A performance analysis of subspace-based methods in the presence ofmodel error. II. Multidimensional algorithms

For pt.I, see ibid., vol.40, no.7, p.1758-74 (1992). In pt.I the performance of the MUSIC algorithms for narrowband direction-of-arrival (DOA) estimation when the array manifold and noise covariance are not correctly modeled was investigated. This analysis is extended to multidimensional subspace-based algorithms including deterministic (or conditional) maximum likelihood, MD-MUSIC, weighted subspace fitting (WSF), MODE, and ESPRIT. A general expression for the variance of the DOA estimates that can be applied to any of the above algorithms and to any of a wide variety of scenarios is presented. Optimally weighted subspace fitting algorithms are presented for special cases involving random unstructured errors of the array manifold and noise covariance. It is shown that one-dimensional MUSIC outperforms all of the above multidimensional algorithms for random angle-independent array perturbations     

基于内插阵列变换的非圆信号MUSIC算法

针对非圆信号的波达方向(DOA)估计问题,提出一种基于内插阵列变换的非圆信号MUSIC算法(VIA-NC-MUSIC算法)。利用真实阵列流型与虚拟阵列流型之间的变换矩阵,将真实协方差矩阵变换为虚拟协方差矩阵,再对虚拟协方差矩阵进行奇异值分解(SVD),利用信号子空间与噪声子空间的正交性,得出算法的空间谱函数。仿真实验表明:存在阵元位置误差的情况下,新算法通过对阵元位置校准数据进行内插阵列变换(VIA),取得与阵元位置校准的非圆信号MUSIC算法(NC-MUSIC算法)相当的估计性能,保持了高估计精度、阵列扩展能力等优点。     

Source localization using recursively applied and projected (RAP)MUSIC

A new method for source localization is described that is based on a modification of the well-known MUSIC algorithm. In classical MUSIC, the array manifold vector is projected onto an estimate of the signal subspace. Errors in the estimate of the signal subspace can make localization of multiple sources difficult. Recursively applied and projected (RAP) MUSIC uses each successively located source to form an intermediate array gain matrix and projects both the array manifold and the signal subspace estimate into its orthogonal complement. The MUSIC projection to find the next source is then performed in this reduced subspace. Special assumptions about the array manifold structure, such as Vandermonde or shift invariance, are not required. Using the metric of principal angles, we describe a general form of the RAP-MUSIC algorithm for the case of diversely polarized sources. Through a uniform linear array simulation with two highly correlated sources, we demonstrate the improved Monte Carlo error performance of RAP-MUSIC relative to MUSIC and two other sequential subspace methods: S and IES-MUSIC. We then demonstrate the more general utility of this algorithm for multidimensional array manifolds in a magnetoencephalography (MEG) source localization simulation     

一种适用于小样本的迭代多重信号分类算法

当样本数不足时,由采样协方差矩阵特征分解得到的噪声子空间偏离其真实值,使得多重信号分类(MUSIC)算法目标角度(DOA)估计性能下降。为了解决这个问题,该文提出了一种迭代算法通过校正信号子空间来提高MUSIC算法性能。该方法首先利用采样协方差矩阵特征分解得到的噪声子空间粗略估计目标角度;其次基于信源的稀疏性和导向矢量的低秩特性,由上一步得到的目标角度以及其邻域角度对应的导向矢量构造一个新的信号子空间;最后通过解一个优化问题来校正信号子空间。仿真结果表明,该算法有效地提高了子空间估计精度。基于新的信号子空间实现MUSIC DOA估计可以使得性能得到改善,且在低样本数下改善尤为明显。     

电磁矢量传感器阵列信号波达角估计的模R投影MUSIC简

 为了充分利用电磁矢量传感器阵列数据中存在的多维结构,本文探讨了具有多维数据结构的电磁矢量传感器阵列多模张量模型的建立,以及模R信号子空间的定义,提出一种基于模R信号子空间投影的MUSIC算法.分析表明:由于模R投影方法可充分利用电磁矢量传感器阵列中的多维结构信息,从而可提高信号子空间的估计精度,进而可使MUSIC算法的性能得以改善.计算机的仿真研究验证了模R投影MUSIC算法明显优于传统MUSIC方法.     

