Statistical performance analysis of a fast stochastic gradient for constrained adaptive time delay estimation

An efficient bi-state stochastic gradient is proposed for spontaneous constrained time delay estimation. The quantized stochastic gradient is an approximation of the polarity of the instantaneous delay estimation error. It is adjusted in such a way that it has a much higher probability to move in the correct direction at each iteration so as to enable a speed-up in the delay estimate to converge to global minimum in steady state. The performance of the delay estimator is evaluated statistically and an analytical solution for its convergence behavior is established. It is demonstrated that the proposed algorithm has at least a two-fold improvement in convergence speed when compared with the conventional approach, and this is verified by extensive simulation results.     

Performance analysis of structured gradient algorithm [antennaarray processing]

The structured gradient algorithm uses a structured estimate of the array correlation matrix to estimate the gradient required for the constrained least mean square algorithm. This structure reflects the structure of the exact array correlation matrix for an equispaced linear array and is obtained by spatial averaging of the elements of the noisy correlation matrix. In its standard form the LMS algorithm does not exploit the structure of the array correlation matrix. The gradient is estimated by multiplying the array output with the receiver outputs. An analysis of the two algorithms is presented to show that the covariance of the gradient estimated by the structured method is less sensitive to the look direction signal than that estimated by the standard method. The effect of the number of elements on the signal sensitivity of the two algorithms is studied     

针对相干信号DOA估计的改进MUSIC算法

针对相干信号波达方向(Direction of Arrival, DOA)估计,提出了一种改进的多重信号分类(Multiple Signal Classification, MUSIC)算法。首先,利用信号协方差矩阵的两个最大特征值所对应的特征向量,构造出两个Toeplitz矩阵;然后,利用前后向空间平滑思想得到这两个矩阵的无偏估计并求和;最后,利用MUSIC算法从中估计出相干信号DOA。和已有方法相比,该方法无需损失阵列孔径且具有更优的DOA估计性能。     

Variable-step blind source separation method with adaptive momentum factor

A variable-step blind source separation algorithm based on the natural gradient with adaptive momentum factor was proposed,which could cope with the determined blind source separation in the environment of stationary and non-stationary.Function estimation mixed matrix was constructed by performance index.The estimated performance index was obtained by the estimated mixed matrix,and the constructor was updated by the estimated performance index.Then,the constructor was plugged with appropriate experienced parameter into the proposed algorithm and step and momentum factor was adaptively adjusted.Finally,the estimation source signals could be obtained.Simulations show that the proposed algorithm is effective to estimate the mixed matrix in the stationary and non-stationary environments,and the proposed algorithm has faster convergence speed and lower steady error as well as separates source signals effectively.     

一种基于奇异值分解的改进信噪比盲估计算法

针对空间分解类信噪比(SNR)估计算法中子空间维数估计复杂度较高,低信噪比下估计偏差较大的问题,提出了一种改进的子空间维数估计算法。该算法首先利用样本自相关矩阵的奇异值序列进行后向差分得到梯度序列,对梯度序列每一项与后5项之和的比值进行搜索,最大比值所对应的奇异值序号作为信号子空间维数,最后计算信噪比。合适数据长度下的仿真结果表明：在信噪比-5 dB~20 dB范围内,常规通信信号的信噪比估计平均偏差小于0.5 dB,标准差小于1 dB;该算法提升了低信噪比下的估计性能,运算量较小,无需知道调制方式、载波频率、符号率等先验信息,在低信噪比时对信噪比时变的跟踪估计更为准确,且对复杂高阶调制信号同样适用。     

A new algorithm for explicit adaptation of time delay

By using an adaptive technique similar to the one developed by Etter and Stearns (1981), a novel constrained algorithm for explicit time delay estimation (TDE) is derived. The adaptive process provides an unbiased delay estimate and its respective performance surface, learning characteristics and delay variance will be given. The mean-square error surface, though a function of the estimated delay only, is multimodal and proper initialization is required to guarantee global convergence. Simulation results are included to validate the convergence behavior of the TDE system     

一种平坦衰落信道下的盲信噪比估计算法

针对基于子空间分解信噪比估计算法中信号子空间维数估计复杂度高、小样本条件下估计偏差大的问题,提出了一种改进的盲信噪比估计算法.该算法首先构造接收信号的自相关矩阵,然后从矩阵奇异值序列的尾部开始,间隔两项依次进行差分得到梯度序列,再以梯度序列相邻两项均值大干特定阈值为条件确定信号子空间的维数,最后求得信噪比.仿真结果表明:信噪比范围为-5～+15 dB时,平坦衰落信道下常用调制信号的信噪比估计标准差小于0.1 dB,与MDL,AIC方法相比,该算法计算量小,且能适应更低的信噪比和更短的数据长度.     

