Computationally efficient 2-D DOA estimation for non-uniform two-L-shaped array

A two-dimensional direction-of-arrival (DOA) estimation method for non-uniform two-L-shaped array is presented in which the element spacing is larger than half-wavelength. To extract automatically paired low-variance cyclically ambiguous direction cosines and high-variance unambiguous direction cosines from the sub-blocks, the proposed method constructs and partitions the cross-correlation matrices. Then, the low-variance unambiguous direction cosines are obtained using the ambiguity resolved technique. Simulation results demonstrate that the proposed method has lower computation complexity and higher resolution than the existing methods especially when the elevation angles are between 70 and 90 degrees.     

均匀平面阵下的二维DOA估计与互耦自校正

针对存在互耦效应时均匀平面阵的测向鲁棒性问题,提出了一种基于秩损准则的互耦自校正算法。根据对互耦效应的先验知识,提出的算法只需将受互耦扰动的阵列响应在变换域中重新排列,便可在后续处理中屏蔽掉互耦效应的不利影响,同时也避免了现有工作中存在的阵列孔径损失问题。借助秩损估计原理,在变换域中设计了一种巧妙的计算步骤,使得方位估计的降维操作得以实现;并且,后续还可通过特征分解法得到更精确的互耦系数估计,以进行阵列误差自校正。与现有的研究工作相比,所提算法无论是在估计精度,还是在计算效率上均有着显著的性能优势。     

Computationally efficient MUSIC based DOA estimation algorithm for FMCW radar

This paper proposes low-cost yet high-accuracy direction of arrival (DOA) estimation for the automotive frequency-modulated continuous-wave (FMCW) radar. The existing subspace-based DOA estimation algorithms suffer from either high computational costs or low accuracy. We aim to solve such contradictory relation between complexity and accuracy by using randomized matrix approximation. Specifically, we apply an easily-interpretable randomized low-rank approximation to the covariance matrix (CM) and approximately compute its subspaces. That is, we first approximate CM \begin{document}${\bf{R} }\in {\mathbb{C}}^{M\times M} $\end{document} through three sketch matrices, in the form of \begin{document}$\mathbf{R}\approx \mathbf{Q}\mathbf{B}{\mathbf{Q}}^{\mathrm{H}} $\end{document}. Here the matrix \begin{document}$\mathbf{Q}\in {\mathbb{C}}^{M\times z} $\end{document} contains the orthonormal basis for the range of the sketch matrix \begin{document}$\mathbf{C}\in {\mathbb{C}}^{M\times z} $\end{document} which is extracted from \begin{document}$ \mathbf{R} $\end{document} using randomized uniform column sampling and \begin{document}$ \mathbf{B}\in {\mathbb{C}}^{z\times z} $\end{document} is a weight-matrix reducing the approximation error. Relying on such approximation, we are able to accelerate the subspace computation by the orders of the magnitude without compromising estimation accuracy. Furthermore, we drive a theoretical error bound for the suggested scheme to ensure the accuracy of the approximation. As validated by the simulation results, the DOA estimation accuracy of the proposed algorithm, efficient multiple signal classification (E-MUSIC), is high, closely tracks standard MUSIC, and outperforms the well-known algorithms with tremendously reduced time complexity. Thus, the devised method can realize high-resolution real-time target detection in the emerging multiple input and multiple output (MIMO) automotive radar systems.     

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.     

三平行线阵改进传播算子算法的波达方向估计

在三平行立体线阵中,传统二维传播算子(Propagator Method,PM)算法进行传播算子估计时,根据划分子阵直接构造的信号协方差矩阵存在较大冗余度.为了降低运算量,可以通过子阵合并的方式,摒弃协方差矩阵的冗余数据,利用重构的协方差矩阵估算传播算子,然后构造新的传播算子,得到与二维波达方向(direction of arrival,DOA)相关的三维超定方程组,再引入非线性最小二乘法处理该方程组求解得二维DOA信息.仿真结果表明,该算法降低了运算量,提高了二维DOA估计的精度.     