Blind DOA and polarization estimation for polarization-sensitive array using dimension reduction MUSIC

A novel blind direction-of-arrival (DOA) and polarization estimation algorithm for polarization-sensitive uniform linear array using dimension reduction multiple signal classification (MUSIC) is proposed in this paper. The proposed algorithm utilizes the signal subspace to obtain an initial estimation of DOA, then estimates more accurate DOA through a one-dimensional (1-D) local searching according to the initial estimation of DOA, and finally obtains polarization parameter estimation via the estimated polarization steering vectors. The proposed algorithm, which only requires a one-dimension local searching, can avoid the high computational cost within multi-dimensional MUSIC algorithm. The simulation results reveal that the proposed algorithm has better DOA and polarization estimation performance than both estimation of signal parameters via rotational invariance technique algorithm and trilinear decomposition algorithm. Furthermore, the proposed algorithm can be suitable for irregular array geometry, obtain automatically paired multi-dimensional parameter estimation, and avoid multi-dimensional searching. Simulation results verify the effectiveness of the proposed algorithm.     

Two-dimensional DOA estimation for acoustic vector-sensor array using a successive MUSIC

This paper discusses the problem of two-dimensional (2D) direction of arrival (DOA) estimation for acoustic vector-sensor array, and derives a successive multiple signal classification (MUSIC) algorithm therein. The proposed algorithm obtains initial estimations of the azimuth and elevation angles obtained from the signal subspace, and uses successively one-dimensional local searches to achieve the joint estimation of 2D-DOA. The proposed algorithm, which requires the one-dimension local searches, can avoid the high computational cost within 2D-MUSIC algorithm. The proposed algorithm can obtain automatically-paired 2D-DOA estimation for acoustic vector-sensor array, and it has better DOA estimation performance than propagator method, estimation of signal parameters via rotational invariance technique algorithm and trilinear decomposition algorithm. Meanwhile, it has very close angle estimation to 2D-MUSIC algorithm. Furthermore, it is suitable for non-uniform linear arrays, works well for the sources with the same azimuth angle, and imposes less constraint on the sensor spacing, which does not have to be restricted within half-wavelength. We have also derived the mean-square error of DOA estimation of the proposed algorithm and the Cramer-Rao bound of DOA estimation. Simulation results verify the usefulness of the proposed algorithm.     

用一种新的空时导向矢量联合估计CDMA信号波达方向与多径时延

本文针对CDMA系统提出了一种不需要训练信号而直接对接收的正常通信信号进行处理,实现感兴趣用户的波达方向(DOA)与多径时延联合估计的新方法.该方法是一种基于空时二维的MUSIC方法,首先建立了一种新的数据结构,并对其形成的相关矩阵进行特征分解,然后采用构造的新导向矢量对特征空间进行搜索.这种方法克服了要求接收信号数小于阵元数的局限,能有效估计时延不同、波达方向相差很小的多径信号的参数.     

加权伪噪声子空间投影的修正MUSIC算法

多重信号分类（multiple signal classification: MUSIC）方法通过计算搜索导向矢量与噪声或信号子空间的距离来估计波达方向,对采样协方差矩阵的依赖性较大。在小快拍或存在强弱临近信号条件下,采样协方差矩阵的估计值与真实值通常存在较大差异,导致估计的噪声或信号子空间发生畸变,严重恶化了MUSIC方法的波达角估计性能。针对该问题,本文提出采用加权伪噪声子空间投影的改进方法（称为wpnMUSIC）。该方法在修正数据相关矩阵的基础上估计与搜索导向矢量对应的伪噪声子空间并利用其在伪噪声子空间的投影值对MUSIC空间谱进行加权处理,在保持子空间处理方法高分辨能力的同时改善了对小快拍和强弱信号的稳健性。理论分析和仿真实验表明本文方法对强弱临近目标的分辨能力优于MUSIC方法。      

