Nonlinear autoregressive and nonlinear autoregressive moving average model parameter estimation by minimizing hypersurface distance

The least squares (LS) can be used for nonlinear autoregressive (NAR) and nonlinear autoregressive moving average (NARMA) parameter estimation. However, for nonlinear cases, the LS results in biased parameter estimation due to its assumption that the independent variables are noise free. The total least squares (TLS) is another method that can used for nonlinear parameter estimation to increase the accuracy of the LS because it specifically accounts for the fact that the independent variables are noise corrupted. TLS has its own limitations, however, mainly because it is difficult for the method to isolate noise from the signal components. We present a new method that is based on minimization of hypersurface distance for accurate parameter estimation for NAR and NARMA models. Computer simulation examples show that the new method results in far more accurate NAR and NARMA model parameter estimates than do either the LS and TLS, with noise that is either white or colored, and retains its high accuracy even when the signal-to-noise ratio (SNR) is as low as 10 dB.     

Nonparametric estimation of mean Doppler and spectral width

This paper proposes a new nonparametric method for estimation of spectral moments of a zero-mean Gaussian process immersed in additive white Gaussian noise. Although the technique is valid for any order moment, particular attention is given to the mean Doppler (first moment) and to the spectral width (square root of the centered second spectral moment). By assuming that the power spectral density (PSD) of the underlying process is bandlimited, the maximum-likelihood estimates of its spectral moments are derived. A suboptimal estimate based on the sample covariance is also studied. Both methods are robust in the sense that they do not rely on any assumption concerning the PSD (besides being bandlimited). Under weak conditions, the set of estimates based on sample covariance is unbiased and strongly consistent. Compared with the classical pulse pair and the periodogram-based estimators, the proposed methods exhibit better statistical properties for asymmetric spectra and/or spectra with large spectral widths, while involving a computational burden of the same order     

An autoregressive moving average tone detector

A new method for estimating tones in an arbitrary spectrum is presented. An autoregressive-moving average estimator is formulated and transformed into a linear regression problem. Many of the shortcomings of an "all pole" model are overcome and simulated test results indicate that the estimates are not particularly sensitive to additive noise. The main advantages of this new method are computational simplicity and robustness in noise environments. The algorithm can be useful in all areas where spectral information must be extracted in a computationally efficient fashion.     

On the estimation of variance for autoregressive and moving average processes (Corresp.)

The sample variance is commonly used to estimate the variance of stationary time series. When the second-order statistics of the process are known up to a scaling factor, this estimator is generally inefficient. In the case of an autoregressive (AR) process with unknown parameters, the sample variance is shown to be asymptotically efficient. However, the sample variance of a moving-average (MA) process with unknown parameters is generally an inefficient estimator. Closed-form expressions are derived for the Cramer-Rao hound associated with the variance estimation problem and for the variance of the sample-variance estimator, for both AR and MA processes.     

Exact likelihood for stationary vector autoregressive moving average processes

Autoregressive moving average (ARMA) models are useful approximants to the kinds of random processes commonly encountered in discrete-time signal processing applications. Such models may be used to compress data in low bit-rate information transmission, to improve frequency resolution in spectrum analysis, and to forecast in economic, meteorological, and other time series.In this paper we discuss several aspects of the maximum likelihood theory of parameter identification in ARMA models. We highlight the role of ‘innovations’ representations in exact likelihood theory and show how internal model structure may be used to speed up calculation of likelihood in either fast Kalman predictor or fast lattice implementations.     

Parameter estimation of two-dimensional moving average randomfields

This paper considers the problem of estimating the parameters of two-dimensional (2-D) moving average random (MA) fields. We first address the problem of expressing the covariance matrix of nonsymmetrical half-plane, noncausal, and quarter-plane MA random fields in terms of the model parameters. Assuming the random field is Gaussian, we derive a closed-form expression for the Cramer-Rao lower bound (CRLB) on the error variance in jointly estimating the model parameters. A computationally efficient algorithm for estimating the parameters of the MA model is developed. The algorithm initially fits a 2-D autoregressive model to the observed field and then uses the estimated parameters to compute the MA model. A maximum-likelihood algorithm for estimating the MA model parameters is also presented. The performance of the proposed algorithms is illustrated by Monte-Carlo simulations and is compared with the Cramer-Rao bound     

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     

Application of autoregressive moving average parametric modeling in magnetic resonance image reconstruction

