High resolution two-dimensional ARMA spectral estimation

The authors present a practical algorithm for estimating the power spectrum of a 2-D homogeneous random field based on 2-D autoregressive moving average (ARMA) modeling. This algorithm is a two-step approach: first, the AR parameters are estimated by solving a version of the 2-D modified Yule-Walker equation, for which some existing efficient algorithms are available; then the MA spectrum parameters are obtained by simple computations. The potential capability and the high-resolution performance of the algorithm are demonstrated by using some numerical examples     

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.     

A fast spectral estimation algorithm based on the FFT

A simple FFT-based algorithm for spectrum estimation is presented. The major difference between this and spectrum estimation using a single pass through the FFT is that the proposed algorithm is iterative and the FFT is used many times in a systematic may to search for individual spectral lines. Using simulated data, the proposed algorithm is able to detect mulitple sinusoids in additive noise. The algorithm is certainly better than the single pass FFT in separating closely spaced sinusoids. Finally the algorithm is applied to some experimental measurements to illustrate its properties     

基于改进互耦系数估计算法的自适应波束形成

阵列信号在实际应用中,常常会面临噪声的干扰,低信噪比(signal noise ratio, SNR)时波束形成器性能会急剧下降.针对该问题,提出一种基于改进互耦系数估计的抗互耦算法的自适应波束形成,即研究信号在不同输入SNR以及不同干扰波达方向(direction of arrival,DOA)估计误差下的互耦系数估计误差;并通过误差分析修正原算法不同SNR下参与估计信号的数目.改进算法改进了导向矢量和期望信号,提高了低SNR下互耦系数估计的准确度,对比分析验证了其在低SNR情况下有更强的抗干扰能力,对互耦现象有着更好的稳健性.     

A SPECTRAL ESTIMATION ALGORITHM USING THE HOUSEHOLDER TRANSFORM

Householder transform is used to triangularize the data matrix, which is basedon the near prediction error equation. It is proved that the sum of squared residuals for eachAR order can be obtained by the main diagonal elements of upper triangular matrix, so thecolumn by column procedure can be used to develop a recursive algorithm for AR modeling andspectral estimation. In most cases, the present algorithm yields the same results as the covariancemethod or modified covariance method does. But in some special cases where the numerical ill-conditioned problems are so serious that the covariance method and modified covariance methodfail to estimate AR spectrum, the presented algorithm still tends to keep good performance. Thetypical computational results are presented finally.     

High frequency ultrasonic backscatter from erythrocyte suspension

Previous studies have shown that ultrasonic backscattering from red blood cells suspended in saline is proportional to the fourth power of frequency for frequencies below 15 MHz, as predicted by Rayleigh scattering theory. Recently, the authors have extended the measurements up to 30 MHz, because scattering of ultrasound by red blood cells may no longer be negligible at these frequencies and can affect, to a great degree, the operation of intravascular imaging devices. The experimental results show that the fourth power dependence on frequency of the backscattering coefficient for porcine erythrocytes suspended in saline solution appears to be valid up to 30 MHz. To confirm this, backscattering cross-section of porcine red cells was computed as a function of frequency using the T-matrix method. Since at higher frequencies the shape of the scatterers may also play a significant role, its effect was investigated by treating the red cell as a sphere, a disc, and a biconcave disc of the same volume. Good agreement was obtained between the experimental and theoretical results     

基于贪婪算法的高分辨信号源DOA估计

确定辐射源的来波方向(DOA)是阵列信号处理的重要研究内容,已经广泛应用于雷达、声纳和无线通信等领域。本文研究了远场窄带信号源的DOA高分辨估计问题。利用信号来波方向在空域具有稀疏性的特点,建立了远场窄带信号源的稀疏表示模型。根据协方差矩阵的特征值分解和贪婪匹配追踪算法原理提出了一种基于特征值分解的多重正交匹配追踪算法（EIG MOMP）。首先,利用特征值分解对阵列接收数据进行降维处理。这一降维操作使得问题转化为了一个具有多重观测向量（MMV）的欠定方程求解问题。接着利用MOMP算法对降维后的数据进行处理,最终得到信号的DOA估计值。该算法实现了在低信噪比下远场窄带信号源的高分辨DOA估计,并具有较低的运算复杂度。将本文提出的算法与传统的Capon算法、多重信号分类算法（MUSIC）以及正交匹配追踪算法（OMP）进行了对比。结果证明,该算法在低信噪比下能取得较好的DOA估计效果,可以针对任意的相干信号源,并且具有高分辨率的优点。      

