信号稀疏表示下的空域-极化域参数估计

为提高二维波达方向(DOA)和极化参数的估计精度,利用入射电磁波信号在空域分布的稀疏性,提出了一种基于信号稀疏表示的空域-极化域参数估计新方法。首先,利用基于中心共点的偶极子和磁环对阵列接收到的电场分量和磁场分量,构建了不包含极化参数的新的协方差矩阵。然后,将该协方差矩阵矢量化,得到其矢量形式的稀疏表示模型,并通过稀疏重构算法获得了波达方向估计结果。最后,结合电场数据分量与磁场数据分量的互协方差矩阵,构建包含极化参数的矢量化观测数据模型,并采用全局最小二乘法计算得到入射信号的极化参数估计结果。计算机仿真结果表明,本文算法可以有效地估计入射信号的波达方向和极化参数,具有较高的估计精度和较强的角度分辨能力。     

利用空间平滑的协方差秩最小化DOA估计方法

针对传统波达方向角估计算法在相干信号及非均匀噪声下估计精度差、分辨率低的问题,基于空间平滑方法,提出一种接收信号协方差矩阵秩最小化波达方向估计方法．在传统空间平滑方法的基础上,所提算法将接收信号协方差矩阵分别左右乘交换矩阵以得到空间后向平滑协方差矩阵;而后基于平滑矩阵的低秩性,将协方差矩阵重构为无噪声协方差矩阵;最后利用传统MUSIC算法实现波达方向估计．仿真结果表明,与传统MUSIC算法、基于矩阵补全理论的MUSIC算法和秩迹最小化算法相比,所提算法能较好地抑制非均匀噪声影响,且在相干条件下具有较好的波达方向估计性能．     

非平稳噪声下稀疏表示的DOA估计算法

为提高非平稳噪声下远场非相干窄带信号波达方向（DOA）的估计精度,提出了一种基于稀疏重构的DOA估计算法.采用类协方差差分算法构造差分矩阵,抑制非平稳噪声的影响;基于类旋转不变子空间参数估计算法基本原理构造稀疏表示模型与权函数;利用加权l₁范数对模型求解,实现DOA估计.仿真结果表明,与传统的协方差差分算法、噪声协方差矩阵估计算法、秩迹最小化算法以及稀疏重构算法相比,所提算法不仅能较好地抑制非平稳噪声的影响,而且在低信噪比、低快拍数情况下具有较强的稳健性和较高的估计精度.     

基于矢量水听器阵的迭代稀疏协方差矩阵拟合波达方向估计方法

针对矢量水听器阵列相干信号方位估计问题,提出了迭代稀疏协方差矩阵拟合波达方向估计(direction of arrival,DOA)算法。基于加权协方差矩阵拟合准则,构建了关于稀疏信号功率的目标函数,利用Frobenius范数性质推导了稀疏信号功率迭代更新的递推式。所提算法利用迭代重构的思想计算离散网格点上信号功率,使得估计的功率更精确,从而获得更加精确的DOA估计。理论分析表明,所提算法求解网格点上信号的功率经过了滤波器的预处理,该滤波器允许指定方向的信号通过并且衰减其他方向的信号,对信号的相关性具有较低的敏感度。仿真实验结果表明,在信噪比为15 dB,非相干信号情况下,所提方法估计的平均误差为多重信号分类高分辨方法的39.4%,迭代自适应稀疏信号表示方法的73.7%;相干信号情况下,所提方法估计的平均误差为迭代自适应稀疏信号表示方法的12.9%。所提算法应用于具有高度相关性目标的DOA估计时,可有效提高目标DOA估计的精度。     

适于相干信号DOA估计的改进矩阵差分方法

提出一种适用于色噪声背景下窄带信号的波达方向估计方法. 假设未知色噪声协方差矩阵具有对称的Toeplitz结构,利用线性变换改变阵列协方差矩阵,并与阵列协方差相减,理论上消除了噪声对算法估计性能的影响. 新差分算法适用于信号不相干或仅有2个信号相干的波达方向估计. 当相干信号多于2个时,通过与空间平滑算法结合,拓展了算法的应用范围. 与传统差分算法相比,新算法避免了“伪”波达方向估计,降低了计算复杂度. 仿真实验结果表明,新算法具有优越的估计性能.     