Novel angle estimation for bistatic MIMO radar using an improved MUSIC

In this article, we study the problem of angle estimation for bistatic multiple-input multiple-output (MIMO) radar and propose an improved multiple signal classification (MUSIC) algorithm for joint direction of departure (DOD) and direction of arrival (DOA) estimation. The proposed algorithm obtains initial estimations of angles obtained from the signal subspace and uses the local one-dimensional peak searches to achieve the joint estimations of DOD and DOA. The angle estimation performance of the proposed algorithm is better than that of estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm, and is almost the same as that of two-dimensional MUSIC. Furthermore, the proposed algorithm can be suitable for irregular array geometry, obtain automatically paired DOD and DOA estimations, and avoid two-dimensional peak searching. The simulation results verify the effectiveness and improvement of the algorithm.     

极化域一空域动态联合谱估计

研究了极化域-空域联合谱的动态更新问题,给出了MUSIC联合谱的自适应递推估计算法。利用指数窗法对阵列协方差矩阵作秩-1更新;然后在矩阵扰动理论基础上,利用矩阵特征分解二阶修正方法更新特征值和特征向量;针对最小特征值重合情形仅对信号子空间进行递推更新,根据更新了的信号子空间得到动态联合谱;最后仿真结果验证了该方法的可靠性。     

A subspace method for direction of arrival estimation ofuncorrelated emitter signals

A novel eigenstructure-based method for direction estimation is presented. The method assumes that the emitter signals are uncorrelated. Ideas from subspace and covariance matching methods are combined to yield a noniterative estimation algorithm when a uniform linear array is employed. The large sample performance of the estimator is analyzed. It is shown that the asymptotic variance of the direction estimates coincides with the relevant Cramer-Rao lower bound (CRB). A compact expression for the CRB is derived for the ease when it is known that the signals are uncorrelated, and it is lower than the CRB that is usually used in the array processing literature (assuming no particular structure for the signal covariance matrix). The difference between the two CRBs can be large in difficult scenarios. This implies that in such scenarios, the proposed methods has significantly better performance than existing subspace methods such as, for example, WSF, MUSIC, and ESPRIT. Numerical examples are provided to illustrate the obtained results     

一种新的基于 EEF 准则的空间声源个数估计算法

针对指数嵌入族（ Exponentially Embedded Families ,EEF）准则在快拍数小于阵元数情况下无法估计声源个数的问题,本文提出一种新的空间声源个数估计算法。首先通过球麦克风阵列采集空间声场高阶信息,建立球阵列信号模型,将声源个数估计扩展到三维空间。继而将观测信号空间分解为信号子空间和噪声子空间,利用最小均方差（ Minimum Mean-Squared Error ,MMSE）方法估计观测信号空间及噪声子空间的协方差矩阵,确保矩阵估计的一致性和准确性。在此基础上改进似然比函数,同时引入新的自由度计算,使得算法在快拍数小于阵元数的情况下能有效估计声源个数。仿真结果表明,在进行空间声源个数估计时,相对于EEF准则,新的算法不仅适用于快拍数小于阵元数情况,同时提高了估计准确率。     

声矢量阵张量分解MUSIC算法

矢量水听器同时、共点测量声场中的声压和振速分量,因此相对于声压水听器能够获取更多的声场信息,多重信号分类算法(MUSIC)是一种具有高分辩能力的方位估计算法,本文对声矢量阵接收信号三阶张量建模,并通过高阶奇异值分解得到信号张量子空间,从而结合MUSIC算法对声源进行方位估计。基于三阶张量奇异值分解得到的信号子空间相比于传统的矩阵奇异值分解得到的信号子空间能够更好地抑制噪声,并且体现了多维数据之间的关联关系,因此方位估计精度更高。计算机仿真结果表明:矢量阵张量分解MUSIC算法性能优于传统矢量阵MUSIC方法。      

Concurrent nulling and locations of multiple interferences inadaptive antenna arrays