Recursive autoregressive spectral estimation by minimization of thefree energy

A digital signal processing technique applicable to power spectrum estimation, designated as the minimum free energy method, is described. With no a priori model assumption and no attempt to extract special features such as sinusoids, one can obtain high resolution even with high noise contamination of the measured signal. The technique is demonstrated by modification of the Burg recursive method of spectral analysis. A recursive minimum free energy method in which the reflection coefficient is chosen at each step is proposed for minimizing the free energy (the Burg energy measure minus the product of a temperature and an information entropy). The method produces a spectral estimator more impervious to high noise contamination than the Burg method and diminishes the Burg tendency to produce spurious peaks     

基于压缩感知的ISAR高分辨成像算法

针对 ISAR 在短孔径条件下存在的方位向分辨率低、易受噪声干扰等问题,基于压缩感知理论,提出了一种适用于短孔径时间模式下的基于压缩感知的ISAR方位向高分辨成像算法--PH-SL0算法。该算法首先构建部分随机化哈达玛矩阵作为量测矩阵,PH 矩阵具有重构精度高、重构需要量测个数少的优点;然后将运算速度快、重构精度高且稳健性好的平滑0-范数法（SL0, smoothed L0-norm）推广应用到雷达复数域进行信号重构,实现 ISAR的横向高分辨成像;最后对在短 CPI条件下提出的 PH-SL0算法的横向分辨率问题进行了理论分析。仿真和实测数据结果表明,所提算法具有更高的聚焦性能、分辨率以及较好的抗噪性能。     

Enhanced autoregressive moving average spectral estimation appliedto the measurement of Doppler spectral width

The measurement of clear-air turbulence with a Doppler radar is investigated. An autoregressive moving average (ARMA) model is proposed to improve the Doppler spectral width estimates. An iterative algorithm that has its origin in system identification is used for the estimation of the ARMA parameters. By taking advantage of a priori knowledge of the correlation matrix, which arises in the derivation of the governing equations of the ARMA parameters, the ARMA spectral estimate can be improved. This improvement is shown in terms of bias and variance of the spectral width estimate     

High resolution NMR spectroscopy using a recursive algorithm

When the DFT (discrete Fourier transform) is used as a method for obtaining NMR (nuclear magnetic resonance) spectrum, resolution of the obtained NMR spectrum depends clearly on spin-spin relaxation times of the nucleus and the sampled number of NMR signal. That is, the NMR spectrum is affected by decay of NMR signal due to the relaxation times and errors associated with discrete approximation of NMR spectrum. As a results, its resolution is degraded and the spectrum disagrees with the density distribution of the nucleus. In the present paper, we propose a new NMR spectrum estimation method for reducing their effects, demonstrating a high resolution NMR spectrum which is closer to the density distribution than that of the DFT. The proposed method is derived from applying the Kalman filter or the recursive least-square method to a NMR signal model based on Bloch equation. Under various conditions, the proposed method is compared with the DFT using a proton 1H NMR signal observed from mayonnaise in a 2 [T] static magnetic field. The results show that if spin-spin relaxation times are known previously, the proposed method can provide a higher resolution NMR spectrum than the DFT. In addition, it is shown that the method can reduce the discrete approximation errors of NMR spectrum. Finally, we demonstrate that if frequency components of sources of NMR signal are present in a limited range in frequency domain of interest, the method can magnify NMR spectrum with a sampling time and interval fixed.     

基于共轭梯度法的空间谱估计算法的实现

针对子空间算法在空间谱估计过程中运算量大、工程实现困难的问题,文中利用共轭梯度算法的快速收敛性进行特征分解,自适应更新信号子空间和噪声子空间,之后使用到ESPRIT算法中,计算出两个子阵的信号空间,利用旋转不变性完成对信号源的跟踪。通过与一般的特征分解算法进行分析和仿真对比后,表明算法不但有快速收敛的特点,而且能够降低算法的计算复杂度。将共轭算法与DOA算法结合,具体分析后,给出算法在FPGA上的实现方案,最后对算法进行了多方面的仿真实验,证明了算法不但可以完成精确的DOA估计,而且能改善子空间算法在实时性和跟踪性上的问题。     

基于宽频带多基线阵列解模糊的波达角估计算法

针对宽频带电子信号侦测系统测向精度与解相位模糊能力这一矛盾问题,根据多基线测向原理,提出一种基于宽频带多基线阵列解模糊的波达角估计算法,并进行了仿真分析。结果表明,该方法可有效求解宽频带多基线阵列相位模糊,提高对目标在相位差测量精度不高情况下的测向精度。     

Commentary on the denominator recursion for Burg's block algorithm

An order-recursive form for the denominator in the equation for the reflection coefficients in Burg's block algorithm was originally presented by N. Andersen in 1978, although its derivation was not given. This recursion was later repeated in a tutorial paper by Kay and Marple, also without derivation, but with data and error indexing defined differently. This letter shows a derivation of the denominator recursion using the notation defined in the latter work and demonstrates that the recursion given there is incorrect. A computer program written in the C language is also presented which implements Burg's algorithm, and includes references to specific equations from the latter work.     