用平行四边形阵列实现闭环形式2维角估计

提出了适用于平行四边形阵列的２维酉ＥＳＰＲＩＴ方法,它是一种闭环形式的高分辨算法,对信号源方位角和仰角估计实现自动配对。给出了两类酉变换矩阵,将复数域的矩阵运算转换到实数域。除了初始变换和最后维数等于信号个数的矩阵特征分解外,整个过程都采用高效的实值计算。最后对算法做了一阶近似渐进性能分析。仿真结果表明算法是有效的。     

Joint-block-sparsity for efficient 2-D DOA estimation with multiple separable observations

In sparsity-based optimization problems, one of the major issue is computational complexity, especially when the unknown signal is represented in multi-dimensions such as in the problem of 2-D (azimuth and elevation) direction-of-arrival (DOA) estimation. In order to cope with this issue, this paper introduces a new sparsity structure that can be used to model the optimization problem in case of multiple data snapshots and multiple separable observations where the dictionary can be decomposed into two parts: azimuth and elevation dictionaries. The proposed sparsity structure is called joint-block-sparsity which enforces the sparsity in multiple dimensions, namely azimuth, elevation and data snapshots. In order to model the joint-block-sparsity in the optimization problem, triple mixed norms are used. In the simulations, the proposed method is compared with both sparsity-based techniques and subspace-based methods as well as the Cramer–Rao lower bound. It is shown that the proposed method effectively solves the 2-D DOA estimation problem with significantly low complexity and sufficient accuracy.

     

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.     

Computationally efficient DOD and DOA estimation for bistatic MIMO radar with propagator method

In this article, we consider a computationally efficient direction of departure and direction of arrival estimation problem for a bistatic multiple-input multiple-output (MIMO) radar. The computational loads of the propagator method (PM) can be significantly smaller since the PM does not require any eigenvalue decomposition of the cross correlation matrix and singular value decomposition of the received data. An improved PM algorithm is proposed to obtain automatically paired transmit and receive angle estimations in the MIMO radar. The proposed algorithm has very close angle estimation performance to conventional PM, which has a much higher complexity than our algorithm. For high signal-to-noise ratio, the proposed algorithm has very close angle estimation to estimation of signal parameters via rotational invariance technique algorithm. The variance of the estimation error and Cramér–Rao bound of angle estimation are derived. Simulation results verify the usefulness of our algorithm.     

A new algorithm for 2-D DOA estimation

In this paper we present a new algorithm to estimate the 2-D direction of arrival (DOA) of narrowband sources lying in the far field of the array. The array consists of matched co-directional triplets, and can be considered as an extension of the 1-D ESPRIT scenario to 2-D. The proposed approach is simple and direct and does not require a search procedure or initialization. Existing algorithms require a search to match the correct elevation and azimuth angles and are computationally more expensive. This technique automatically pairs the azimuth and elevation angles by marking them. The computational complexity is twice that of 1-D ESPRIT. Simulation results and comparisons with other existing algorithms are presented to demonstrate the performance of the proposed technique.     

Computationally efficient DOA estimation for coprime linear array: a successive signal subspace fitting algorithm

ABSTRACT

In this paper, direction of arrival (DOA) estimation of multiple signals with coprime array is investigated and signal subspace fitting (SSF) method is linked to the coprime array, which achieves a better DOA estimation performance than the traditional uniform array. While the SSF method requires expensive computational cost in the case of multiple signals due to the multidimensional global angular searching, we propose a successive SSF (S-SSF) algorithm from a computationally efficient perspective. In the proposed algorithm, we employ rotational invariance and coprime property to obtain the initial estimates. Then, via a successive scheme, we transform the traditional multidimensional global angular searching problem into one-dimensional partial angular searching one. Consequently, the computational complexity has been significantly reduced. Specifically, the proposed S-SSF algorithm can obtain almost the same DOA estimation performance as SSF but with remarkably lower complexity. Finally, Cramer-Rao Bound (CRB) is provided and numerical simulations demonstrate the effectiveness of the proposed algorithm.     

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。     

均匀线阵目标到达角估计的压缩感知方法研究

为了缓解表面波雷达在天线阵列小型化后角度分辨率低的问题,采用压缩感知理论,提出一种小型天线阵列表面波雷达目标到达角估计的方法。将到达角估计问题转化为稀疏信号表示的重建问题。建立了稀疏信号模型,分析了应用条件,将角度和速度空间离散化以构造字典,设计了基于实时海态信息的测量矩阵,设计匹配算法完成信号重构。仿真结果表明,若满足准确重建条件,即使在小型天线阵列的情况下,也能以计算资源为代价改善方位分辨率。     

