Reduced-Dimensional Polynomial Rooting-Based Multiple Parameter Estimation for Polarization Sensitive Coprime Arrays: A Full Array Extraction Perspective

Generally, multi-dimensional spectral peak search (SPS) in parameter estimation for polarization sensitive coprime linear arrays (PS-CLAs) requires heavy computational burden. To resolve this problem, we propose a search-free algorithm for multi-parameter estimation with PS-CLAs in this paper. Specifically, different from the decomposition algorithms, we first reconstruct the total received signal of PS-CLA as the signal extracted from a large uniform linear array, which enables to offer a spectrum function only with regard to direction of arrival (DOA) by utilizing rank reduction estimator. Subsequently, we employ the polynomial root finding technique instead of one-dimensional SPS to directly calculate the DOA estimates. Furthermore, a quadratic optimization problem is established for the polarization parameters and in particular, the closed-form solutions are provided by utilizing Lagrange multiplier approach. Finally, numerical simulations illustrate that the proposed search-free algorithm can obtain improved estimation accuracy with remarkably low complexity.

     

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.     

基于连续蚁群优化算法的小快拍加权子空间拟合快速算法

该文针对加权子空间拟合(WSF)算法多维非线性优化计算量大,难以工程应用的问题,将连续空间蚁群算法与加权子空间拟合算法相结合,提出了基于蚁群算法的加权子空间拟合(Ant Colony Optimization based Weighted Subspace Fitting,ACO-WSF) 方位估计新方法。该方法利用连续蚁群算法中的信息量高斯核概率分布函数,经过有限次迭代得到加权子空间拟合算法的非线性全局最优解。仿真结果表明,低信噪比、小快拍条件下该方法估计性能与WSF方法基本相同,优于MUSIC方法,而且显著减少了计算量。     

Multi-Source DOA Estimation Using an Acoustic Vector Sensor Array Under a Spatial Sparse Representation Framework

This paper investigates the estimation of the two-dimensional direction of arrival (2D-DOA) of sound sources using an acoustic vector sensor array (AVSA) within a spatial sparse representation (SSR) framework (AVS-SSR-DOA). SSR-DOA estimation methods rely on a pre-defined grid of possible source DOAs and essentially suffer from the grid-effect problem: Reducing the size of the grid spacing leads to increased computational complexity. In this paper, we propose a two-step approach to tackle the grid-effect problem. Specifically, omnidirectional sensor array-based SSR-DOA estimation firstly provides initial low-cost DOA estimates using a coarse grid spacing. Secondly, a closed-form solution is derived by exploring the unique subarray manifold matrix correlation and subarray signal correlation of the AVSA, which allows for DOA estimates between the pre-defined angles of the grid and potentially achieves higher DOA estimation accuracy. To further alleviate the estimation bias due to noise and sparse representation model errors, line-fitting (LF) techniques and subspace techniques (ST) are employed to develop two novel DOA estimation algorithms, referred to as AVS-SSR-LF and AVS-SSR-ST, respectively. Extensive simulations validate the effectiveness of the proposed algorithms when estimating the DOAs of multiple sound sources. The proposed AVS-SSR-ST algorithm achieves high DOA estimation accuracy and is robust to various noise levels and source separation angles.     

一种基于改进PSO的随机最大似然算法

随机最大似然算法(Stochastic Maximum Likelihood,SML)具有优越的波达方位(Direction-of-Arrival,DOA)估计性能,但SML解析过程较高的计算复杂度限制了该算法在实际系统中的应用.针对SML计算复杂度高的问题,提出一种低复杂度的粒子群优化算法(Particle Swarm Optimization,PSO),解决了传统PSO算法中粒子数多和迭代次数多的双重缺点.首先,根据天线获得的信号,将旋转不变子空间法(Estimation of Signal Parameters via Rotational Invariance Techniques,ESPRIT)求得的闭式解作为DOA的预估计值,同时计算系统此时的信噪比以及SML在此信噪比下的克拉-美罗界(Cramer-Rao bound,CRB).然后,根据DOA预估计值和当前CRB值在SML最优解的近邻范围内确定较小的初始化空间,并在该空间初始化少量粒子.最后通过设计合适的惯性因子w,使粒子以合理的速度搜索最优解.实验结果表明,改进PSO算法所需的粒子个数和迭代次数大约是传统PSO算法的1/5,降低了SML的解析复杂度,计算时间是传统PSO算法的1/10,因此在收敛速度上也有显著的优势.     

