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.     

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.     

一种采用协方差矩阵稀疏表示的DOA估计方法

提出一种新的基于样本协方差矩阵稀疏表示的联合波达方向估计方法.该方法对传统的基于协方差矩阵稀疏表示的模型进行改进,仅利用协方差矩阵的部分信息来进行波达方向估计,无须已知噪声功率,以极小的孔径损失换取算法的稳健性.虽然是基于样本统计信息(即协方差矩阵)的波达方向估计方法,但是其原理与传统的角度高分辨估计方法(MUSIC,CAPON)不同,该算法对具有任意相关性的信号源能进行有效的波达方向估计,不需要进行去相关处理,且具有很高的分辨力及估计精度.     

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。     

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.     

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。     

一种改进的二维扩展DOA估计方法

经典的DOA估计方法对目标信号源的分布特性非常敏感,导致DOA估计性能严重恶化,为了降低信源扩展对算法性能的影响,该文利用圆阵协方差矩阵的特点,直接由接收信号协方差矩阵的两条次对角线元计算分布式目标到达角,并提出了两种到达角估计方法,即直接由协方差矩阵的两条次对角线得到两维到达角的闭合解,和另一种利用两条次对角线构造最小二乘方程来估计分布源的两维到达角.计算机仿真结果表明,它们对均匀圆阵小角度扩展信号DOA估计具有良好的性能.     

基于矩阵填充的互质阵列欠定DOA估计方法

为了解决现有基于互质阵列的DOA估计方法舍弃差联合阵列中非均匀虚拟阵元而导致最大可估计信号数损失的问题,提出了一种基于矩阵填充的DOA估计方法。首先,根据差联合阵列与波程差一一对应的特性,构造一个部分元素缺失的Toeplitz化的阵列协方差矩阵,建立了基于矩阵填充的DOA估计模型,并验证了该模型满足零空间性质;然后,根据低秩矩阵填充理论,将DOA估计问题转化为矩阵核范数最小化问题进行求解,通过不定点延续算法将该协方差矩阵中的零元素进行填充恢复为完整协方差矩阵;最后,对协方差矩阵进行奇异值分解,转化为多项式求根,得到DOA的估计。仿真实验结果验证了本文方法的有效性和优越性。实验结果表明,本文方法能够对差联合阵列中的空洞部分进行有效填充,增加了可利用的阵列自由度,提高了可估计信号数,同时能够有效避免传统稀疏重构算法中由于角度域离散化导致的基不匹配问题对估计性能的影响,提高了估计精度和分辨力。     

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．     

Fast space-time adaptive processing method by using the sparse representation

One of the key problems of space-time adaptive processing (STAP) is how to estimate the clutter covariance matrix (CCM) accurately with a small number of samples when the clutter environment is heterogeneous. The CCM estimation methods based on sparse representation (CCM-SR) can achieve a good estimation performance with only one or a few samples, which significantly improves the convergence rate of the STAP. By using the sparsity characteristic of the clutter spectrum, the CCM-SR method estimates the clutter spectrum and yields a good estimation of the CCM. However, there are often many pseudo-peaks in the clutter spectrum estimated by the sparse representation (SR), which will cause a CCM estimation error. By exploiting the special relationship of the clutter ridge curve between space domain and Doppler domain, we can eliminate the pseudo-peaks in the clutter spectrum effectively via fitting the curve of the clutter ridge and improve the estimation accuracy of the CCM. In addition, a byproduct of our method is the estimation of the flying parameters (the velocity of the radar platform, the crab angle and so on). Experimental results show that the proposed method can improve the performance of conventional STAP based on sparse representation (STAP-SR) and obtain a good estimation of the flight parameters.     

一种新的稀疏重构的DOA估计算法

为提高低信噪比和较少快拍数条件下远场窄带信号波达方向的估计精度,提出一种新的基于加权l₁范数的稀疏重构波达方向的估计算法．该算法首先采用前后向空间平滑技术获得阵列输出数据协方差矩阵;其次构造出改进Capon算法空间谱函数中的倒谱系数矢量,设计得到符合加权l₁范数的权值矩阵;最后通过奇异值分解对接收数据进行降维处理,获得基于稀疏重构的加权l₁ 范数约束问题模型．仿真结果表明,在低信噪比或快拍数较少的情况下,该算法能够有效地抑制空间谱伪峰和保证较强的稳健性,且信源不需要进行相关处理,仍能获得很高的估计精度．     

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.     