非均匀噪声环境下基于矩阵补全的DOA估计方法

针对传统的信号波达方向（DOA）估计算法无法适用于实际应用中非均匀噪声、数据不完整等情况的问题,提出了一种结合矩阵补全理论和最大似然交替投影算法的DOA估计方法。在背景噪声为非均匀噪声的情况下,该方法通过对只有部分元素已知的阵列协方差矩阵进行矩阵补全,将稀疏矩阵重构为无噪声协方差矩阵,然后利用最大似然交替投影算法实现对DOA的估计。实验仿真表明:该DOA估计方法能够有效恢复不完整数据并抑制非均匀噪声的影响,而且在低信噪比条件下,仍具有较好的DOA估计性能。     

基于加权l1范数稀疏信号表示的DOA估计

为了在小样本、低信噪比以及高信源相关性的条件下都能对波达方向(direction of arrival,DOA)进行精确估计,基于压缩感知理论,利用目标信号空间分布的稀疏性,提出了基于加权l_1范数稀疏信号表示的DOA估计算法.该算法对l_1-奇异值分解(singular value decomposition,SVD)算法进行改进,对接收矩阵进行预处理,根据子空间的正交性确定加权矩阵,以加权l_1范数作为最小化的目标函数进行优化得到稀疏信号,进而得到信号的DOA.仿真结果表明,通过加权处理的l_1范数下稀疏信号重构方法能有效抑制偏差,在低信噪比下能够准确稳定地估计出DOA,并且能够提高估计精度.     

基于阵列协方差矩阵列向量稀疏表示的高分辨波达方向估计

提出了两种基于稀疏重构的高分辨波达方向(DOA)估计方法。对空间进行粗、细两步网格划分,并在相应的过完备基下获得阵列协方差矩阵列向量的稀疏表示,分别基于剔除及差分处理抑制噪声干扰影响。采用lp范数约束正则化迭代加权最小范数(FOCUSS)算法进行稀疏重构,在重构过程中,对过完备基进行奇异值分解并剔除奇异值小于阈值项以减小计算量,并解决过完备基条件数过大带来的病态问题。仿真结果验证了所提算法的有效性和鲁棒性。     

基于噪声子空间二阶锥规划求解的宽带波达方向估计算法

现有宽带子空间类方位估计方法需要对庞大的空时联合采样相关矩阵进行特征分解运算以获得好的估计性能,计算复杂度高.提出一种基于噪声子空间二阶锥规划求解、计算有效的宽带波达方向估计算法.该算法将宽带信号低秩模型的噪声子空间估计转换为凸最优理论中的二阶锥规划问题,实现宽带源方位估计,整个过程不需要估计样本协方差矩阵,不需要矩阵特征值分解或奇异值分解,运算量低.给出算法的理论分析、实现步骤.统计性能比较表明该算法分辨门限低、方位估计精度高.千岛湖湖试结果证明该算法在实际声纳阵系统中可有效实现宽带源波达方向估计.     

一种用于矩形阵列的二维波达方向估计方法

针对现有使用均匀矩形阵列或稀疏矩形阵列的二维无格波达方向估计方法的性能欠佳的问题,提出一种基于二阶特普利茨矩阵重构和二维旋转不变参数估计技术的无格波达方向估计方法。使用均匀矩形阵列或稀疏矩形阵列,对其接收信号的协方差矩阵进行二阶特普利茨结构表达,通过log-det稀疏测度与正定约束构造约束优化问题,并使用优化最小算法求解,最后通过二维旋转不变参数估计技术估计源的二维波达方向,即方位角与俯仰角。这种方法需要多次求解半定规划问题,计算复杂度相对较高,但能获得更好的波达方向估计性能。在仿真实验中,这种方法在均匀矩形阵列或稀疏矩形阵列条件下均有非常低的均方根误差,接近克拉美罗界,证明了其良好的波达方向估计性能。     

A Singular Value Thresholding Based Matrix Completion Method for DOA Estimation in Nonuniform Noise

Usually, the problem of direction-of-arrival (DOA) estimation is performed based on the assumption of uniform noise. In many applications, however, the noise across the array may be nonuniform. In this situation, the performance of DOA estimators may be deteriorated greatly if the non-uniformity of noise is ignored. To tackle this problem, we consider the problem of DOA es-timation in the presence of nonuniform noise by leveraging a singular value thresholding (SVT) based matrix completion method. Different from that the traditional SVT method apply fixed threshold, to improve the performance, the proposed method can obtain a more suitable threshold based on careful estimation of the signal-to-noise ratio(SNR) levels. Specifically, we firstly employ an SVT-based matrix completion method to estimate the noise-free covariance matrix. On this basis, the signal and noise subspaces are obtained from the eigendecomposition of the noise-free cov-ariance matrix. Finally, traditional subspace-based DOA estimation approaches can be directly ap-plied to determine the DOAs. Numerical simulations are performed to demonstrate the effective-ness of the proposed method.     