Computationally efficient direction-of-arrival estimation of non-circular signal based on subspace rotation technique

In order to solve the problem that the high computational burden of the multiple signal classification algorithm of non-circular signal (NC-MUSIC) in direction-of-arrival (DOA) estimation,a novel computationally efficient DOA estimation algorithm based on subspace rotation technique was proposed.Firstly,the partitioning of noise subspace matrix and the subspace rotation technique (SRT) were used to construct a new reduced-dimension noise subspace.Then,the two-dimensional peak searching was converted to the one-dimensional peak searching on the basis of the separation of variables and the orthogonality between the new reduced-dimension noise subspace and the space spanned by the columns of the extended manifold matrix.The proposed algorithm can enhance the computational efficiency by means of the conversion of the two-dimensional peak searching into the one-dimensional peak searching and the removal of redundant computations.Theoretical analysis and simulation results show that the proposed algorithm can reduce the computational complexity to less than 5% as compared to NC-MUSIC algorithm on the premise of ensuring the accuracy of DOA estimation.Especially,the efficiency advantage of the proposed algorithm is more obvious in scenarios where the large numbers of sensors are required.     

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。     

基于变换域APSO的任意阵列宽带DOA估计算法

为了提高宽带信号来波方向（Direction-of-arrival, DOA）估计精度并降低计算复杂度, 本文结合已知的发射信号波形, 提出了一种基于变换域加速粒子群最优化（Accelerated Particle Swarm Optimization, APSO）的宽带DOA估计算法, 该算法适用于任意阵列和低采样率情况。首先对阵列接收数据进行匹配滤波以及傅里叶变换处理,其次根据频域宽带阵列数据模型,利用确定性极大似然（Deterministic Maximum Likelihood, DML）准则构建宽带DOA估计的空间谱函数,然后采用变换域APSO算法对空间谱函数进行最大值搜索,搜索结果即为DOA估计值。该算法无需DOA预估计,不依赖空间谱函数的梯度信息,计算复杂度低。仿真实验表明,所提算法具有高估计精度和低计算复杂度,在信噪比为20?dB时,DOA估计均方根误差为0.02°。      

基于网格部分细化的DOA估计方法

计算复杂度和估计精确度一直是波达方向(DOA)估计研究的重点。现有基于压缩感知的DOA估计算法与传统算法相比具有一定优势,但这些稀疏信号重建模型都是将角度空间等间距划分,仍存在算法计算复杂度较高和估计精确度较低的问题。针对这些问题,提出一种对角度空间网格进行部分细化的DOA估计方法。该方法包括裂变过程和学习过程,裂变过程通过产生新网格点对角度空间进行细化,学习过程通过迭代不断逼近波达方向。仿真结果表明,提出的算法耗时较少,而且在非常稀疏的初始网格划分的条件下(初始间隔为20°),仍可以获得较高的估计精确度。     

矢量传感器阵列MIMO雷达高精度二维DOA与极化联合估计

该文采用矢量传感器配置下的十字型阵列MIMO雷达系统,提出一种新的2维高精度DOA与极化参数联合估计算法。首先根据MIMO雷达虚拟阵列导向矢量的特点,通过降维矩阵的设计及回波数据的降维变换,将高维回波数据转换至低维信号空间;然后基于传播算子获得对应信号子空间的估计,利用收、发阵列阵元间长基线对应的旋转不变性和极化矢量中电场矢量和磁场矢量的叉积进行2维高精度DOA估计和解模糊处理,同时利用与阵列结构无关的极化域旋转不变性进行极化辅角和极化相位差的联合估计。该矢量传感器MIMO雷达阵列可同时获取MIMO雷达的波形分集和矢量传感器的极化分集,无需额外增加阵元和硬件开销,能够有效扩展阵列孔径,提高参数估计性能;同时通过降维变换及传播算子,在获取信噪比增益的同时,能够实现2维高精度DOA和2维极化矢量的联合估计及参数的自动配对,有效降低数据处理维数和参数估计的运算复杂度;最后,仿真结果验证了理论分析的正确性和算法的有效性。     

