基于稀疏重构的阵列信号多参数估计
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摘要
信源参数估计是阵列信号处理领域的主要研究内容之一，在雷达、声呐、无线通信、医学成像、电子对抗及地震勘探等领域有着重要的应用价值。传统的信源参数估计方法中以子空间类方法最具代表性，然而正是由于子空间理论框架的限制，其存在的共有以及特有的一些缺点目前还无法被完全突破。近年来，随着压缩感知理论体系的出现和不断完善，作为其核心理论的稀疏信号重构引起了国内外学者的广泛关注。从稀疏信号重构角度进行阵列信号参数估计可以获得诸如高分辨率、强噪声鲁棒性和无需信源数的先验信息等诸多潜在优势，稀疏重构理论和方法为解决或者规避传统信源参数估计方法中存在的问题提供了一条可能的途径。
现有基于稀疏重构的信源参数估计方法主要集中于远场源的一维DOA参数估计，且大多存在估计偏或者全局最优性不能保证等问题。本文以鲁棒的阵列信号多参数估计的理论需求为牵引，以稀疏信号重构为数学处理手段，在系统分析与评价现有代表性稀疏重构算法在信源参数估计中的适用性的基础上，由浅入深、循序渐进的对阵列远场源DOA和功率参数估计、阵列远近场混合源DOA和距离参数估计，以及极化敏感阵列下的远场源DOA、功率和极化参数估计问题进行深入的研究。旨在稀疏信号重构框架下为不同场景下的阵列信号多参数估计问题研究提供新而有效的解决思路。
本文的主要贡献与创新性工作包括：
1.在高斯白噪声、未知非均匀噪声背景下，应用TLP、DC分解理论以及求和平均运算，提出了基于二阶统计量向量稀疏表示和l0范数逼近的DOA和功率参数联合估计新算法。从理论上证明了所提的l0范数逼近稀疏重构算法不仅是收敛的，而且是稳定的、渐进无偏的。分别采用差异原则和交叉验证选择合理的正则化参数和调整参数。该算法不仅可以有效地抑制高斯白噪声和未知非均匀噪声，而且克服了现有l1范数约束方法（如LASSO、BPDN或Group LASSO）中普遍存在的估计偏的问题，获得了更高的分辨率、估计精度和噪声鲁棒性，而且无需精确的初始条件。
2.在未知色噪声背景下，利用协方差差分可以有效抑制具有对称Topelitz结构的色噪声的特性，提出了基于Adaptive LASSO和协方差差分的DOA和功率估计新算法。借助过完备基矩阵的特殊结构，利用留一交叉验证的一种特殊形式来选择合理的正则化参数。该算法不仅有效地抑制了色噪声的影响，获得了更高的DOA和功率参数估计精度，而且避免了噪声协方差矩阵的估计以及无需信源数的先验信息。同时还可以通过对谱峰值正负号的判断，简单而有效地解决应用协方差差分技术带来的伪峰区分问题。
3.针对对称均匀线性阵列，分别在二阶统计量域和四阶累积量域构建稀疏观测模型，基于多维参数求解转化为多个一维参数分别求解的思想，提出了基于四阶累积量向量稀疏表示和重加权l1范数约束的远近场混合源参数估计方法、基于加权l1范数约束和MUSIC的远近场混合源参数估计方法。分别采用交叉验证和L曲线法选择合理的正则化参数。所提的两种新算法在保证参数估计精度的同时，不仅有效地降低了计算复杂度、避免了不必要的网格划分和参数配对过程，而且还适用于远场源和近场源情况下的参数估计，是一类通用的算法。
4.率先将稀疏重构思想拓展至极化敏感阵列，提出了交叉电偶极子阵下基于稀疏重构的DOA、功率和极化参数估计新算法。讨论了如何在极化敏感阵列下基于稀疏重构获得精确的多参数估计以及如何借助极化信息来进一步改善算法的适用性和参数估计性能。仿真结果显示所提算法不仅可以同时估计信源的DOA、功率和极化参数，而且可以获得改进的分辨率和噪声鲁棒性，同时还可借助极化信息有效地区分两个入射角度一样的信源信号。
本文在稀疏信号重构理论框架下，对标量阵列和矢量阵列下的信号多参数估计问题进行了深入的研究。提出的上述新算法，在估计精度、噪声鲁棒性、分辨率和对信源数的敏感性等方面较现有方法均有一定的改善，为进一步研究基于稀疏重构理论的阵列信号处理相关问题提供参考。
Source parameter estimation is one of the most important issues in array signalprocessing. Thus it has played a fundamental role in many applications involving radar,sonar, wireless communication, medical imaging，electronic surveillance and seismicexploration, etc. Among the traditional source parameter estimation methods, a classof the most representative one is subspace-based method. However, the common andpeculiar drawbacks of this class of methods cannot be completely overcome since thelimitation of the subspace framework. Recently, the sparse signal reconstruction hasattracted wide attention of scholars with the emergence and continuous improvementof compressed sensing theory. Source parameter estimation from sparse signalreconstruction perspective can bring many potential advantages, such as highresolution, good robustness to noise and without knowing the prior knowledge of thesource number. It can be regarded that the sparse signal reconstruction theory andmethod provide a possible way to solve or circumvent the problems existed in thetraditional source parameter estimation methods.