Computationally efficient angle estimation for signals with knownwaveforms

This paper presents a large sample decoupled maximum likelihood (DEML) angle estimator for uncorrelated narrowband plane waves with known waveforms and unknown amplitudes arriving at a sensor array in the presence of unknown and arbitrary spatially colored noise. The DEML estimator decouples the multidimensional problem of the exact ML estimator to a set of 1-D problems and, hence, is computationally efficient. We shall derive the asymptotic statistical performance of the DEML estimator and compare the performance with its Cramer-Rao bound (CRB), i.e., the best possible performance for the class of asymptotically unbiased estimators. We will show that the DEML estimator is asymptotically statistically efficient for uncorrelated signals with known waveforms. We will also show that for moderately correlated signals with known waveforms, the DEML estimator is no longer a large sample maximum likelihood (ML) estimator, but the DEML estimator may still be used for angle estimation, and the performance degradation relative to the CRB is small. We shall show that the DEML estimator can also be used to estimate the arrival angles of desired signals with known waveforms in the presence of interfering or jamming signals by modeling the interfering or jamming signals as random processes with an unknown spatial covariance matrix. Finally, several numerical examples showing the performance of the DEML estimator are presented in this paper     

Closed-form 2-D angle estimation with rectangular arrays in elementspace or beamspace via unitary ESPRIT

The UCA-ESPRIT is a closed-form algorithm developed for use in conjunction with a uniform circular array (UCA) that provides automatically paired source azimuth and elevation angle estimates. The 2-D unitary ESPRIT is presented as an algorithm providing the same capabilities for a uniform rectangular array (URA). In the final stage of the algorithm, the real and imaginary parts of the ith eigenvalue of a matrix are one-to-one related to the respective direction cosines of the ith source relative to the two major array axes. The 2-D unitary ESPRIT offers a number of advantages over other proposed ESPRIT based closed-form 2-D angle estimation techniques. First, except for the final eigenvalue decomposition of a dimension equal to the number of sources, it is efficiently formulated in terms of real-valued computation throughout. Second, it is amenable to efficient beamspace implementations that are presented. Third, it is applicable to array configurations that do not exhibit identical subarrays, e.g., two orthogonal linear arrays. Finally, the 2-D unitary ESPRIT easily handles sources having one member of the spatial frequency coordinate pair in common. Simulation results are presented verifying the efficacy of the method     

Computationally efficient subspace-based method for direction-of-arrival estimation without eigendecomposition

A computationally simple direction-of-arrival (DOA) estimation method with good statistical performance is attractive in many practical applications of array processing. In this paper, we propose a new computationally efficient subspace-based method without eigendecomposition (SUMWE) for the coherent narrowband signals impinging on a uniform linear array (ULA) by exploiting the array geometry and its shift invariance property. The coherency of incident signals is decorrelated through subarray averaging, and the space is obtained through a linear operation of a matrix formed from the cross-correlations between some sensor data, where the effect of additive noise is eliminated. Consequently, the DOAs can be estimated without performing eigendecomposition, and there is no need to evaluate all correlations of the array data. Furthermore, the SUMWE is also suitable for the case of partly coherent or incoherent signals, and it can be extended to the spatially correlated noise by choosing appropriate subarrays. The statistical analysis of the SUMWE is studied, and the asymptotic mean-squared-error (MSE) expression of the estimation error is derived. The performance of the SUMWE is demonstrated, and the theoretical analysis is substantiated through numerical examples. It is shown that the SUMWE is superior in resolving closely spaced coherent signals with a small number of snapshots and at low signal-to-noise ratio (SNR) and offers good estimation performance for both uncorrelated and correlated incident signals.     

一种信号频率及二维到达角联合估计新方法

提出了一种窄带信源频率、俯仰角及方位角联合估计新方法.该方法选择特定序号阵元输出计算的高阶累积量构造4个矩阵,然后在累积量域构造三面阵,并分析了该三面阵低秩分解的唯一性,接着利用分解得到的4个对角阵联合估计信源参数.该方法无须参数配对,无须谱峰搜索,适用于任意加性高斯噪声环境.仿真结果表明该算法是有效的.     

On the application of the global matched filter to DOA estimation with uniform circular arrays

The problem of estimating the direction of arrivals (DOA) of narrowband sources impinging on a uniform circular array is considered. We present a method that uses as input the values of a small number of uniformly spaced beams and apply a model-fitting approach taking into account the statistical properties of the beams. The approach, which is called the "global matched filter" fits simultaneously to the observations all the elements needed to explain them. It chooses, among all the representations satisfying a constraint with a sensible physical interpretation, the one with minimal energy. The method drastically improves upon the conventional beamformer and has a performance comparable with the best high-resolution (HR) techniques. It further applies when the number of sources exceeds the number of sensors: a situation that cannot be handled by standard HR techniques.     

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.