An approach for concurrent nulling and location (CANAL) of multiple interferences impinging on an array antenna is presented. It is based on the principle of constructing the signal and the noise subspaces from the nulling weights which correspond to different steering directions. In this respect, the data snapshots and their estimated covariance matrix are not required. As in the MUSIC algorithm, the basis of the noise subspace is then used to form a spectrum in which the peak locations define the estimated angles of arrivals. Applebaum optimum weights are employed to delineate the properties of the proposed approach under the assumption of narrowband uncorrelated jamming sources, and providing that the number of steering directions exceeds the number of interferences. CANAL is presented for the general case of unknown noise power. The effect of the desired signal presence on the performance Is discussed     

一种新的阵元位置误差有源校正算法

阵列天线位置的不确定性会严重影响阵列天线的测向性能。文中基于子空间类测向方法,在远场情况下,提出了一种新的估计阵元位置误差的有源校正算法。该算法是以迭代的形式给出,其目标函数建立在信号子空间基本性质的基础上,适用于多个校正源同时存在的情况,并且可以应用于任意阵列形式。计算机仿真验证了文中的算法具有较快的收敛速度和较高的参数估计精度。     

Min-norm interpretations and consistency of MUSIC, MODE and ML

The multiple signal characterization (MUSIC) approach, its generalization to correlated signals known as the method of direction estimation (MODE), and the deterministic maximum likelihood (ML) approach for bearing estimation in array processing are shown to be signal subspace fitting approaches in a minimum norm sense. MODE, for example, is shown to be an approach in which the array manifold is linearly estimated from principal empirical eigenvectors in a minimum weighted Frobenius norm sense. Using the min-norm interpretations, a unified proof for strong consistency of the three approaches is provided for stationary and ergodic signals     

A new subspace identification algorithm for high-resolution DOA estimation

In this paper, we propose a new direction of arrival (DOA) estimator for sensor-array processing. The estimator is based on a linear algebraic connection between the standard subspace model of the array correlation matrix and a special signal-plus-interference model, which we develop in this paper. The estimator we propose is a signal subspace scaled MUSIC algorithm, which we call SSMUSIC. It is not a subspace weighted MUSIC, because the scaling depends on the eigenstructure of the estimated signal subspace. SSMUSIC has the advantage of simultaneously estimating the DOA and the power of each source. We employ a second-order perturbation analysis of the estimator and derive stochastic representations for its bias and squared-error. We compare the new DOA estimator with the MUSIC estimator, based on these representations. Numerical results demonstrate the superior performance of SSMUSIC relative to MUSIC and the validity of the perturbation results.     

Application of signal subspace approach to high-resolution narrowband array processing

The paper first briefly reviews some subspace techniques for high-resolution array processing. It is shown that existing high-resolution techniques like the MUSIC algorithm are based on visual inspection of the spatial spectrum. It is not a scientifically valid means of assessing resolution of a spectrum estimator. The paper then proposes a technique based on a combination of optimal processing and signal subspace extraction for high-resolution array processing. Numerical results show that the proposed technique not only achieves superresolution of the spectrum, but also provides power estimates of the arrivals.     

柱面共形阵列高性能低复杂度DOA估计算法

针对柱面共形阵列的波达方向(DOA)估计问题,从信号子空间的角度分析了在阵元遮挡下应用多重信号分类(MUSIC)算法的性能缺陷。在此基础上提出通过偏置常数的方法克服经典MUSIC算法的阵元遮挡问题。进一步提出一种基于数据自适应子阵分割的快速DOA估计算法,该方法先利用稀疏采样的偏置MUSIC算法进行DOA预估,依此确定所需要的子阵及二维搜索区域,确定MUSIC算法的搜索范围,进而得到高精确度的DOA估计。利用子阵分割的方法进行DOA估计,避免了经典MUSIC算法因阵元遮挡导致运算量大、精确度低等问题。仿真结果表明,该方法能大幅度降低运算复杂度,同时提高DOA估计精确度。