Multivariate ARMA modeling by scalar algorithms

An algorithm for multichannel autoregressive moving average (ARMA) modeling which uses scalar computations only and is well suited for parallel implementation is proposed. The given ARMA process is converted to an equivalent scalar, periodic ARMA process. The scalar autoregressive (AR) parameters are estimated by first deriving a set of modified Yule-Walker-type equations and then solving them by a parallel, order recursive algorithm. The moving average (MA) parameters are estimated by a least squares method from the estimates of the input samples obtained via a high-order, periodic AR approximation of the scalar process     

High-Resolution ARMA Estimation of Mixed Spectra

In this paper, we propose a high-resolution autoregressive moving average (ARMA) modeling technique for signals which are a sum of sinusoids embedded in colored noise. The approach is based on a special ARMA model. We show that an approximation to this model can be found through the central solution of Nevanlinna-Pick interpolation. In this context, it can reach a very fine resolution with a special arrangement of filterbank poles. A very efficient iterative algorithm will then be presented to achieve such desired arrangement. We also derive theoretical expressions for the variance of interpolation values for both continuous and mixed spectra for complex poles. Computer simulations show that the approach is very powerful in joint power spectrum and frequency estimation and provides superior performance with respect to traditional techniques.     

Performance analysis of estimation algorithms of nonstationary ARMA processes

The correlation analysis based methods are not suitable for identifying parameters of nonstationary autoregressive (AR), moving average (MA), and ARMA systems. By using estimation residuals in place of unmeasurable noise terms in information vector or matrix, we develop a least squares based and gradient based algorithms and establish the consistency of the proposed algorithms without assuming noise stationarity, ergodicity, or existence of higher order moments. Furthermore, we derive the conditions for convergence of the parameter estimation. The simulation results validate the convergence theorems proposed.     

ARMA谱估计的高阶关联神经网络优化方法

本文基于全反馈高阶关联神经网络优化理论，提出了一种将神经网络优化方法应用于ARMA谱估计（ARMA－NNO法）的理论框架。该方法与迄今为止所见方法的区别在于，它直接面对ARMA扩展的Yule—Walker方程的非线性，同时估计出模型的AR和MA两部分参数。描述估计质量的加权均方误差被当作神经网络能量函数，从而导出了ARMA－NNO法的Lyapunov方程。文中讨论了此法的实现方案，给出了几个谱估计实例，通过与其它几种ARMA谱估计方法的比较，证明了它的有效性。     

Models for setting ATM parameter values

In ATM networks, a user should negotiate at connection set-up a traffic contract which includes traffic characteristics and requested QoS. The traffic characteristics currently considered are the Peak Cell Rate, the Sustainable Cell Rate, the Intrinsic Burst Tolerance and the Cell Delay Variation (CDV) tolerance(s). The values taken by these traffic parameters characterize the so-called Worst Case Traffic that is used by CAC procedures for accepting a new connection and allocating resources to it. Conformance to the negotiated traffic characteristics is defined, at the ingress User to Network Interface (UNI) and at subsequent Inter Carrier Interfaces (ICIs), by algorithmic rules based on the Generic Cell Rate Algorithm (GCRA) formalism. Conformance rules are implemented by policing mechanisms that control the traffic submitted by the user and discard excess traffic. It is therefore essential to set traffic characteristic values that are relevant to the considered cell stream, and that ensure that the amount of non-conforming traffic is small. Using a queueing model representation for the GCRA formalism, several methods are available for choosing the traffic characteristics. This paper presents approximate methods and discusses their applicability. We then discuss the problem of obtaining traffic characteristic values for a connection that has crossed a series of switching nodes. This problem is particularly relevant for the traffic contract components corresponding to ICIs that are distant from the original source.     

On 2-D recursive LMS algorithms using ARMA prediction for ADPCMencoding of images

A two-dimensional (2D) linear predictor which has an autoregressive moving average (ARMA) representation well as a bias term is adapted for adaptive differential pulse code modulation (ADPCM) encoding of nonnegative images. The predictor coefficients are updated by using a 2D recursive LMS (TRLMS) algorithm. A constraint on optimum values for the convergence factors and an updating algorithm based on the constraint are developed. The coefficient updating algorithm can be modified with a stability control factor. This realization can operate in real time and in the spatial domain. A comparison of three different types of predictors is made for real images. ARMA predictors show improved performance relative to an AR algorithm.     