New method for estimating 2-D DOA in the coherent source environment based on data matrix reconstruction

The performance of classical two dimensional (2-D) Direction-Of-Arrival (DOA) estimation algorithms degrade substantially in the presence of coherent environment. A new DOA matrix method——DOA matrix method based on data matrix reconstruction (DMR-DOAM) is proposed for 2-D DOA estimation in the coherent source environment. The proposed algorithm reconstructs two Toeplitz equivalent covariance matrices by using cross-correlation information among receiving data from arrays. Decorrelation and 2-D DOA estimation can be realized via the eigen-decomposition of the new DOA matrix. The algorithm can retain the advantages of the traditional DOA matrix method, such as automatical parameter alignment and no need of 2-D search spectrum peak. The equivalent covariance matrices only use the middle column of classical covariance matrices, so the calculation amount is reduced, and the algorithm can be realized easily. Furthermore, the paper analyzes the estimation performance and influencing factors of the proposed algorithm. Theoretical analyses and simulation results both show that the proposed algorithm is effective.     

DOA Estimation Method Using Sparse Repres-entation with Orthogonal Projection

In order to reduce the effect of noises on DOA estimation, this paper proposes a direc-tion-of-arrival (DOA) estimation method using sparse representation with orthogonal projection (OPSR). The OPSR method obtains a new covariance matrix by projecting the covariance matrix of the array data to the signal subspace, leading to the elimination of the noise subspace. After-wards, based on the new covariance matrix after the orthogonal projection, a new sparse representa-tion model is established and employed for DOA estimation. Simulation results demonstrate that compared to other methods, the OPSR method has higher angle resolution and better DOA estima-tion performance in the cases of few snapshots and low SNRs.     

2-D DOA estimation of coexisting uncorrelated and coherent signals

The common two dimensional (2-D) direction of arrival (DOA) estimation algorithms for coexisting uncorrelated and coherent signals are based on the complex array structure, such as the uniform rectangular array, so the computational complexity is high and the array aperture is not utilized efficiently. By taking advantage of the L-shape array and adopting an efficient method to eliminate the Gaussian noise, a new 2-D DOA estimation method is proposed. Firstly, the DOAs of the uncorrelated signals are estimated and the influence of the coherent signals is eliminated by utilizing its characteristics. Then, the data covariance matrix containing the coherent information only is obtained by exploiting the Toeplitz property of the uncorrelated signals, and the DOAs of the coherent signals are estimated by the direction finding method based on the compressed sensing theory. Theoretical analysis and simulation results show that the proposed method has a small computational load, high array aperture as well as excellent estimation performance.     

DOA estimation of coexisted noncoherent and coherent signals via sparse representation of cleaned array covariance matrix

A new direction finding method is presented to deal with coexisted noncoherent and coherent signals without smoothing operation. First the direction-of-arrival (DOA) estimation task is herein reformulated as a sparse reconstruction problem of the cleaned array covariance matrix, which is processed to eliminate the affection of the noise. Then by using the block of matrices, the information of DOAs which we pursuit are implied in the sparse coefficient matrix. Finally, the sparse reconstruction problem is solved by the improved M-FOCUSS method, which is applied to the situation of block of matrices. This method outperforms its data domain counterpart in terms of noise suppression, and has a better performance in DOA estimation than the customary spatial smoothing technique. Simulation results verify the efficacy of the proposed method.     

基于均匀面阵的相干信号源二维DOA估计新方法

相干信号源的来波方向(Direction of Arrival,DOA)估计问题一直是阵列信号处理技术的一个研究热点。现实环境中的信号源多为相干的,针对此问题提出一种改进的相干信号源二维DOA估计算法。通过对接收信号协方差矩阵进行矩阵重构处理,将采样数据协方差矩阵的秩恢复到等于信号源的个数;对重构的协方差矩阵进行特征分解,构造出信号子空间矩阵和噪声子空间矩阵,将两个子空间矩阵联合构造出新的空间谱函数;基于新的空间谱函数进行二维谱峰搜索,即可估计出多个入射信号的二维DOA。使用计算机软件进行仿真验证,仿真结果表明了所提方法的有效性。