Real-valued DOA estimation for uniform linear array with unknown mutual coupling

In this paper, we propose a real-valued direction-of-arrival (DOA) estimation method for uniform linear arrays (ULAs) in the presence of unknown mutual coupling. By taking advantage of the special structure of the mutual coupling matrix for ULAs, the effect of mutual coupling is eliminated by the inherent mechanism of the proposed method. Moreover, the computational complexity is reduced by a factor of at least four after further performing a unitary transformation capable of converting a complex covariance matrix into a real one. We also investigate the performance loss due to the imperfect structure of the mutual coupling matrix under the NEC-2 code. Experimental results with respect to the NEC-2 code illustrate that our new method even outperforms a state-of-the-art method in the literature.     

A covariance matrix shrinkage method with Toeplitz rectified target for DOA estimation under the uniform linear array

A covariance matrix shrinkage method is proposed to make an improvement of the direction of arrival (DOA) estimation under a uniform linear array in a scenario where the number of sensors is large and the sample size is relatively small. The main contribution is that we provide a shrinkage target with Toeplitz structure and deduce a closed-form estimation of the shrinkage coefficient. The closed-form and the expectation of the shrinkage coefficient estimate are calculated based on the unbiased and consistent estimates of the trace and moments of a Wishart distributed covariance matrix. The statistical property of the shrinkage coefficient estimate is discussed through theoretical analysis and simulations, which demonstrate the shrinkage coefficient estimate can ensure that the proposed covariance matrix estimate is a good compromise between the sample covariance matrix (SCM) and the target. The root-mean-square-error (RMSE) simulations of DOA estimation show that the proposed method can improve the multiple signal classification (MUSIC) DOA estimation performance in the case of low signal-to-noise ratio (SNR) with small sample size, and also can provide a satisfactory performance at high SNR.     

DOA estimation in unknown colored noise using covariance differencing and sparse signal recovery

A direction-of-arrival （DOA） estimation algorithm is presented based on covariance differencing and sparse signal recovery, in which the desired signal is embedded in noise with unknown covariance. The key point of the algorithm is to eliminate the noise component by forming the difference of original and transformed covariance matrix, as well as cast the DOA estimation considered as a sparse signal recovery problem. Concerning accuracy and complexity of estimation, the authors take a vectorization operation on difference matrix, and further enforce sparsity by reweighted l1-norm penalty. We utilize data-validation to select the regularization parameter properly. Meanwhile, a kind of symmetric grid division and refinement strategy is introduced to make the proposed algorithm effective and also to mitigate the effects of limiting estimates to a grid of spatial locations. Compared with the covariance-differencing-based multiple signal classification （MUSIC） method, the proposed is of salient features, including increased resolution, improved robustness to colored noise, distinguishing the false peaks easily, but with no requiring of prior knowledge of the number of sources.     

DOA estimation of wideband sources using a harmonic source modeland uniform linear array

We consider the problem of estimation of the DOAs of multiple wideband sources incident on a uniform linear array (ULA) in the presence of spatially and temporally white Gaussian noise (WGN). The approach presented builds up on the IQML algorithm suggested by Bresler and Macovski (1986) for the case of narrowband DOA estimation. It is shown that the concept of an ARMA model for the observed data vector for the narrowband case can be generalized to model an appropriately stacked, space-time data vector obtained by combining the space-time samples. The coefficients of the corresponding 2-D predictor polynomial can be used to represent the null subspace of the wideband array steering matrix, and rooting of the polynomial at each frequency, separately, gives the DOA estimates. These separate estimates at multiple frequencies are combined into a single DOA estimate in a least squares sense. This leads to the formulation of an IQML like procedure for the spatial parameter estimation of wideband sources. Like its narrowband counterpart, the proposed approach is applicable to both noncoherent and coherent sources. The performance of the proposed method is studied via extensive computer simulations and by comparison with the Cramer-Rao bounds     

短快拍条件下均匀矩形阵中的二维DOA估计

二维波达方向（Direction of Arrival,DOA）估计能获取比一维DOA估计更多的空间位置信息,但是二维多重信号分类(Multiple Signal Classification,MUSIC)、二维子空间旋转不变估计技术(Estimation Signal Parameter via Rotational Invariance Techniques,ESPRIT）等经典算法依赖于大量的快拍数据,当快拍数据不足时估计性能严重下降甚至失效。针对上述问题,将迭代自适应方法拓展到二维DOA估计,提出了一种适用于矩形面阵的二维DOA估计算法,首先利用加权最小二乘法估计出信号幅值,然后利用循环迭代技术对估计结果进行更新。由于每次估计结果均来自上一次迭代,而不依赖于快拍数据,因此该算法在短快拍条件下具有很高的估计精度和分辨率。仿真结果表明,在短快拍条件下,该算法具有优越的估计性能。     

DOA estimation and self-calibration algorithm for uniform circular array

Based on the banded circulate and symmetric Toeplitz model for the mutual coupling of a uniform circular array, a decoupling direction of arrival (DOA) estimation and self-calibration algorithm is proposed. The new algorithm provides an accurate DOA estimation without the knowledge of mutual coupling. In addition, the mutual coupling coefficients for array self-calibration can be achieved simultaneously. Instead of multidimensional nonlinear search or iterative computation, the algorithm only uses a one-dimensional search and can reduce the computation burden. Simulation results demonstrate the validity of the proposed method.     