采用降秩多级维纳滤波器的二维DOA估计快速算法

针对双平行线阵的二维波达方向(DOA)估计问题,为有效降低计算复杂度,提出了一种基于降秩多级维纳滤波器(MSWF)的快速算法。首先利用MSWF的前向递推实现信号子空间的快速估计,无需估计协方差矩阵和特征分解;然后,通过MUSIC算法对方位角和俯仰角的估计进行分维估计,使二维DOA估计退化为两个一维DOA估计问题,且方位角和俯仰角自动配对,进一步降低了运算量。仿真结果表明,该方法的估计精度优于同样基于双平行线阵提出的波达方向矩阵法(DOAM),俯仰角兼并时同样适用,计算复杂度低,适用于实时性要求高的应用背景。     

Off-grid DOA estimation algorithm based on unitary transform and sparse Bayesian learning

A rapid off-grid DOA estimating method of RV-OGSBL was raised based on unitary transformation,against the problem of traditional sparse Bayesian learning (SBL) algorithm in solving effectiveness of signal’s DOA estimation under condition of lower signal noise ratio (SNR).Actual received signal of uniform linear array was generated through constructing augment matrix as the processing signal used by DOA estimation.Then,estimation model was transformed from complex value to real value by using unitary transformation.In the next step,off-grid model and sparse Bayesian learning algorithm were combined together to process the realization of DOA estimation iteratively.The accuracy of estimation could made relatively high.The simulation result demonstrates that the RV-OGSBL method not only maintains the performance of traditional SBL algorithm,but also reduces the computational complexity significantly.Under the situation of lower signal noise ratio (SNR) and low number of snapshots,the running time of algorithm is reduced about 50%.This shows the RV-OGSBL method is a rapid DOA estimation algorithm.     

无参考信号条件下基于MSWF的DOA估计算法

现有基于多级维纳滤波(MSWF)的子空间法波达方向(DOA)估计算法复杂度较低,但需要先验的参考信号.论文从MSWF求解线性预测问题入手,将基于MSWF的线性预测和子空间两种不同的DOA估计方法结合起来,提出了一种实用的低复杂度DOA估计算法.该算法无需构造专门的参考信号,在低信噪比或信源数估计不准的情况下,算法依然具有较好的稳健性和估计性能.仿真实验验证了本文的结论.     

基于双向传播算子的互质面阵二维波达方向估计

针对谱峰搜索的二维波达方向估计中现有算法复杂度高,精度受搜索间隔影响较大的问题,给出了一种双向传播算子的互质面阵二维波达方向估计算法,实现了俯仰角和方位角的低复杂、高精度、无模糊联合估计.该方法首先将互质阵列引入到二维波达方向估计中,构造互质平面阵模型,然后采用两次旋转不变传播算子方法计算出不同阵列流型方向上的旋转因子矩阵,根据旋转因子矩阵解算出目标信号的俯仰角和方位角,同时利用互质理论消除了稀疏阵列角度估计的不确定性,证明了互质阵列模型下采用双向传播算子方法进行俯仰角和方位角估计的无模糊性.对算法的复杂度进行理论分析,并给出了平面阵列角度估计的克拉美罗界推导.理论分析与仿真结果表明,算法不需要进行角度匹配和谱峰搜索,在相同条件下的均方根误差性能优于均匀平面阵的多重信号分类算法,并且以较低的复杂度无模糊的达到了高维网格搜索的精度.     