基于相似度算法的伪码起始位置变步长估计

针对非合作DSSS信号中伪随机码的起始位置进行研究分析,以获取完整周期的扩频调制信息。借鉴图像处理领域中对图像匹配的处理方法,提出一种基于平均相似度的方法,估计DSSS信号中伪码的起始位置。理论分析和Matlab仿真结果表明,提出的算法能够在低信噪比的情况下,以较小的误差估计出伪码的起始位置。以伪码周期和速率的估计作为先决条件,基于平均相似度法进行变步长搜索,估计伪码的起始位置,估计误差在半个伪码码片宽度之内。     

Estimation algorithms for dynamic tracer studies using positron-emission tomography

Algorithms are developed for estimating statistics for use by parameter estimation algorithms in dynamic tracer studies utilizing positron-emission tomography and requiring high temporal resolution. Two types of statistics are considered. One can be used with the expectation-maximization algorithm to compute maximum likelihood parameter estimates, and the other computes a histogram of activity levels versus time for use with weighted least squares parameter estimation algorithms. An estimator of the variance of this histogram is also given. Variants for use with both time-of-flight and projection data collected at high frame rates are presented. The algorithms account for the effects of attenuation, randoms, detector efficiency, and nonuniform sampling.     

Automatic generation of starting values for the simulation ofmicrowave oscillators by frequency domain techniques

A new approach to the start-up problem inherent to the large-signal analysis of autonomous circuits in the frequency domain is presented. By insertion of a simple network, depending on one parameter, the oscillator is damped to the stability limit where a linear analysis yields good results. The steady state of the undamped oscillator is then obtained by a continuation method corresponding to the successive removal of the damping network. With this procedure the degenerate solution may be excluded in a straightforward manner     

ARMA-cepstrum Recursion Algorithm for the Estimation of the MA Parameters of 2-D ARMA Models

This paper considers the problem of estimating the moving average (MA) parameters of a two-dimensional autoregressive moving average (2-D ARMA) model. To solve this problem, a new algorithm that is based on a recursion relating the ARMA parameters and cepstral coefficients of a 2-D ARMA process is proposed. On the basis of this recursion, a recursive equation is derived to estimate the MA parameters from the cepstral coefficients and the autoregressive (AR) parameters of a 2-D ARMA process. The cepstral coefficients are computed benefiting from the 2-D FFT technique. Estimation of the AR parameters is performed by the 2-D modified Yule–Walker (MYW) equation approach. The development presented here includes the formulation for real-valued homogeneous quarter-plane (QP) 2-D ARMA random fields, where data are propagated using only the past values. The proposed algorithm is computationally efficient especially for the higher-order 2-D ARMA models, and has the advantage that it does not require any matrix inversion for the calculation of the MA parameters. The performance of the new algorithm is illustrated by some numerical examples, and is compared with another existing 2-D MA parameter estimation procedure, according to three performance criteria. As a result of these comparisons, it is observed that the MA parameters and the 2-D ARMA power spectra estimated by using the proposed algorithm are converged to the original ones     

扩频信号的自回归滑动平均谱估计识别技术研究

提出了利用自回归滑动平均谱估计分析识别扩频信号，给出了模型参数估计算法。最后以二元直扩信号为例，用MATLAB软件进行了模拟仿真，验证了方法的可行性与优越性。     

Threshold values and convergence properties of majority-based algorithms for decoding regular low-density parity-check codes

This work presents a detailed study of a family of binary message-passing decoding algorithms for low-density parity-check (LDPC) codes, referred to as "majority-based algorithms." Both Gallager's algorithm A (G/sub A/) and the standard majority decoding algorithm belong to this family. These algorithms, which are, in fact, the building blocks of Gallager's algorithm B (G/sub B/), work based on a generalized majority-decision rule and are particularly attractive for their remarkably simple implementation. We investigate the dynamics of these algorithms using density evolution and compute their (noise) threshold values for regular LDPC codes over the binary symmetric channel. For certain ensembles of codes and certain orders of majority-based algorithms, we show that the threshold value can be characterized as the smallest positive root of a polynomial, and thus can be determined analytically. We also study the convergence properties of majority-based algorithms, including their (convergence) speed. Our analysis shows that the stand-alone version of some of these algorithms provides significantly better performance and/or convergence speed compared with G/sub A/. In particular, it is shown that for channel parameters below threshold, while for G/sub A/ the error probability converges to zero exponentially with iteration number, this convergence for other majority-based algorithms is super-exponential.     

ARMA噪声中的正弦波检测

本文提出一种ＡＲＭＡ噪声中正弦波检测的方法，本方法先用改进的Ｐｒｏｎｙ法估计可能存在的正弦波，然后利用一种综合考虑衰减因子以及ＭＵＳＩＣ值的准则从估计结果中区分正统率波的真伪。数值例子表明，本文方法比Ｐｒｏｎｇ方法及ＭＵＳＩＣ方法具有更高的分辨力。     

IC制造中的ARMA模型分析与动态工艺控制

提出了动态工艺条件控制的概念,即通过引入自适应算法ARMA,可对集成电路制造工艺效果进行预测,并根据预测结果,对工艺条件加以实时的调整控制,达到改善成品率的目的.采用动态工艺条件控制,打破了几十年来IC制造的固定模式,是IC制造领域具有重大创新性的提法.     