六角形阵列相干信号二维DOA估计

提出了一种基于扩展重构相关矩阵去相干的二维DOA估计算法。针对六角形阵列的结构特点,首先对各个阵元的接收数据求其共轭矩阵来扩展阵列,扩展后的阵列分为3个六角形子阵列,以此为基础,求得各子阵列的自相关矩阵及互相关矩阵来扩展重构相关矩阵,从而实现解相干的目的,最后利用二维MUSIC算法进行DOA估计。该算法在不减少阵列有效孔径的前提下,增加了可估计相干源数目,并且能够得到较好的估计性能。最后,通过计算机仿真证实了该算法的有效性。      

一种用于无线通信DOA估计的改进MUSIC算法研究

MUSIC算法是一种空间谱估计算法,在对宽带信号进行空间谱估计时,该算法需要较长的观测时间来估计协方差矩阵,不利于高速运动目标的定位。提出了基于驾驶协方差矩阵(STCM)的MUSIC算法,该算法首先对每个频带的CSDM进行特征分解,然后利用各频带的噪声子空间求得噪声空间的STCM,进而利用噪声空间的STCM直接得到整个宽带信号的空间谱估计结果。仿真表明该算法在保证高分辨率的同时,需要较短观测时间,适用于较低信噪比、具有较小观测方差。     

基于多级阻塞的稳健相干自适应波束形成

针对期望信号波达角(DOA)估计误差较大时相干波束形成性能下降的问题,该文提出一种基于多级阻塞的稳健相干自适应波束形成算法。该算法首先定义阻塞矩阵,推导多级阻塞原理,并利用其滤除阵列接收信号中的期望信号;然后给出空间中只存在期望信号时,子阵与全阵间阵列流型的映射关系,据此推导全阵扩展变换,并证明其在干扰信号存在条件下的有效性;最终利用扩展变换获取全阵最优权矢量,实现相干波束形成。该算法对期望信号波达角估计误差稳健,且无需干扰信号来向的先验信息,同时可以有效避免阵列孔径的损失。仿真分析验证了算法的优越性和理论分析的有效性。     

Efficient subspace-based algorithm for adaptive bearing estimation and tracking

In some practical applications of array processing, the directions of the incident signals should be estimated adaptively, and/or the time-varying directions should be tracked promptly. In this paper, an adaptive bearing estimation and tracking (ABEST) algorithm is investigated for estimating and tracking the uncorrelated and correlated narrow-band signals impinging on a uniform linear array (ULA) based on the subspace-based method without eigendecomposition (SUMWE), where a linear operator is obtained from the array data to form a basis for the space by exploiting the array geometry and its shift invariance property. Specifically, the space is estimated using the least-mean-square (LMS) or normalized LMS (NLMS) algorithm, and the directions are updated using the approximate Newton method. The transient analyses of the LMS and NLMS algorithms are studied, where the "weight" (i.e., the linear operator) is in the form of a matrix and there is a correlation between the "additive noise" and "input data" that involve the instantaneous correlations of the received array data in the updating equation, and the step-size stability conditions are derived explicitly. In addition, the analytical expressions for the mean-square error (MSE) and mean-square deviation (MSD) learning curves of the LMS algorithm are clarified. The effectiveness of the ABEST algorithm is verified, and the theoretical analyses are corroborated through numerical examples. Simulation results show that the ABEST algorithm is computationally simple and has good adaptation and tracking abilities.     

Linear prediction based adaptive algorithm for a complex sinusoidal frequency estimation

The complex direct frequency estimation (CDFE) adaptive algorithm is developed and proposed in this paper. The motivation of this work is obtained from the previous real DFE (RDFE) adaptive algorithm. The methodology of the CDFE is based on the linear prediction property of complex sinusoidal signals. The proposed algorithm is unbiased and computationally efficient. Moreover, it is easy to implement and appropriate for real-time applications. In addition, the convergence behavior is analyzed and the steady-state mean square error (MSE) of the frequency estimate is derived in closed form. Computer simulations are treated to corroborate the theoretical analysis.     