Improved coherent DOA estimation algorithm for uniform linear arrays

An improved algorithm on coherent direction-of-arrival (DOA) estimation is presented in this article, with the objective to overcome the unsatisfactory performances of estimation of signal parameter via rotational invariance techniques (ESPRIT)-like algorithms (Han and Zhang, IEEE Antennas and Wireless Propagation Letters 2005;4:443–446). On the basis of trilinear model by reconstructing a series of Toeplitz matrix from the co-variance matrix of array output, our proposed algorithm is to resolve the DOAs of coherent signals, which not only has much better DOA estimation performance than algorithms of ESPRIT-like and multi-invariance ESPRIT but also identifies more DOAs than ESPRIT-like algorithm. Simulation results demonstrate its validity.     

多径条件下均匀线阵DOA估计及互耦误差自校正

针对多径信道环境下存在互耦误差的均匀线阵,提出了一种联合波达方向估计及互耦 误差自校正算法。在不改变阵列互耦误差的条件下,首先利用虚拟阵列平移预处理方法,将 相干信源协方差矩阵恢复到满秩。进而利用互耦误差的对称Toeplitz特性,基于子空间原理 构造一代阶函数,采用秩损的方法得到互耦误差条件下的DOA估计及阵列互耦误差。数值仿 真结果表明,该算法具有良好的DOA估计性能与互耦误差自校正性能。     

均匀圆阵部分阵元失效情况下的DOA估计方法

在空间谱估计中,均匀圆阵(Uniform Circular Array--UCA)具有诸多优点,其得到广泛的应用.但在用MUSIC 算法测向时,一旦某一个或几个阵元通道失效,则通道数据变成无效数据,导致测向性能严重恶化,甚至完全失效.本文对在均匀圆阵部分通道失效的情况下,利用均匀圆阵其余阵元数据实现对信号来波方向进行有效估计的方法进行了分析和验证.其原理在于,直接将失效阵元进行隔离,利用剩余阵元形成的非均匀圆阵,进行MUSIC算法测向.该方法能在较高信噪比条件下实现和原阵列几乎相同的估计精度,在较低信噪比、信号数较小的条件下,也能取得良好的估计性能,大大增强了整个阵列谱估计的稳健性和鲁棒性.     

基于均匀圆阵的空时二维波达方向估计算法

提出了一种适合于均匀圆阵的空时二维波达方向估计方法,该方法先利用模式激励技术对接收数据进行变换,再利用变换后数据之间的互相关关系将数据进一步映射到空时域,然后构造出一对空时DOA矩阵束,通过矩阵束的广义特征值就能够计算出所有入射信号的方位角和俯仰角.该方法完全避免了DOA矩阵类方法中难以克服的角度兼并问题,与UCA-ESPRIT算法相比,减小了孔径损失,使能够估计的信号数目增加了一倍.该方法具有免搜索和参数自动配对的特点.仿真结果证明了该算法的性能.     

Adaptive estimation in linear systems with unknown Markovian noise statistics

The asymptotic behavior of a Bayes optimal adaptive estimation scheme for a linear discrete-time dynamical system with unknown Markovian noise statistics is investigated. Noise influencing the state equation and the measurement equation is assumed to come from a group of Gaussian distributions having different means and covariances, with transitions from one noise source to another determined by a Markov transition matrix. The transition probability matrix is unknown and can take values only from a finite set. An example is simulated to illustrate the convergence.     

均匀圆阵下的宽带信号DOA估计算法

为了解决传统宽带信号DOA估计在全频段作谱峰搜索所得空间谱分辨率较低和计算量非常大的问题,新算法采用FFT变换,仅仅通过采用选取的部分频带数据进行基于子空间的空间谱估计,不仅可以提高宽带信号DOA估计的分辨率,同时减少了运算量。文章介绍了算法实现过程,并对算法计算量进行了定量分析,分辨率和误差性能则通过仿真进行比较分析。另外,算法以均匀圆阵为模型,相对于线阵结构,使所得结论更加具有实用性。     

A modified likelihood function approach to DOA estimation in thepresence of unknown spatially correlated Gaussian noise using a uniformlinear array

The problem of modified ML estimation of DOAs of multiple source signals incident on a uniform linear array (ULA) in the presence of unknown spatially correlated Gaussian noise is addressed here. Unlike previous work, the proposed method does not impose any structural constraints or parameterization of the signal and noise covariances. It is shown that the characterization suggested here provides a very convenient framework for obtaining an intuitively appealing estimate of the unknown noise covariance matrix via a suitable projection of the observed covariance matrix onto a subspace that is orthogonal complement of the so-called signal subspace. This leads to a formulation of an expression for a so-called modified likelihood function, which can be maximized to obtain the unknown DOAs. For the case of an arbitrary array geometry, this function has explicit dependence on the unknown noise covariance matrix. This explicit dependence can be avoided for the special case of a uniform linear array by using a simple polynomial characterization of the latter. A simple approximate version of this function is then developed that can be maximized via the-well-known IQML algorithm or its variants. An exact estimate based on the maximization of the modified likelihood function is obtained by using nonlinear optimization techniques where the approximate estimates are used for initialization. The proposed estimator is shown to outperform the MAP estimator of Reilly et al. (1992). Extensive simulations have been carried out to show the validity of the proposed algorithm and to compare it with some previous solutions     