Characterization and estimation of two-dimensional ARMA models

A class of finite-order two-dimensional autoregressive moving average (ARMA) is introduced that can represent any process with rational spectral density. In this model the driving noise is correlated and need not be Gaussian. Currently known classes of ARMA models or AR models are shown to be subsets of the above class. The three definitions of Markov property are discussed, and the class of ARMA models are precisely stated which have the noncausal and semicausal Markov property without imposing any specific boundary conditions. Next two approaches are considered to estimate the parameters of a model to fit a given image. The first method uses only the empirical correlations and involves the solution of linear equations. The second method is the likelihood approach. Since the exact likelihood function is difficult to compute, we resort to approximations suggested by the toroidal models. Numerical experiments compare the quality of the two estimation schemes. Finally the problem of synthesizing a texture obeying an ARMA model is considered.     

Best stable and invertible approximations for ARMA systems

A method is proposed for finding the best stable and invertible approximations for an autoregressive moving average (ARMA) system, relative to a general quadratic metric in the coefficient space. Mathematically, the problem is equivalent to projecting the regression and moving average vectors of the system onto the set S of coefficients of monic Schur polynomials. The geometry of S is too complex to allow the problem to be approached directly in the ARMA coefficient space. A solution is obtained by constrained steepest descent in the hypercube of reflection coefficients, which is homomorphic to S     

ARMA modeling of fourth-order cumulants and phase estimation

A new procedure is proposed for ARMA modeling of fourth-order cumulants and trispectrum estimation of non-Gaussian stationary random processes. The new procedure is applied to the identification of nonminimum phase systems for both phase and magnitude response estimation. It is demonstrated by means of comprehensive simulation examples that the ARMA approach exhibits improved performance over conventional trispectrum methods. ARMA model order selection criteria based on fourth-order cumulants are presented and their performance evaluated. The computational complexity of the ARMA and conventional trispectrum methods is also examined. The new procedure does not require knowledge of the non-Gaussian distribution.This work was supported by the Office of Naval Research under Contract No. ONR-N00014-86-K-0219.     

ARMA models, prewhitening, and minimum cross entropy

The problem of spectral estimation on the basis of observations from a finite stretch of a stationary time series is considered, in connection with knowledge of a prior estimate of the spectral density. A reasonable posterior spectral density estimate would be the density that is closest to the prior according to some measure of divergence, while at the same time being compatible with the data. The cross entropy has often been proposed to serve as such a measure of divergence. A correction of the original minimum-cross-entropy spectral analysis (MCESA) method of J.E. Shore (see IEEE Trans. Acoust. Speech Signal Process, vol.29, p.230-7, 1981) to traditional prewhitening techniques and to autoregressive moving average (ARMA) models is pointed out and a fast approximate solution of the minimum cross entropy problem is proposed. The solution is in a standard multiplicative form, that is, the posterior is equal to the prior multiplied by a correction factor     

Blind and total identification of ARMA mode in higher ordercumulants domain

A novel recursive algorithm for identifying orders and parameters of ARMA models driven by a sequence of nonGaussian random signals is investigated. The input sequence is assumed to be unobservable and the conditions are based on properties of the model output cumulants of the third order. In every cycle of updating the model order, the proposed algorithm minimizes a quadratic cost function to determine the parameters. The novelty of the approach is that the model orders and parameters are all estimated without a priori knowledge; the system is blind. The identification process is said to be total because the model parameters together with the model order are estimated in the same process. Owing to its order-recursive nature, the proposed algorithm requires little computational complexity and exhibits fast convergence behavior. Simulation results verify that Gaussian noises present at the output do not have noticeable effects on the identifiability and the accuracy of estimation     

Variance and Covariance Computations for 2-D ARMA Processes

An algorithm is presented to compute the variance of the output of a two-dimensional (2-D) stable auto-regressive moving-average (ARMA) process driven by a white noise bi-sequence with unity variance. Actually, the algorithm is dedicated to the evaluation of a complex integral of the form , where and G(z₁,z₂) = B(z₁, z₂) / A(z₁, z₂) is stable (z₁,z₂)-transferfunction. Like other existing methods, the proposed algorithmis based on the partial-fraction decomposition G(z₁,z₂)G(z ₁ ^-1 , z ₂ ^-1 ) = X(z₁, z₁) / A(z₁,z₂)+ X(z ₁ ^-1 , z ₂ ^-1 ) / A(z ₁ ^-1 , z ₂ ^-1 ). However,the general and systematic partial-fraction decomposition schemeof Gorecki and Popek [1] is extended to determine X(z₁,z₂).The key to the extension is that of bilinearly transforming thediscrete (z₁, z₂)-transfer function G(z₁,z₂)into a mixed continuous-discrete (s₁, z₂)-transferfunction . As a result, the partial-fraction decomposition involves only efficient DFT computations for the inversion of a matrix polynomial, and the value of I is finally determined by the residue method with finding the roots of a 1-D polynomial. The algorithm is very easy to implement and it can be extended to the covariance computation for two 2-D ARMA processes.