宽带独立信号和相干信号的DOA估计

当独立信号和相干信号共存时,传统四阶累积量方法无法估计出宽带相干信号的来波方向(DOA),针对这个问题提出了一种新方法。该方法首先通过离散傅里叶变换,将宽带阵列接收数据分解为若干个窄带信号,构造出各个窄带频率处的自相关矩阵,再通过MUSIC(Multiple Signal Classification)算法估计出各个窄带信号的DOA,将各个窄带信号的空间谱相加求平均,通过谱峰搜索得到宽带独立信号的DOA;然后分离出独立信号的信息,构造出一个只包含宽带相干信号信息的矩阵,最后通过稀疏重构的方法估计出相干信号的DOA。计算机仿真结果证明该算法的正确性和有效性。     

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。      

Learning Behaviors of Stochastic Gradient Radial Basis Function Network Algorithms for Odor Sensing Systems

Learning behaviors of a radial basis function network (RBFN) using a singular value decomposition (SVD) and stochastic gradient (SG) algorithm, together named RBF‐SVD‐SG, for odor sensing systems are analyzed, and a fast training method is proposed. RBF input data is from a conducting polymer sensor array. It is revealed in this paper that the SG algorithm for the fine‐tuning of centers and widths still shows ill‐behaving learning results when a sufficiently small convergence coefficient is not used. Since the tuning of centers in RBFN plays a dominant role in the performance of RBFN odor sensing systems, our analysis is focused on the center‐gradient variance of the RBFN‐SVD‐SG algorithm. We found analytically that the steady‐state weight fluctuation and large values of a convergence coefficient can lead to an increase in variance of the center‐gradient estimate. Based on this analysis, we propose to use the least mean square algorithm instead of SVD in adjusting the weight for stable steady‐state weight behavior. Experimental results of the proposed algorithm have shown faster learning speed and better classification performance.     

基于四阶循环累积量的DOA估计方法

提出了一种新的波达方向估计算法,该算法构造了一个“谱相关DOA矩阵”,并基于此矩阵进行DOA估计。理论分析表明,通过谱相关矩阵的特征值分解,就可以得到源信号的DOA,该方法不需要进行谱峰搜索,同时利用循环平稳特性,可以有效抑制平稳噪声和滤除与信号循环频率不同的干扰信号,从而大大提高了算法的检测能力。另外还给出了相干信号DOA解决方法。     

基于Toeplitz矩阵重构的相干信源二维DOA估计算法

针对空间相干信源的二维DOA估计问题,提出一种基于Toeplitz矩阵重构的新算法。采用垂直放置的L形阵列,通过对重构的Toeplitz矩阵进行特征分解,得到对应的噪声子空间,并用MUSIC算法进行有限次一维搜索,先后估计出俯仰角和相应的方位角。与空间平滑处理算法相比,不减少阵元的有效孔径,具有更强解相干能力,估计性能也优于后者。最后计算机仿真结果证实了算法的有效性和可行性。     

High-resolution direction finding: the missing data case

This paper considers the problem of estimating the direction-of-arrival (DOA) of one or more signals using an array of sensors, where some of the sensors fail to work before the measurement is completed. Methods for estimating the array output covariance matrix are discussed. In particular, the maximum-likelihood (ML) estimate of this covariance matrix and its asymptotic accuracy are derived and discussed. Different covariance matrix estimates are used for DOA estimation together with the MUSIC algorithm and with a covariance matching technique. In contrast to MUSIC, the covariance matching technique can utilize information on the estimation accuracy of the array covariance matrix, and it is demonstrated that this yields a significant performance gain     

Direction finding for wide-band signals using an interpolated array

The authors derive a new direction-finding algorithm for multiple wideband signals received by an arbitrary array and analyze its performance. Using an interpolation technique, they generate a set of virtual arrays, each for a different frequency band, having the same array manifold. The convergence matrices of these arrays are added to produce a composite covariance matrix. Direction-of-arrival (DOA) estimates are obtained by eigendecomposition of this composite covariance matrix using the narrowband MUSIC algorithm or its variants. Closed-form expressions for the asymptotic covariance matrix of the DOA estimation errors are derived using a perturbation analysis, evaluated for specific cases, and compared with the Cramer-Rao lower bound. Special attention is given to correlated and coherent signals. The formulas for the error covariance are quite general and can be modified to provide results for other wideband DOA estimation algorithms     

基于阵列结构的盲源分离算法

利用源信号的统计独立性提出了一种由混合信号和分离信号估计混合矩阵的算法,避免了一次矩阵求逆运算。同时,利用天线阵列的结构信息提出了一种直接重构混合矩阵的算法,该算法不需要估计源信号的载频和入射角。仿真结果表明,所提算法与基于来波方向估计的盲分离算法性能相当,在信号入射角间隔较大时,所提算法性能优于普通的盲分离算法,并且大大减少了运算量。