Estimation of frequencies and damping factors by two-dimensionalESPRIT type methods

In this paper, we consider two-dimensional (2-D) signals modeled by the sum of damped cisoids. We propose two high-resolution approaches to estimate their frequencies and damping factors. Both high-resolution methods are based on the shift-invariance structure of the signal subspace related to each dimension. The first one estimates the frequency components in both dimensions as in the matrix enhancement and matrix pencil (MEMP) method before pairing them with a new algorithm. The second one consists of the direct estimation of the signal frequency pairs without an additional step to pair the frequencies related to each dimension. We show how these methods can estimate the scattering points of radar images     

二维正弦波检测的直接数据法

本文用一种新方法证明了,二维正弦波频率服从的二维特征多项式可取四种不同形式,并提出了一种直接数据法,借助它可直接利用观测数据本身高分辨检测出白噪声中的多个二维正弦波。     

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.     

An ESPRIT-like method for quadratic phase coupling estimation

Two algorithms are proposed for estimating the quadratically coupled frequency pairs (QC pairs) in a signal consisting of complex sinusoids in white noise. Three matrices are constructed from the complex third-order cumulants of the noisy signal, the second and third being time shifted versions of the first. The list of coupled frequencies is obtained from the rank reducing numbers of the matrix pencil formed from the first matrix and either of the latter two. The first algorithm then pairs these components by relating quadratic coupling to the intersection of generalized eigenspaces corresponding to two of these frequencies. The coupling strengths are also obtained in terms of generalized eigenvectors in this intersection space. The second algorithm constructs a two-parameter matrix pencil using all the three matrices. The rank reducing pairs of this pencil on the unit circle yield the QC pairs and the associated generalized eigenvectors: the coupling strengths     

二维谱估计算法的空间探测性能分析及验证

针对二维谱估计算法的空间探测性能分析的需求,从计算速度、计算量、顽健性、计算精度以及实际工程应用的角度出发,对基于L型阵列的二维MUSIC、二维干涉仪、二维增广矩阵束的谱估计算法进行了简要介绍,并对上述二维谱估计算法的性能进行了仿真分析,得到了3种算法的角度RMSE的对比分析,可知在同样仿真条件下,二维增广矩阵束算法最优,二维MUSIC算法次之,二维干涉算法最差。同时,构建了相应的试验场景,通过试验分析上述二维谱估计算法的空间探测性能,得到的试验结论与仿真结论一致。在此基础上,提出了二维增广矩阵束算法可扩展应用到雷达测控一体化系统的思路。     

Asymptotic properties of 2-D MUSIC estimator and comparison to 2-D MP estimator

The MUSIC estimator of two-dimensional frequencies (2-D MUSIC) is studied assuming a one-measurement data model with deterministic phases and additive complex white Gaussian noise. The large sample estimation covariance of the 2-D MUSIC is derived and compared to that of the 2-D matrix pencil (MP) estimator. The theoretical estimation variances for both the MP and MUSIC estimators are compared with the simulated MP and MUSIC estimation variances and the Cramer-Rao Bound (CRB). In the single 2-D sinusoid case, the most revealing form of the estimation covariance for both estimators are provided. The results shown in this paper are valid for a median range of SNR.     

白噪声中二维谐波的二维ARMA建模

本文研究了白噪声中二维谐波的二维ＡＲＭＡ建模问题，并从理论上探讨了利用所建立的二维ＡＲＭＡ模型进行二维谐波信号频率估计的方法。     

基于一种超分辨率算法的三维散射中心提取方法

针对转台-弧形导轨测量方法,在二维MEMP方法的基础上,提出一种适用于三维散射中心提取的超分辨率算法.该方法利用Hankel矩阵的结构特性,以及子空间不变技术等,实现对信号三维参数的正确估计,并且无需额外的配对步骤.对八个散射点组成的立方体模型的数值仿真表明,该算法可以正确估计信号参数对,并对噪声的鲁棒性较强.进一步将三维参数估计问题扩展到N维情况,给出了具有较普遍意义的N维参数估计公式.     