基于阵列流型盲辨识的MIMO雷达二维DOD和二维DOA联合估计

MIMO（Multiple Input Multiple Output）雷达基于分集增益理念,使其相对于相控阵雷达,在目标探测、参数测量、多目标分辨及干扰识别和抑制等方面具有明显优势.目标角度估计是雷达目标参数测量的核心内容,也是雷达对空域目标进行定位和跟踪的前提.本文基于双L型阵列,提出了一种高精度低复杂度的双基地MIMO雷达二维离开角和二维到达角联合估计的新算法.通过对匹配滤波后的阵列接收数据进行子空间分解,实现了阵列流形矩阵的盲辨识,进而获得目标二维到达角和二维离开角的闭式解.所提算法估得的收发四维角（二维离开角和二维到达角）能够自动配对,与2-D ESPRIT（Two Dimensional Estimating Signal Parameters via Rotational Invariance Techniques）算法相比,运算复杂度约是其三分之一,角估计性能相当.仿真实验证明了所提算法以较低的运算复杂度,实现了对目标收发四维角的高精度联合估计.     

多子阵互耦条件下的一维波达方向估计及互耦自校正

该文研究多子阵(multiple subarrays)阵元互耦条件下的波达方向(DOA)估计,假设阵列由多个位置已知的均匀线阵(ULA)组成,但线阵阵元间存在互耦效应。利用均匀线阵互耦矩阵的带状、对称Toeplitz性及多子阵互耦矩阵的块状对角特性,提出了一种解耦合波达方向估计及互耦自校正算法。该算法在未知阵元互耦参数的情况下,可准确估计出信源的波达方向。另外,算法在精确估计波达方向的同时,还可准确估计出阵元间的互耦系数,实现多子阵的互耦自校正。算法的波达方向估计只需一维谱峰搜索,避免了通常多参数联合估计的多维非线性搜索及迭代运算,可明显减小算法运算量。文中讨论了算法参数可辨识性的必要条件,并分析计算了多参数联合估计的克拉美-罗界(CRB)。理论分析及蒙特卡罗仿真结果表明,该算法具有计算量小、DOA估计分辨力高、互耦校正效果好等优点。     

Direction-of-Arrival Method Based on Randomize-Then-Optimize Approach

The direction-of-arrival (DOA) estimation problem can be solved by the methods based on sparse Bayesian learning (SBL). To assure the accuracy, SBL needs massive amounts of snapshots which may lead to a huge computational workload. In order to reduce the snapshot number and computational complexity, a randomize-then-optimize (RTO) algorithm based DOA estimation method is proposed. The “learning” process for updating hyperparameters in SBL can be avoided by using the optimization and Metropolis-Hastings process in the RTO algorithm. To apply the RTO algorithm for a Laplace prior, a prior transformation technique is induced. To demonstrate the effectiveness of the proposed method, several simulations are proceeded, which verifies that the proposed method has better accuracy with 1 snapshot and shorter processing time than conventional compressive sensing (CS) based DOA methods.     

修正MUSIC算法对相关信号源的DOA估计性能

本文介绍了用修正ＭＵＳＩＣ算法提高相关信号源ＤＯＡ估计性能的方法。理论分析表明,采用该方法后,可将相关信号源的相关系数平均降低为原来的６３％,因而可改善ＭＵＳＩＣ算法对相关信号源的ＤＯＡ估计性能。且该方法不影响对非相关信号源ＤＯＡ的估计,计算量也无明显增加。计算机仿真实验结果验证了上述理论分析的正确性。     

交替投影算法的二维拓展

交替投影(AP)的极大似然算法由于其最接近CR下界的良好似然估计性能和适当的计算量受到人们的重视.本文通过采用直角交叉的两个直线阵实现了AP算法的二维拓展,计算量约与两个一维DOA估计计算量相当.     

Doa estimation using a sparse linear model based on eigenvectors

To reduce high computational cost of existing Direction-Of-Arrival (DOA) estimation techniques within a sparse representation framework, a novel method with low computational complexity is proposed. Firstly, a sparse linear model constructed from the eigenvectors of covariance matrix of array received signals is built. Then based on the FOCal Underdetermined System Solver (FOCUSS) algorithm, a sparse solution finding algorithm to solve the model is developed. Compared with other state-of-the-art methods using a sparse representation, our approach also can resolve closely and highly correlated sources without a priori knowledge of the number of sources. However, our method has lower computational complexity and performs better in low Signal-to-Noise Ratio (SNR). Lastly, the performance of the proposed method is illustrated by computer simulations.