基于稀疏重构的阵列信号多参数估计

发布时间：2018-06-07 13:53

本文选题：阵列信号处理 + 信源参数估计　；参考：《吉林大学》2014年博士论文

【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。
[Abstract]:The source parameter estimation is one of the main research fields in the field of array signal processing. It has important application value in radar, sonar, wireless communication, medical imaging, electronic countermeasures and seismic exploration. The subspace class method is the most representative of the traditional source parameter estimation methods, but it is due to the limit of the subspace theory frame. In recent years, with the emergence and continuous improvement of the theory of compressed sensing theory, sparse signal reconstruction, as its core theory, has aroused wide attention of scholars both at home and abroad. Such as high resolution, strong noise robustness and prior information without the need for the number of sources, sparse reconstruction theory and methods provide a possible way to solve or avoid the existing problems in the traditional source parameter estimation method.
The existing estimation methods of source parameters based on sparse reconstruction mainly focus on the one dimension DOA parameter estimation of far field sources, and most of them have the problem of estimation bias or global optimality. In this paper, the theoretical requirement of Robust Array Signal multi parameter estimation is tractive and sparse signal signal reconstruction is used as a mathematical processing method. Based on the applicability of the existing representative sparse reconstruction algorithm in the source parameter estimation, the problem of the estimation of the power and polarization parameters of the array far field source DOA and power parameter estimation, the array far and near field hybrid source DOA and the distance parameter estimation, the far field source DOA under the polarization sensitive array, and the estimation of the power and polarization parameters are carried out in the light of the existing representative sparse reconstruction algorithm. The aim of this study is to provide a new and effective solution for multi parameter estimation of array signals in different scenarios under the framework of sparse signal reconstruction.
The main contributions and innovative work of this article include:
1. under the background of Gauss white noise and unknown nonuniform noise, a new algorithm for joint estimation of DOA and power parameters based on the sparse representation of the two order statistics vector and the approximation of the l0 norm is proposed by using the TLP, DC decomposition theory and the summation mean operation. It is theoretically proved that the proposed l0 norm approximation sparse reconstruction algorithm is not only convergent, but also a new algorithm. It is stable, asymptotically unbiased. Using the principle of difference and cross validation, we choose reasonable regularization parameters and adjustment parameters. This algorithm can not only effectively suppress Gauss white noise and unknown nonuniform noise, but also overcome the existing L1 norm constraint methods (such as LASSO, BPDN or Group LASSO). It achieves higher resolution, estimation accuracy and noise robustness, and does not require precise initial conditions.
2. under the background of unknown color noise, the characteristic of color noise with symmetric Topelitz structure can be effectively suppressed by covariance difference. A new algorithm for DOA and power estimation based on Adaptive LASSO and covariance difference is proposed. The algorithm not only effectively inhibits the influence of color noise, but also obtains higher accuracy of DOA and power parameter estimation, and avoids the estimation of the noise covariance matrix and the prior information of the number of sources without the need of the number of sources. The problem of pseudo peak distinction is brought about by the operation.
3. for symmetric and uniform linear array, the sparse observation model is constructed in the two order statistics domain and the four order cumulant domain respectively. Based on the multi-dimensional parameter solution to the idea of multiple one-dimensional parameters, a method based on the four order cumulant vector sparse representation and the heavy weighted L1 norm constraint is proposed. The weighted L1 norm constraint and the far and near field hybrid source parameter estimation method of MUSIC are used to select the reasonable regularization parameters with the cross validation and the L curve method respectively. The two new algorithms not only effectively reduce the computational complexity, but also avoid unnecessary mesh division and parameter matching process. It is also applicable to parameter estimation in far-field sources and near field sources. It is a general algorithm.
4. first, the sparse reconstruction idea is extended to the polarization sensitive array, and a new algorithm for estimating the power and polarization parameters based on the sparse reconfiguration is proposed in the cross electric dipole array based on the sparse reconfiguration. How to obtain accurate multi parameter estimation and how to improve the algorithm by polarization information is discussed under the sparse reconfiguration of the polarization sensitive array. The simulation results show that the proposed algorithm can not only estimate the DOA, power and polarization parameters of the source at the same time, but also obtain improved resolution and noise robustness. At the same time, the proposed algorithm can also be effectively divided into two signal source signals with the aid of polarization information.
Under the framework of sparse signal reconstruction, this paper studies the multi parameter estimation of signal under scalar array and vector array. The new algorithm proposed in this paper has a certain improvement in estimation accuracy, noise robustness, resolution and sensitivity to the number of sources. Sparse reconstruction theory provides reference for array signal processing.
【学位授予单位】：吉林大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TN911.23

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