The modeling of data is an alternative to conventional use of the fast Fourier transform (FFT) algorithm in the reconstruction of magnetic resonance (MR) images. The application of the FFT leads to artifacts and resolution loss in the image associated with the effective window on the experimentally-truncated phase encoded MR data. The transient error modeling method treats the MR data as a subset of the transient response of an infinite impulse filter (H(z) = B(z)IA(z)). Thus, the data are approximated by a deterministic autoregressive moving average (ARMA) model. The algorithm for calculating the filter coefficients is described. It is demonstrated that using the filter coefficients to reconstruct the image removes the truncation artifacts and improves the resolution. However, determining the autoregressive (AR) portion of the ARMA filter by algorithms that minimize the forward and backward prediction errors (e.g., Burg) leads to significant image degradation. The moving average (MA) portion is determined by a computationally efficient method of solving a finite difference equation with initial values. Special features of the MR data are incorporated into the transient error model. The sensitivity to noise and the choice of the best model order are discussed. MR images formed using versions of the transient error reconstruction (TERE) method and the conventional FFT algorithm are compared using data from a phantom and a human subject. Finally, the computational requirements of the algorithm are addressed.     

High resolution ultrasonic backscatter coefficient estimation based on autoregressive spectral estimation using Burg's algorithm

An autoregressive (AR) method for spectral estimation was applied toward the task of estimating ultrasonic backscatter coefficients from small volumes of tissue. High spatial resolution is desirable for generating images of backscatter coefficient. Data was acquired from a homogeneous tissue-mimicking phantom and from a normal human liver in vivo. The AR method was much more resistant to gating artifacts than the traditional DFT (discrete Fourier transform) approach. The DFT method consistently underestimated backscatter coefficients at small gate lengths. Therefore backscatter coefficient image formation will be quantitatively more meaningful if based on AR spectral estimation rather than the DFT. The autoregressive method offers promise for enhanced spatial resolution and accuracy in ultrasonic tissue characterization and nondestructive evaluation of materials.     

Special problems in the estimation of power-law spectra as appliedto topographical modeling

An increasing number of topographical studies find that natural surfaces possess power-law roughness spectra. Power-law spectra introduce unique difficulties in the spectral estimation process. The authors describe how an improper window choice allows leakage that yields a spectral estimate that is insensitive to the spectral slope. In addition, the commonly used Fourier-based spectral estimates have higher variances than other available estimators. Higher variance is particularly problematic when data records are short, as is often the case in remote sensing studies. The authors show that Capon's spectral estimator has less variance than Fourier-based estimators and measures the spectral slope more accurately. The authors also show how estimates of a 2D roughness spectrum can be obtained from estimates of the 1D spectrum for the isotropic power-law case     

激光传感器在车辆宽高超限检测中的应用

为了提高超限检测工作的效率、减轻超限工作人员的工作强度,实现超限检测的自动化,设计了采用德国SICK公司具有双脉冲技术的二维激光脉冲测距传感器的智能对动态车辆的宽高检测系统.采用激光传感器进行快速测量,利用PC工控机和可视化编程软件VB的网络内核与传感器进行数据的实时传输及处理,同时还设计了界面友好的上位机控制软件.现...     

An empirical investigation of the properties of the autoregressive spectral estimator

The autoregressive (AR) spectral estimator is used to make high resolution spectral estimates based on short data records. Measures of a frequency averaged normalized bias and normalized variance of the spectral estimates are introduced. A large number of spectra are generated. Based on the above mentioned measures and visual inspection of the estimates of the generated spectra, the AR and the conventional tapered and transformed (TT) spectral estimates are compared. It is shown that the AR spectral estimator is as stable as that given by its asymptotic variance. It is also shown that the AR spectral estimator is most powerful in estimating narrow spectral peaks with a high signal-to-interference ratio in the signal bandwidth.     

Nonlinear maximum likelihood estimation of autoregressive timeseries

Describes an algorithm for finding the exact, nonlinear, maximum likelihood (ML) estimators for the parameters of an autoregressive time series. The authors demonstrate that the ML normal equations can be written as an interdependent set of cubic and quadratic equations in the AR polynomial coefficients. They present an algorithm that algebraically solves this set of nonlinear equations for low-order problems. For high-order problems, the authors describe iterative algorithms for obtaining a ML solution     

