿真证明了方法的有效性。
4.第五章提出了一种利用地面特显点回波对分布式小卫星阵列进行校正和空间
模糊抑制近而成像的方法。用多颗分布式小卫星雷达构成编队飞行，可以提高
多项雷达探测任务的性能，其潜在性能、成本和可靠性大大超过单颗大卫星雷
达。然而分布式小卫星阵列的误差，特别是三维基线误差和各通道的幅相误差，
严重制约着这种高效性能的发挥，必须加以校正，而国内外现有的文献中都没
有涉及到这种高速运动超大稀疏阵列校正方面的研究。本章从分析小卫星雷达
接收的数据回波空时频特性出发，首先由地面的特显点估计出分布式小卫星的
沿航向误差，然后结合自校正方法估计包括垂直航向误差在内的其他误差分
量，最后分别估计得到多个多普勒相同(由于频率欠采样)而方位各不相同地块
的空间导向矢量。本章第四节利用估计出的各地块的空间导向矢量并结合阵列
方向图调零方法提出了一种抑制空I司模糊近而完成大观测带、高方位分辨力
SAR成像的处理方法，该算法主要运算量集中在一次方位回波FFT和一次矩阵
求逆运算上，避免了多次方位FFT、估计协方差矩阵和其求逆运算，因而较己
有小卫星成像方法的运算量要小。最后的计算机仿真试验验证了方法的有效
性。
5.第六章主要针对前章方法的不足，即阵列误差估计需要地面特显点和阵列不能
有较大的垂直基线，提出了一种基于小卫星雷达接收回波数据的高速运动、超
大稀疏阵列的校正方法。由于小卫星平台上的天线孔径较小，回波信号中会存
在距离或者方位多普勒模糊，对于稀疏孔径的SAR成像和地面运动目标检测
(GMTI)应用，文中采用较低脉冲重复频率以保证距离不模糊(可以获得大观测
条带宽度)，而此时接收的回波数据存在方位多普勒模糊，然后对存在方位模
糊的回波数据进行多普勒处理以获得几个空间角度确知的校正源信号，最后利
用这些校正源信号对阵列误差进行估计、补偿。大量仿真结果表明，只要星间
测量和轨道控制精度控制在分米数量级，使用本文提出的方法可以很好的实现
对这种高速运动超大稀疏阵列误差的估
The problem of parameter estimation and array calibration with sub-Nyquist sampling is studied in this doctoral dissertation. Sampling the signals under Nyquist's theory is very difficult when they are in a wide band. It is urge to develop new techniques to deal with such difficulty. Sub-Nyquist sampling which is considered the perfect way to overcome this difficulty can allivate the burden with the system's design complexity. To estimate the directions-of-arrival(DOAs) from the samples of the array without ambiguity demands the interval between any two elements be less than the half of the wavelength of the signal with the maximum frequency. This restriction aggravates the mutual coupling of the signals with comparable low frequencies. Spatial sub-Nyquist which can not only allivate the mutual coupling between elements but also improve the estimation performance of DO As is considered a right technique to solve such problem. The problem of calibrate the highly sparse space- borne array is studied in the last two chapters. Two methods is proposed to remedy the sparse array through the analysis of the echoes from the illuminated area of the small satellite antenna. The detailed content included in every chapter is listed bellow:1. In chapter 2, a novel frequency estimation algorithm for wideband signal with sub-Nyquist sampling is proposed. With the aid of information provided by the auxiliary delayed sampling channel and the aliased frequency estimation for wideband signal with sub-Nyquist sampling, we can solve the frequency aliasing due to sub-Nyquist sampling. This method can reduce the complexity of the overall hardware at the cost of an auxiliary sampling channel. Furthermore, in order to alleviate the computation burden for its practicability, a more simplified algorithm based on propagator method(PM)is put forward. The simplified algorithm which is developed for practice in this chapter does not need to estimate the sample covariance matrix and only need to do one eigendecomposition with comparable lower dimensions to obtain the frequency estimation. A new method base on different sampling frequency to estimate frequencies from wide-band under-sampled data is also proposed in this chapter. The proposed method is not sensitive to the amplitude and phase errors of both channels and data obtained from two channels can be processed separately, thus it has a wider applied field than existing methods. At last, the effectiveness of the proposed algorithm is verified via computer simulations.