无需信源数目的声矢量阵相干源方位估计算法

针对相干源方位估计问题,本文在PVFS（Particle Velocity Field Smoothing）算法的基础上,提出一种新的算法。该算法通过对PVFS算法构造出的协方差矩阵进行特征值分解,利用得到的特征值及特征向量构造新的噪声子空间,然后运用子空间原理实现相干源的方位估计。该算法无需已知相干源的信源数目且不会损失阵列孔径,具有较好的相干源方位估计性能,计算机仿真结果验证了本文算法的有效性。     

Matrix reconstruction high accuracy DOA estimation algorithm on the Nested array

For the nested array, the covariance matrix of the receiving data is pulled into a column vector by using the Khatri-Rao product, which is equivalent receiving data turned into the single snapshot. In the case of the covariance matrix being vectored, a new matrix reconstruction is presented to build up the rank of the new covariance matrix and the ESPRIT algorithm of an improved matrix reconstruction is proposed in this paper. The covariance matrix on the virtual array will be restored and more matrices can be reconstructed by using this approach.Then, the DOA estimation is obtained based on the ESPRIT algorithm of matrix reconstruction. Simulation results demonstrate that the proposed method achieves accurate DOA estimation when the number of targets is larger than that of array elements.     

降维STAP中稀疏恢复的角度多普勒通道选择方法

在机载雷达信号处理中,高强度的地杂波严重影响信号检测性能,而空时自适应处理(STAP)是一种有效抑制杂波的技术。实际处理中,由于杂波的非均匀性,空时自适应处理往往面临着可用有效样本数较少的问题,同时机载雷达处理的信号维度极为庞大。为了解决这些问题,提出了一种基于稀疏恢复的降维STAP通道选择方法。利用少量样本通过稀疏恢复的方法估计出全维度的杂波协方差矩阵(CCM),并以此为依据评估各个通道的重要性,选择合适的通道构造出降维后的杂波协方差矩阵并进行STAP处理,解决了有效样本较少的问题,同时保证了降维算法的性能。数值仿真验证了算法有效且比典型的稀疏STAP算法效果更好,讨论了在不同样本数下,输出性能与通道数的关系,结论具有工程应用意义。     

非圆信号的二维相干测向新方法

传统的二维相干测向算法都是针对圆信号提出的,且要求大快拍数和较多阵元数,在低信噪比时估计性能较差.通过充分利用非圆信号的特点和L型阵列的结构优势,提出了一种非圆信号的二维解相干新方法.该方法利用阵列接收信号数据及其共轭信号数据,重新构造阵列接收数据矩阵,有效地扩展了阵列孔径;同时,提出了一种修正的空间平滑技术进行解相干,最后采用ESPRIT算法实现相干信号的二维DOA估计.所提方法具有阵列利用率高的优点,能够有效弥补传统二维测向算法阵列利用率低的缺点,提高了ESPRIT算法在低信噪比时的估计性能.实验仿真结果表明,所提方法能够有效实现二维相干信号估计并且估计性能优良.     

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.     

一种改进的RootMUSIC快速算法

MUSIC算法是一种基于特征结构的子空间类超分辨算法,该算法性能优良,但需要估计协方差矩阵并进行特征分解和谱峰搜索,运算量较大。研究了波达方向估计问题并提出了一种改进的快速算法,该算法利用协方差矩阵的子矩阵得到信号子空间,无需特征分解,只需估计该子矩阵,然后用多项式求根的方法代替谱峰搜索,故该快速算法运算复杂度远低于MU-SIC算法,同时性能损失并不太大。理论分析和计算机仿真结果表明此算法是有效的。     

基于数据阵共轭重构的MUSIC角估计算法

介绍了一种利用接收数据及其共轭重构得到新的数据矩阵,然后借助于数据阵奇异值分解实现的修正MUSIC算法,并指出了这将有助于改善协方差矩阵特征值的分布,从而提高信号到达方向(DOA)的估计性能。在相同的信噪比和快拍数条件下,该方法无论是在角估计的均方误差、信号源角分辨能力等方面均优于普通的MUSIC算法,并给出了验证理论分析的计算机仿真结果。     

基于数据阵共轭重构的

This paper gives a modified MUSIC (MMUSIC) algorithm based on the singularity decomposition of the data matrix which is re-constructed by the received data and their conjugatings. This method can change the eigenvalue distributions of the covariance matrix and improve the performances of the signal DOA estimation. With the same SNR and snapshot number, the performances of MMUSIC algorithm are better than that of MUSIC algorithm not only in the estimation of DOA of singals, but also in the resolution of the arrival angle for singals. Finally, the simulation results confirming the theoretical analysis are presented.