The existing sparse-reconstruction-based source parameter methods mainlyconcentrate on estimating far-field DOA parameter，and most of them either sufferfrom estimation bias or cannot guarantee the global optimality. This paper focuses onresearching robust array signal multi-parameter estimation problems utilizing sparsesignal reconstruction. We first analyze and evaluate the suitability of classical sparsesignal reconstruction algorithms on source parameter estimation, and successivelypropose far-field DOA and power estimation, mixed far-field and near-field DOA andrange estimation, as well as polarized far-field DOA, power and polarizationestimation algorithms by proceeding in an orderly way and step by step. Our aim isto provide a series of new and effective ideas for array signal multi-parameterestimation problem in sparse signal reconstruction framework.
The main contributions and innovative points of this dissertation are listed asfollows:
1. We propose a new DOA and power estimation algorithm using a sparserepresentation of second-order statistics vector andl0-norm approximation inGaussian white noise and unknown nonuniform noise, based on TLP, DC decomposition and sum-average arithmetic. Theoretically, we prove that theproposedl0-norm approximation algorithm is not only convergent, but also stableand asymptotic unbiased. The regularization parameter and tunning parameter areselected properly by discrepancy principle and cross-validation, respectively. Theproposed algorithm, in addition to eliminating the influence of Gaussian white noiseand unknown nonuniform noise effectively, and overcoming the estimation biasinvolved in the existingl1-norm constraint reconstruction algorithms (such asLASSO、BPDN or Group LASSO), gains an improved resolution, estimationaccuracy and robustness to noise. Meanwhile, it can estimate the source parameterswithout the need of an accurate initialization.
2. Exploiting the characteristic that covariance differencing can eliminate thesymmetric Toeplitz colored noise effectively, we propose a novel DOA and powerestimation algorithm jointly using Adaptive LASSO and covariance differencing inunknown colored noise. We use a special case of cross-validation to select theregularization parameter properly on the basis of the special structure ofovercomplete basis matrix. The proposed algorithm can not only eliminate theinfluence of colored noise effectively and gain improved DOA and power estimationaccuracy, but also avoid the pre-estimation of noise covariance matrix. Meanwhile, itcan estimate DOA and power parameters without knowing the prior knowledge ofsource number, and the false peaks brought by covariance differencing can be easilydistinguished by judging the sign of spatial spectrum.
3. By utilizing symmetric uniform linear array, we construct two kinds of sparseobservation models in second-order statistics and fourth-order cumulant domainrespecitvely. Sequentially, we propose two new mixed source localization algorithms,namely mixed far-field and near-field source parameter estimation based on a sparserepresentation of cumulant vectors and reweightedl1-norm constraint, mixedfar-field and near-field source parameter estimation jointly using weightedl1-normconstraint and MUSIC, using the idea that transforming multidimensional parametersolution into multiple one-dimensional parameter. The proposed two kinds of newalgorithms not only decrease the computational complexity effectively, avoid theunnecessary grid division and parameter-pairing process, but also suitable forfar-field and near-field source parameter estimation. Meanwhile, the estimationaccuracy can also be guaranteed. In a word, they can be regarded as a class ofcommon algorithm.
4. We extend the sparse signal reconstruction to polarized sensitive array for thefirst time in source parameter estimation field, and further propose a new DOA、power and polarization estimation algorithm. We discuss in depth on how to obtainaccurate multi-parameter estimation using sparse signal reconstruction with polarized sensitive array, and also demonstrate how to exploit polarized information to improvethe suitability and estimation performance of the algorithm. Simulation results showthat the proposed algorithm can not only estimate DOA, power and polarizationparameters simultaneously, but also achieve an improved resolution and robustness tonoise. Moreover, the proposed algorithm can distinguish two sources with same DOAsuccessfully by utilizing polarized information.