2. In chapter 3, using the proposed frequency estimation method in chapter 2 and the state-space realization approach, a subspace based algorithm to estimate the frequency, DOA and range of near-field sources is proposed, which does not need any spectral peak searching and the 3-D parameters are automatically paired. Moreover, the proposed method is applicable to arbitrary additive Gaussian noise environment. The effectiveness of the proposed algorithm is verified via computer simulations.3. In chapter 4, a novel method for joint frequency, 2-D direction-of-arrrival and polarization estimation of transverse electromagnetic waves based on arbitrary L-shaped vector sensor(VS)array is proposed. VS consists of six co-located but diversely polarized antennas separately measuring all six electromagnetic-field components of an incident wavefield. Sub-Nyquist temporal sampling is introduced to reduce the complexity of the system design. Furthermore, sub-Nyquist spatial sampling, which can further reduce the mutual coupling among VSs, is combined to improve the estimation performance of spatial parameters. The CRLB is also derived in the end of this paper to verify the efficiency of this method.4. In chapter 5, a novel calibration method is proposed which is adapted to the distributed small satellites array. A constellation composed of several distributed small satellite radars can cooperate to improve the performance of multiple missions, therefore it has several advantages over a larger, single space-borne radar of being well in pe
1．第二章提出了一种基于延迟和旋转不变子空间(ESPRIT)方法的欠采样频率估计算法。欠采样所引入的模糊可以通过延迟相位差和提出的解模糊算法来加以消除。为进一步降低算法运算复杂度，文中使用传播算子思想(PM)简化了提出的算法，并且弥补了已有基于PM进行参数估计时存在信号空间维数损失的缺陷，使之具有更好的参数估计性能。然而分析发现，已有的欠采样频率估计算法频率估计精度严重依赖于延迟线精度和有、无延迟采样通道一致性，因此在本章中也给出了一种基于双模数转换器(ADC)的欠采样频率估计算法，该方法克服了已有方法的不足，并且所提出的欠采样频率估计算法可以通过给单路ADC在不同时刻配以不同的采样时钟而实现，这可在一定程度上减小包括ADC在内的硬件设备量，具有一定的意义。
2．第三章结合前章提出的频率欠采样频率估计方法给出了一种近场源频率、DOA和距离的联合估计算法。本章采用类似状态空间的方法对阵列接收的近场源信号进行建模，然后通过一定的运算直接获得各近场源三个参数的闭式解。已有的近场源参数估计算法都假定信源频率已知，在频率未知时失效，并且已有的大部分近场源参数估计算法需要复杂的搜索运算，参数间需要配对。相比之下，
本章虽然进行的是频率、DOA和距离三维参数的估计，但算法中没有复杂的搜索运算，并且所估计的参数自动配对，有一定的优越性。
3．第四章提出了一种时空欠采样条件下基于矢量传感器(VS)阵列的横平面电磁波(TEM)信号频率、DOA和极化的估计算法。为了降低对宽频带信号高速采样的压力，本章仍然采用频率欠采样的方法。同时，为了降低不同频率信号在
采样环境下的参数估计及阵列校正方法研究
VS间的互祸，文中对信号采用了空间欠采样的方法。不同于已有的空间欠采
样解模糊方法要求阵列的排布遵循一定的法则，本章VS的应用可大大放宽布
阵约束，使得传感器排布更加随意。同时，VS的稀疏排布减小了不同频率信
号在传感器间的互祸，增大了阵列孔径，提高了算法对信号DOA的估计精度。
最后的计算机仿真证明了方法的有效性。
4.第五章提出了一种利用地面特显点回波对分布式小卫星阵列进行校正和空间
模糊抑制近而成像的方法。用多颗分布式小卫星雷达构成编队飞行，可以提高
多项雷达探测任务的性能，其潜在性能、成本和可靠性大大超过单颗大卫星雷
达。然而分布式小卫星阵列的误差，特别是三维基线误差和各通道的幅相误差，
严重制约着这种高效性能的发挥，必须加以校正，而国内外现有的文献中都没
有涉及到这种高速运动超大稀疏阵列校正方面的研究。本章从分析小卫星雷达
接收的数据回波空时频特性出发，首先由地面的特显点估计出分布式小卫星的
沿航向误差，然后结合自校正方法估计包括垂直航向误差在内的其他误差分
量，最后分别估计得到多个多普勒相同(由于频率欠采样)而方位各不相同地块
的空间导向矢量。本章第四节利用估计出的各地块的空间导向矢量并结合阵列
方向图调零方法提出了一种抑制空I司模糊近而完成大观测带、高方位分辨力
SAR成像的处理方法，该算法主要运算量集中在一次方位回波FFT和一次矩阵
求逆运算上，避免了多次方位FFT、估计协方差矩阵和其求逆运算，因而较己
有小卫星成像方法的运算量要小。最后的计算机仿真试验验证了方法的有效
性。
5.第六章主要针对前章方法的不足，即阵列误差估计需要地面特显点和阵列不能
有较大的垂直基线，提出了一种基于小卫星雷达接收回波数据的高速运动、超
大稀疏阵列的校正方法。由于小卫星平台上的天线孔径较小，回波信号中会存
在距离或者方位多普勒模糊，对于稀疏孔径的SAR成像和地面运动目标检测
(GMTI)应用，文中采用较低脉冲重复频率以保证距离不模糊(可以获得大观测
条带宽度)，而此时接收的回波数据存在方位多普勒模糊，然后对存在方位模
糊的回波数据进行多普勒处理以获得几个空间角度确知的校正源信号，最后利
用这些校正源信号对阵列误差进行估计、补偿。大量仿真结果表明，只要星间
测量和轨道控制精度控制在分米数量级，使用本文提出的方法可以很好的实现
对这种高速运动超大稀疏阵列误差的估