基于特征向量的多谱线自旋回波串信号参数估计

针对存在加性高斯白噪声多参数变量的多谱线自旋回波串(Spin Echo Train,SET)信号参数估计问题,提出基于特征向量的2-D参数估计方法.将SET信号构造成2-D数据矩阵,按照不同的方式构造Hankel块矩阵束,利用子空间转移不变结构解得特征向量,依据特征向量的结构规律获得衰减因子和频率,基于最小二乘方法进一步获得信号幅度估计.该方法具有自动配对的能力,在相对高信噪比以及频率可分辨的情况下能够实现参数的有效估计,且计算复杂度较低.仿真数据结果证明了算法的有效性.     

基于EMEMP的雷达二维信号融合成像新方法

雷达信号融合成像是一种能显著提高成像分辨率的参数化新方法.基于改进的Root-Music的传统融合方法对噪声敏感, 且存在模型极点失配的问题.本文通过将MEMP(Matrix Enhancement and Matrix Pencil)的二维频率估计方法推广到稀疏数据域,提出了一种基于扩展矩阵增强矩阵束(EMEMP)的融合新方法.此方法首先构造每一维联合增强矩阵,使其满足MEMP算法的配对要求,然后利用MEMP方法估计模型极点,进行极点配对,然后估计模型系数,最后内插频谱以达到融合的目的.实验结果表明相对于传统融合方法,该方法解决了极点失配的问题,提高了模型参数估计的稳健性.     

High resolution two-dimensional minimum free energy AR spectral estimation

We extend the minimum free energy (MFE) parameter estimation method to 2-D fields. This 2-D MFE method may be used to determine autoregressive (AR) model parameters for spectral estimation of 2-D fields. It may also be used to provide AR models for texture synthesis. The performance of the technique for closely spaced sinusoids in white noise is demonstrated by numerical example. Better results can be achieved than with the multidimensional Levinson algorithm.     

Matrix-based higher order spectral analysis for three-wave couplingprocesses

Composite linear and quadratic systems produce three-wave coupling when stimulated by random phase input sinusoids. Due to the nonlinearity of the system, the output frequencies are arithmetically related to the input. Using third-order cumulant statistics and their associated bispectrum, techniques are devised based on phase-insensitive matrix structures for detection and frequency estimation of coupling frequencies. The separation of the third-order cumulant series into symmetric and skew-symmetric portions allows one to exploit their characteristic eigendecompositions for frequency estimation. After symmetrization, biphases can be easily extracted as coefficients of the cumulant sequence. Using a generalized eigenvector representation, one can relate symmetric and skew-symmetric bases by a subspace rotation algorithm. Biphases can be estimated directly from generalized eigenvalues of the matrix pencil formed by symmetric and skew-symmetric matrices. The dimensionality of the matrices can be reduced through the use of cumulant projections that yield a slice of the bispectrum. The Radon transform procedure is related to bispectral processing through an isotropic radial-slice Volterra filter. The compact third-order Kronecker product matrix formulation and algorithms for coupling frequency estimation can also be converted for use in biphase estimation. Simulations showing the performance of the above procedures are also presented for both synthetic and biomedical time series     

A pencil-MUSIC algorithm for finding two-dimensional angles andpolarizations using crossed dipoles

The authors study the problem of finding two-dimensional (2-D) angles of wave arrival and wave polarizations using a uniform rectangular array of crossed dipoles. The method presented effectively exploits the redundancy in this array via 2-D moving-window smoothing to handle coherent sources and to achieve optimum noise sensitivity. The method combines the computational advantages of the MUSIC and matrix pencil approaches. The method is shown in simulation to be nearly optimum compared with the Cramer-Rao bound     

A high-resolution technique for multidimensional NMR spectroscopy

A scheme for estimating frequencies and damping factors of multidimensional nuclear magnetic resonance (NMR) data is presented-multidimensional NMR data can be modeled as the sum of several multidimensional damped sinusoids. The estimated frequencies and damping factors of multidimensional NMR data play important roles in determining protein structures. The authors present a high-resolution subspace method for estimating the parameters of NMR data, Unlike other methods, this algorithm makes full use of the rank-deficiency and Hankel properties of the prediction matrix composed of NMR data. Hence, it can estimate the signal parameters under low signal-to-noise ratio (SNR) by using a few data points. The effectiveness of the new algorithm is confirmed by computer simulations and it is tested by experimental data     