Feedback capacity of the first-order moving average Gaussian channel

Despite numerous bounds and partial results, the feedback capacity of the stationary nonwhite Gaussian additive noise channel has been open, even for the simplest cases such as the first-order autoregressive Gaussian channel studied by Butman, Tiernan and Schalkwijk, Wolfowitz, Ozarow, and more recently, Yang, Kavccaronicacute, and Tatikonda. Here we consider another simple special case of the stationary first-order moving average additive Gaussian noise channel and find the feedback capacity in closed form. Specifically, the channel is given by Y_i=X_i+Z_i, i=1,2,..., where the input {X _i} satisfies a power constraint and the noise {Z_i} is a first-order moving average Gaussian process defined by Z_i=alphaU_i-1+U_i, |alpha|les 1, with white Gaussian innovations U_i, i=0,1,.... We show that the feedback capacity of this channel is C_FB=-log x₀ where x₀ is the unique positive root of the equation rhox²=(1-x²)(1-|alpha|x)² and rho is the ratio of the average input power per transmission to the variance of the noise innovation U_i. The optimal coding scheme parallels the simple linear signaling scheme by Schalkwijk and Kailath for the additive white Gaussian noise channel-the transmitter sends a real-valued information-bearing signal at the beginning of communication and subsequently refines the receiver's knowledge by processing the feedback noise signal through a linear stationary first-order autoregressive filter. The resulting error probability of the maximum likelihood decoding decays doubly exponentially in the duration of the communication. Refreshingly, this feedback capacity of the first-order moving average Gaussian channel is very similar in form to the best known achievable rate for the first-order autoregressive Gaussian noise channel given by Butman     

窄线宽光纤激光器线宽测量的研究进展

光纤激光器在许多领域都有着重要的应用,随着科技的发展,对光纤激光器线宽的要求也越来越高,因此如何精确地测量激光器的线宽也尤为重要。简要介绍了目前在测量激光器线宽方面的研究进展,着重介绍了几种测量线宽的方法及其原理,对各种方法的优缺点进行了分析。     

Maximum likelihood estimation of signals in autoregressive noise

Time series modeling as the sum of a deterministic signal and an autoregressive (AR) process is studied. Maximum likelihood estimation of the signal amplitudes and AR parameters is seen to result in a nonlinear estimation problem. However, it is shown that for a given class of signals, the use of a parameter transformation can reduce the problem to a linear least squares one. For unknown signal parameters, in addition to the signal amplitudes, the maximization can be reduced to one over the additional signal parameters. The general class of signals for which such parameter transformations are applicable, thereby reducing estimator complexity drastically, is derived. This class includes sinusoids as well as polynomials and polynomial-times-exponential signals. The ideas are based on the theory of invariant subspaces for linear operators. The results form a powerful modeling tool in signal plus noise problems and therefore find application in a large variety of statistical signal processing problems. The authors briefly discuss some applications such as spectral analysis, broadband/transient detection using line array data, and fundamental frequency estimation for periodic signals     

Recovering of autoregressive spectral estimates of signals buried in noise

In this paper, we propose a noise modeling that does not destroy AR structure of buried signals in noise independently of its nature (white or colored, Gaussian or not) and its variance. Expression of perturbed AR coefficients is derived and proposed restoration does not use any a-priori information on the nature of noise and its variance. It is shown that AR coefficients are closer to nominal ones (noise-free) in the presence of noise for lower frequency contents with respect to the sampling frequency of corresponding continuous-time processes from which samples are taken for AR estimation. For unknown frequency contents, denoising of AR coefficients is obtained by decreasing the time interval separating samples used by AR estimation. A model order selection adapted to degraded signal-to-noise ratios is proposed. Performances of the proposed recovering of original AR spectra are demonstrated via signals buried in white and colored noise. Observed results are in accordance with the developed theory.     

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     

Two-dimensional noisy autoregressive estimation with application to joint frequency and direction of arrival estimation

The present study addresses the problem of two-dimensional autoregressive estimation in the presence of additive white noise. The estimation method is based on combining the low-order and high-order Yule-Walker equations. The noise-compensated YW equations are solved using an iterative algorithm. The proposed method is also applied to joint frequency and direction of arrival estimation in uniform linear arrays. Using simulation study, the performance of the proposed algorithm is evaluated and compared with other methods.     

紫外飞秒激光的脉宽测量方法

相对于近红外波段的飞秒激光脉冲，紫外波段的飞秒脉冲由于具有单光子能量高、聚焦特性好、电离率高和成丝阈值低等优点，在高功率密度光场的产生、等离子体光物理等领域有着越来越广阔的应用前景，成为激光技术的研究热点。随着紫外飞秒激光技术的发展，传统的脉宽测量方法不能满足需求。指出了紫外飞秒激光脉宽测量研究的主要进展，讨论了目前可用于紫外飞秒激光脉宽的测量方法，主要有双光子荧光测量法、互相关法、简并四波混频法、多光子电离法，介绍了相关测量原理与特点。在此基础上，对紫外飞秒激光脉宽测量技术研究前景进行了展望。