The multi-parameter estimation for array signals with scalar and vector array isstudied deeply in this paper from sparse signal reconstruction perspective. Comparedwith the existing methods, the proposed several algorithms provided an improvedperformance on estimation accuracy, robustness to noise, resolution and sensitivity tothe number of sources, etc. The research results of this paper will provide referencefor further study on array signal processing issues based on sparse signalreconstruction.
现有基于稀疏重构的信源参数估计方法主要集中于远场源的一维DOA参数估计，且大多存在估计偏或者全局最优性不能保证等问题。本文以鲁棒的阵列信号多参数估计的理论需求为牵引，以稀疏信号重构为数学处理手段，在系统分析与评价现有代表性稀疏重构算法在信源参数估计中的适用性的基础上，由浅入深、循序渐进的对阵列远场源DOA和功率参数估计、阵列远近场混合源DOA和距离参数估计，以及极化敏感阵列下的远场源DOA、功率和极化参数估计问题进行深入的研究。旨在稀疏信号重构框架下为不同场景下的阵列信号多参数估计问题研究提供新而有效的解决思路。
本文的主要贡献与创新性工作包括：
1.在高斯白噪声、未知非均匀噪声背景下，应用TLP、DC分解理论以及求和平均运算，提出了基于二阶统计量向量稀疏表示和l0范数逼近的DOA和功率参数联合估计新算法。从理论上证明了所提的l0范数逼近稀疏重构算法不仅是收敛的，而且是稳定的、渐进无偏的。分别采用差异原则和交叉验证选择合理的正则化参数和调整参数。该算法不仅可以有效地抑制高斯白噪声和未知非均匀噪声，而且克服了现有l1范数约束方法（如LASSO、BPDN或Group LASSO）中普遍存在的估计偏的问题，获得了更高的分辨率、估计精度和噪声鲁棒性，而且无需精确的初始条件。
2.在未知色噪声背景下，利用协方差差分可以有效抑制具有对称Topelitz结构的色噪声的特性，提出了基于Adaptive LASSO和协方差差分的DOA和功率估计新算法。借助过完备基矩阵的特殊结构，利用留一交叉验证的一种特殊形式来选择合理的正则化参数。该算法不仅有效地抑制了色噪声的影响，获得了更高的DOA和功率参数估计精度，而且避免了噪声协方差矩阵的估计以及无需信源数的先验信息。同时还可以通过对谱峰值正负号的判断，简单而有效地解决应用协方差差分技术带来的伪峰区分问题。
3.针对对称均匀线性阵列，分别在二阶统计量域和四阶累积量域构建稀疏观测模型，基于多维参数求解转化为多个一维参数分别求解的思想，提出了基于四阶累积量向量稀疏表示和重加权l1范数约束的远近场混合源参数估计方法、基于加权l1范数约束和MUSIC的远近场混合源参数估计方法。分别采用交叉验证和L曲线法选择合理的正则化参数。所提的两种新算法在保证参数估计精度的同时，不仅有效地降低了计算复杂度、避免了不必要的网格划分和参数配对过程，而且还适用于远场源和近场源情况下的参数估计，是一类通用的算法。
4.率先将稀疏重构思想拓展至极化敏感阵列，提出了交叉电偶极子阵下基于稀疏重构的DOA、功率和极化参数估计新算法。讨论了如何在极化敏感阵列下基于稀疏重构获得精确的多参数估计以及如何借助极化信息来进一步改善算法的适用性和参数估计性能。仿真结果显示所提算法不仅可以同时估计信源的DOA、功率和极化参数，而且可以获得改进的分辨率和噪声鲁棒性，同时还可借助极化信息有效地区分两个入射角度一样的信源信号。
本文在稀疏信号重构理论框架下，对标量阵列和矢量阵列下的信号多参数估计问题进行了深入的研究。提出的上述新算法，在估计精度、噪声鲁棒性、分辨率和对信源数的敏感性等方面较现有方法均有一定的改善，为进一步研究基于稀疏重构理论的阵列信号处理相关问题提供参考。
Source parameter estimation is one of the most important issues in array signalprocessing. Thus it has played a fundamental role in many applications involving radar,sonar, wireless communication, medical imaging，electronic surveillance and seismicexploration, etc. Among the traditional source parameter estimation methods, a classof the most representative one is subspace-based method. However, the common andpeculiar drawbacks of this class of methods cannot be completely overcome since thelimitation of the subspace framework. Recently, the sparse signal reconstruction hasattracted wide attention of scholars with the emergence and continuous improvementof compressed sensing theory. Source parameter estimation from sparse signalreconstruction perspective can bring many potential advantages, such as highresolution, good robustness to noise and without knowing the prior knowledge of thesource number. It can be regarded that the sparse signal reconstruction theory andmethod provide a possible way to solve or circumvent the problems existed in thetraditional source parameter estimation methods.