A novel approach for DOA estimation in unknown correlated noise fields

The key of the subspace-based Direction Of Arrival （DOA） estimation lies in the estimation of signal subspace with high quality. In the case of uncorrelated signals while the signals are temporally correlated, a novel approach for the estimation of DOA in unknown correlated noise fields is proposed in this paper. The approach is based on the biorthogonality between a matrix and its Moore-Penrose pseudo inverse, and made no assumption on the spatial covariance matrix of the noise. The approach exploits the structural information of a set of spatio-temporal correlation matrices, and it can give a robust and precise estimation of signal subspace, so a precise estimation of DOA is obtained. Its performances are confirmed by computer simulation results.     

Maximum likelihood DOA estimation and asymptotic Cramer-Rao boundsfor additive unknown colored noise

This paper is devoted to the maximum likelihood estimation of multiple sources in the presence of unknown noise. With the spatial noise covariance modeled as a function of certain unknown parameters, e.g., an autoregressive (AR) model, a direct and systematic way is developed to find the exact maximum likelihood (ML) estimates of all parameters associated with the direction finding problem, including the direction-of-arrival (DOA) angles Θ, the noise parameters α, the signal covariance Φ_s, and the noise power σ². We show that the estimates of the linear part of the parameter set Φ_s and σ² can be separated from the nonlinear parts Θ and α. Thus, the estimates of Φ_s and σ² become explicit functions of Θ and α. This results in a significant reduction in the dimensionality of the nonlinear optimization problem. Asymptotic analysis is performed on the estimates of Θ and α, and compact formulas are obtained for the Cramer-Rao bounds (CRB's). Finally, a Newton-type algorithm is designed to solve the nonlinear optimization problem, and simulations show that the asymptotic CRB agrees well with the results from Monte Carlo trials, even for small numbers of snapshots     

一种最小冗余线阵的目标DOA估计方法

针对目标波达方向(DOA)估计的子空间类算法工程实现上的问题,提出了一种次最小冗余线阵的目标DOA估计方法。该方法应用孔径合成理论和最小冗余线阵理论,在保证阵列孔径等价的前提下,从工程应用的实际问题出发,对次最小冗余线阵的阵元配置进行研究。在分析MUSIC及MMUSIC算法的基础上,对次最小冗余线阵进行仿真。通过与相同孔径的均匀线阵和最小冗余线阵对比表明,次最小冗余线阵与相同孔径的均匀线阵性能相仿,并有更小的计算复杂度,比最小冗余线阵有更大的阵元灵活性,可以解决一般最小冗余线阵不能解决的相干信源的DOA估计问题。     

ICA-based direction-of-arrival estimation of uncorrelated and coherent signals with uniform linear array

A novel approach for direction-of-arrival (DOA) estimation of uncorrelated and coherent signals with uniform linear array is proposed in this paper. First, the mixing matrix, which contains all azimuth information of signal sources, is estimated by independent component analysis. Afterward, several parameter equations are established upon the new mixing matrix. Finally, all DOAs of coherent and uncorrelated signals are estimated by solving these equations. Compared with traditional methods, the proposed method has higher angle resolution and estimation accuracy. Moreover, the signal number resolved by our approach can exceed the number of array elements. Simulation results have demonstrated the efficiency of the proposed method.     

Global identification of continuous-time-systems with unknown noise covariance (Corresp.)

Global convergence pf the maximum likelihood estimates of unknown parameters of a continuous-time stochastic linear dynamical system is investigated when the observation noise covariance is unknown. The unknown parameter set is assumed to be finite. The situation where the true parameter does not belong to the unknown parameter set is considered as well as the situation where the true model is included in the unknown parameter set. Convergence is proved under a certain sufficient condition called the identifiability condition.     

分布式电磁矢量传感器阵的二维测向算法

采用由分布式电磁矢量传感器组成的稀疏线阵,针对相干信号提出了一种扩展孔径2维波达角(Two Dimensional DirectionofArrival,2D DOA)估计算法.通过构造增强矩阵来消除信号的相干性,利用稀疏线阵包含的向量特性、x轴和y轴空间相位因子获得高精度无模糊估计.与传统算法相比,算法不但保留了传感器的向量特性,而且增大传感器各分量之间的间距以及传感器之间的间距来获得2D孔径扩展,具有更高的测向精度.仿真验证了本文算法的有效性.     

基于最优子阵划分ESPRIT的任意线阵高精度DOA估计算法

为了提高任意阵列的波达方向(direction of arrival, DOA)估计性能,从对子阵阵元选取进行优化的角度出发,提出了基于最优子阵划分旋转不变信号参数估计技术(estimation of signal parameters via rotational invariance techniques,ESPR...