The problem of parameter estimation and array calibration with sub-Nyquist sampling is studied in this doctoral dissertation. Sampling the signals under Nyquist's theory is very difficult when they are in a wide band. It is urge to develop new techniques to deal with such difficulty. Sub-Nyquist sampling which is considered the perfect way to overcome this difficulty can allivate the burden with the system's design complexity. To estimate the directions-of-arrival(DOAs) from the samples of the array without ambiguity demands the interval between any two elements be less than the half of the wavelength of the signal with the maximum frequency. This restriction aggravates the mutual coupling of the signals with comparable low frequencies. Spatial sub-Nyquist which can not only allivate the mutual coupling between elements but also improve the estimation performance of DO As is considered a right technique to solve such problem. The problem of calibrate the highly sparse space- borne array is studied in the last two chapters. Two methods is proposed to remedy the sparse array through the analysis of the echoes from the illuminated area of the small satellite antenna. The detailed content included in every chapter is listed bellow:1. In chapter 2, a novel frequency estimation algorithm for wideband signal with sub-Nyquist sampling is proposed. With the aid of information provided by the auxiliary delayed sampling channel and the aliased frequency estimation for wideband signal with sub-Nyquist sampling, we can solve the frequency aliasing due to sub-Nyquist sampling. This method can reduce the complexity of the overall hardware at the cost of an auxiliary sampling channel. Furthermore, in order to alleviate the computation burden for its practicability, a more simplified algorithm based on propagator method(PM)is put forward. The simplified algorithm which is developed for practice in this chapter does not need to estimate the sample covariance matrix and only need to do one eigendecomposition with comparable lower dimensions to obtain the frequency estimation. A new method base on different sampling frequency to estimate frequencies from wide-band under-sampled data is also proposed in this chapter. The proposed method is not sensitive to the amplitude and phase errors of both channels and data obtained from two channels can be processed separately, thus it has a wider applied field than existing methods. At last, the effectiveness of the proposed algorithm is verified via computer simulations.
2. In chapter 3, using the proposed frequency estimation method in chapter 2 and the state-space realization approach, a subspace based algorithm to estimate the frequency, DOA and range of near-field sources is proposed, which does not need any spectral peak searching and the 3-D parameters are automatically paired. Moreover, the proposed method is applicable to arbitrary additive Gaussian noise environment. The effectiveness of the proposed algorithm is verified via computer simulations.3. In chapter 4, a novel method for joint frequency, 2-D direction-of-arrrival and polarization estimation of transverse electromagnetic waves based on arbitrary L-shaped vector sensor(VS)array is proposed. VS consists of six co-located but diversely polarized antennas separately measuring all six electromagnetic-field components of an incident wavefield. Sub-Nyquist temporal sampling is introduced to reduce the complexity of the system design. Furthermore, sub-Nyquist spatial sampling, which can further reduce the mutual coupling among VSs, is combined to improve the estimation performance of spatial parameters. The CRLB is also derived in the end of this paper to verify the efficiency of this method.4. In chapter 5, a novel calibration method is proposed which is adapted to the distributed small satellites array. A constellation composed of several distributed small satellite radars can cooperate to improve the performance of multiple missions, therefore it has several advantages over a larger, single space-borne radar of being well in pe
引文
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