The existing sparse-reconstruction-based source parameter methods mainlyconcentrate on estimating far-field DOA parameter，and most of them either sufferfrom estimation bias or cannot guarantee the global optimality. This paper focuses onresearching robust array signal multi-parameter estimation problems utilizing sparsesignal reconstruction. We first analyze and evaluate the suitability of classical sparsesignal reconstruction algorithms on source parameter estimation, and successivelypropose far-field DOA and power estimation, mixed far-field and near-field DOA andrange estimation, as well as polarized far-field DOA, power and polarizationestimation algorithms by proceeding in an orderly way and step by step. Our aim isto provide a series of new and effective ideas for array signal multi-parameterestimation problem in sparse signal reconstruction framework.
The main contributions and innovative points of this dissertation are listed asfollows:
1. We propose a new DOA and power estimation algorithm using a sparserepresentation of second-order statistics vector andl0-norm approximation inGaussian white noise and unknown nonuniform noise, based on TLP, DC decomposition and sum-average arithmetic. Theoretically, we prove that theproposedl0-norm approximation algorithm is not only convergent, but also stableand asymptotic unbiased. The regularization parameter and tunning parameter areselected properly by discrepancy principle and cross-validation, respectively. Theproposed algorithm, in addition to eliminating the influence of Gaussian white noiseand unknown nonuniform noise effectively, and overcoming the estimation biasinvolved in the existingl1-norm constraint reconstruction algorithms (such asLASSO、BPDN or Group LASSO), gains an improved resolution, estimationaccuracy and robustness to noise. Meanwhile, it can estimate the source parameterswithout the need of an accurate initialization.
2. Exploiting the characteristic that covariance differencing can eliminate thesymmetric Toeplitz colored noise effectively, we propose a novel DOA and powerestimation algorithm jointly using Adaptive LASSO and covariance differencing inunknown colored noise. We use a special case of cross-validation to select theregularization parameter properly on the basis of the special structure ofovercomplete basis matrix. The proposed algorithm can not only eliminate theinfluence of colored noise effectively and gain improved DOA and power estimationaccuracy, but also avoid the pre-estimation of noise covariance matrix. Meanwhile, itcan estimate DOA and power parameters without knowing the prior knowledge ofsource number, and the false peaks brought by covariance differencing can be easilydistinguished by judging the sign of spatial spectrum.
3. By utilizing symmetric uniform linear array, we construct two kinds of sparseobservation models in second-order statistics and fourth-order cumulant domainrespecitvely. Sequentially, we propose two new mixed source localization algorithms,namely mixed far-field and near-field source parameter estimation based on a sparserepresentation of cumulant vectors and reweightedl1-norm constraint, mixedfar-field and near-field source parameter estimation jointly using weightedl1-normconstraint and MUSIC, using the idea that transforming multidimensional parametersolution into multiple one-dimensional parameter. The proposed two kinds of newalgorithms not only decrease the computational complexity effectively, avoid theunnecessary grid division and parameter-pairing process, but also suitable forfar-field and near-field source parameter estimation. Meanwhile, the estimationaccuracy can also be guaranteed. In a word, they can be regarded as a class ofcommon algorithm.
4. We extend the sparse signal reconstruction to polarized sensitive array for thefirst time in source parameter estimation field, and further propose a new DOA、power and polarization estimation algorithm. We discuss in depth on how to obtainaccurate multi-parameter estimation using sparse signal reconstruction with polarized sensitive array, and also demonstrate how to exploit polarized information to improvethe suitability and estimation performance of the algorithm. Simulation results showthat the proposed algorithm can not only estimate DOA, power and polarizationparameters simultaneously, but also achieve an improved resolution and robustness tonoise. Moreover, the proposed algorithm can distinguish two sources with same DOAsuccessfully by utilizing polarized information.
The multi-parameter estimation for array signals with scalar and vector array isstudied deeply in this paper from sparse signal reconstruction perspective. Comparedwith the existing methods, the proposed several algorithms provided an improvedperformance on estimation accuracy, robustness to noise, resolution and sensitivity tothe number of sources, etc. The research results of this paper will provide referencefor further study on array signal processing issues based on sparse signalreconstruction.
引文
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