Using the matrix pencil method to estimate the parameters of a sumof complex exponentials

The approximation of a function by a sum of complex exponentials is a problem that is at least two centuries old. Fundamentally, all techniques discussed in this article proceed from using the same sequence of data samples and vary only, but importantly, in how those samples are used in achieving the parameter estimation. All of these techniques, in other words, seek the same quantitative parameters to represent the sampled data, but use different routes to get there. The techniques for estimating the parameters are either linear or nonlinear. The linear techniques are emphasized in this presentation. In particular, the matrix pencil method is described, which is more robust to noise in the sampled data. The matrix pencil approach has a lower variance of the estimates of the parameters of interest than a polynomial-type method (Prony's method belongs to this category), and is also computationally more efficient. A bandpass version of the matrix pencil can be implemented in hardware, utilizing an AT&T DSP32C chip operating in real time. A copy of the computer program implementing the matrix pencil technique is given in the appendix     

一种新的波达方向和多普勒频率估计算法

基于均匀圆形阵列,提出了一种同时估计空间非相干信号源方位角、仰角和多普勒频率的快速算法。该方法对均匀圆阵的输出信号进行模式空间转换,使得阵列流形具有类似于均匀线阵的形式,然后通过构造相应的数据矩阵得到传播算子的最小二乘（LS）估计,并由传播算子构造出一个特殊的低维矩阵,其特征值给出多普勒频率估计,特征向量舍有阵列流形的信息。结合模式空间阵列流形的性质,给出了一种DOA估计的总体最小二乘算法,在低信噪比条件下可提高测向精度。该方法不需要谱峰搜索和参数配对,具有运算量小的优点。计算机仿真验证了该方法的有效性。     

Near Maximal 2-D Sinusoid Identification From Limited Data

We describe a novel method to identify a large number of two-dimensional (2-D) sinusoids from very limited data. Starting with the noiseless exponential superposition model, we derive the 2-D linear prediction equations for the data, and present a general 2-D exponential identification algorithm based on one-dimensional (1-D) rooting techniques. Then we enhance this general algorithm for the special case of 2-D sinusoid identification by using conjugate-reverse data to increase the number of identifiable sinusoids and by using FFT to avoid polynomial rooting. Noise is handled by least-squares solutions of the linear prediction equations and the polynomial equations. Numerical simulations demonstrate that our algorithm provides a competitive alternative to existing algorithms     

Extrapolation of time-domain responses from three-dimensionalconducting objects utilizing the matrix pencil technique

In this paper, we use the matrix pencil approach to extrapolate time-domain responses from three-dimensional (3-D) conducting objects that arise in the numerical solution of electromagnetic field problems. By modeling the time functions as a sum of complex exponentials, we can eliminate some of the instabilities that arise in late times for the electric-field integral equation in the time domain. However, this method can also be utilized for extending the responses obtained using a finite-difference time-domain (FDTD) formulation     

Reducing the Number of Elements in a Linear Antenna Array by the Matrix Pencil Method

The synthesis of a nonuniform antenna array with as few elements as possible has considerable practical applications. This paper introduces a new non-iterative method for linear array synthesis based on the matrix pencil method (MPM). The method can synthesize a nonuniform linear array with a reduced number of elements, and can be also used to reduce the number of elements for linear arrays designed by other synthesis techniques. In the proposed method, the desired radiation pattern is first sampled to form a discrete pattern data set. Then we organize the discrete data set in a form of Hankel matrix and perform the singular value decomposition (SVD) of the matrix. By discarding the non-principal singular values, we obtain an optimal lower-rank approximation of the Hankel matrix. The lower-rank matrix actually corresponds to fewer antenna elements. The matrix pencil method is then utilized to reconstruct the excitation and location distributions from the approximated matrix. Numerical examples show the effectiveness and advantages of the proposed synthesis method.      

一种基于3D-ESPRIT的散射中心参数估计算法

基于雷达目标的三维散射中心模型,提出了利用目标频域数据的3D-ESPRIT参数估计方法.该方法不需进行参数配对,不需要计算相关矩阵,计算量较小.仿真实验结果表明,该方法能够对雷达目标散射中心给出比较准确的估计值.与3D-MP(矩阵束)方法的估计结果相比较,验证了算法的正确性.