Two-dimensional spectrum estimation using noncausal autoregressive models

Two-dimensional (2-D) spectrum estimation from raw data is of interest in signal and image processing. A parametric technique for spectrum estimation using 2-D noncausal autoregressive (NCAR) models is given. The NCAR models characterize the statistical dependency of the observation at location s on its neighbors in all directions. This modeling assumption reduces the spectrum estimation problem to two subproblems: the choice of appropriate structure of the NCAR model and the estimation of parameters in NCAR models. By assuming that the true structure of the NCAR model is known, we first analyze the existence and uniqueness of Gaussian maximum likelihood (GML) estimates of NCAR model parameters. Due to the noncausal nature of the models, the computation of GML estimates is burdensome. By assuming specific boundary conditions, computationally tractable expressions are obtained for the likelihood function. Expressions for the asymptotic covariance matrix of the GML estimates as well as the simultaneous confidence bands for the estimated spectrum using GML estimates are derived. Finally, the usefulness of the method is illustrated by computer simulation results.     

Bispectrum estimation using a MISO autoregressive model

Bispectra are third-order statistics that have been used extensively in analyzing nonlinear and non-Gaussian data. Bispectrum of a process can be computed as the Fourier transform of its bicumulant sequence. It is in general hard to obtain reliable bicumulant samples at high lags since they suffer from large estimation variance. This paper proposes a novel approach for estimating bispectrum from a small set of given low lag bicumulant samples. The proposed approach employs an underlying MISO system composed of stable and causal autoregressive components. We provide an algorithm to compute the parameters of such a system from the given bicumulant samples. Experimental results show that our approach is capable of representing non-polynomial spectra with a stable underlying system model, which results in better bispectrum estimation than the leading algorithm in the literature.     

High spectral resolution time-frequency distribution kernels

A new class of time-frequency distribution (TFD) kernels is introduced. Members in this class satisfy the desirable TFD properties and simultaneously provide local autocorrelation functions (LAF) that are amenable to high-frequency resolution modeling techniques. It is shown that members of the proposed class are product kernels, fast implementation multiplication-free kernels, recursive kernels, and optimum kernels with respect to autoterm localization     

Parameter estimation for autoregressive Gaussian-mixture processes:the EMAX algorithm

The problem of estimating parameters of discrete-time non-Gaussian autoregressive (AR) processes is addressed. The subclass of such processes considered is restricted to those whose driving noise samples are statistically independent and identically distributed according to a Gaussian-mixture probability density function (pdf). Because the likelihood function for this problem is typically unbounded in the vicinity of undesirable, degenerate parameter estimates, the maximum likelihood approach is not fruitful. Hence, an alternative approach is taken whereby a finite local maximum of the likelihood surface is sought. This approach, which is termed the quasimaximum likelihood (QML) approach, is used to obtain estimates of the AR parameters as well as the means, variances, and weighting coefficients that define the Gaussian-mixture pdf. A technique for generating solutions to the QML problem is derived using a generalized version of the expectation-maximization principle. This technique, which is referred to as the EMAX algorithm, is applied in four illustrative examples; its performance is compared directly with that of previously proposed algorithms based on the same data model and that of conventional least-squares techniques     

ARMA spectral estimation based on partial autocorrelations

This paper presents a new method for estimating the coefficients of autoregressive moving-average parameters of stationary time series. The method is based on computing the sample autocorrelations of the given time series and fitting an ARMA model so as to approximate the partial autocorrelations in a least-squares sense. When the given time series are characterized by spectral zeroes near the unit circle, they tend to have relatively long sequences of nonzero partial autocorrelations; hence the new method is especially effective in such cases. This paper contains a derivation of all necessary mathematical details, as well as several numerical examples illustrating the performance.     

High resolution parametric modelling for two-dimensional radar target using prony algorithm

On the conditions of low-resolution radar, a parametric model for two-dimensional radar target is described here according to the theory of electromagnetic scattering and the geometrical theory of diffraction. A high resolution estimation algorithm to extract the model parameters is also developed by building the relation of the scattering model and Prony model. The analysis of Cramer-Rao bound and simulation show that the method here has better statistical performance. The simulated analysis also indicates that the accurate extraction of the diffraction coefficient of scattering center is restricted by signal to noise ratio, radar center frequency and radar bandwidth.