A Novel Technique for the Identification of ARMA Systems Under Very Low Levels of SNR

In this paper, a novel technique for the identification of minimum-phase autoregressive moving average (ARMA) systems from the output observations in the presence of heavy noise is presented. First, starting from the conventional correlation estimator, a simple and accurate ARMA correlation (ARMAC) model in terms of the poles of the ARMA system is presented in a unified manner for white noise and impulse-train excitations. The AR parameters of the ARMA system are then obtained from the noisy observations by developing and using a residue-based least-squares correlation-fitting optimization technique that employs the proposed ARMAC model. As for the estimation of the MA parameters, it is preceded by the application of a new technique intended to reduce the noise present in the residual signal that is obtained by filtering the noisy ARMA signal via the estimated AR parameters. A scheme is then devised whereby the task of MA parameter estimation is transformed into a problem of correlation-fitting of the inverse autocorrelation function corresponding to the noise-compensated residual signal. In order to demonstrate the effectiveness of the proposed method, extensive simulations are performed by considering synthetic ARMA systems of different orders in the presence of additive white noise and the results are compared with those of some of the existing methods. It is shown that the proposed method is capable of estimating the ARMA parameters accurately and consistently with guaranteed stability for signal-to-noise ratio (SNR) levels as low as $-{5}~{hbox {dB}}$ . Simulation results are also provided for the identification of a human vocal-tract system using natural speech signals showing a superior performance of the proposed technique in terms of the power spectral density of the synthesized speech signal.      

Autocorrelation model-based identification method for ARMA systems in noise

A novel method for parameter estimation of minimum-phase autoregressive moving average (ARMA) systems in noise is presented. The ARMA parameters are estimated using a damped sinusoidal model representation of the autocorrelation function of the noise-free ARMA signal. The AR parameters are obtained directly from the estimates of the damped sinusoidal model parameters with guaranteed stability. The MA parameters are estimated using a correlation matching technique. Simulation results show that the proposed method can estimate the ARMA parameters with better accuracy as compared to other reported methods, in particular for low SNRs.     

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     

An efficient approach to ARMA modeling of biological systems withmultiple inputs and delays

Presents a new approach to AutoRegressive Moving Average (ARMA or ARX) modeling which automatically seeks the best model order to represent investigated linear, time invariant systems using their input/output data. The algorithm seeks the ARMA parameterization,which accounts for variability in the output of the system due to input activity and contains the fewest number of parameters required to do so. The unique characteristics of the proposed system identification algorithm are its simplicity and efficiency in handling systems with delays and multiple inputs. The authors present results of applying the algorithm to simulated data and experimental biological data. In addition, a technique for assessing the error associated with the impulse responses calculated from estimated ARMA parameterizations is presented. The mapping from ARMA coefficients to impulse response estimates is nonlinear, which complicates any effort to construct confidence bounds for the obtained impulse responses. Here a method for obtaining a linearization of this mapping is derived, which leads to a simple procedure to approximate the confidence bounds     

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。     

基于ARMA模型的无线传感器网络可信数据采集方法

在传感器节点受到能量和带宽严重制约的情况下,如何合理、有效地利用有限的资源来采集有效、可信的数据,成为当前无线传感器网络（Wireless Sensor Network,WSN）研究的热点问题之一。在分析了大量WSN感知数据的基础上,利用时间序列对数据进行建模处理,得出了适合WSN的数据处理模型ARMA（1,1）,同时利用基于移动Agent的中间件技术,提出了基于ARMA的无线传感器网络可信数据采集方法。理论和实验结果表明,该方法可保证采集数据的高度可信,同时显著提高了网络的整体性能,有效的减少网络的能耗,延长了网络的生命周期。     

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.     

A recursive maximum likelihood algorithm for ARMA spectral estimation

A spectral estimation technique is presented for autoregressive moving-average (ARMA) processes. The technique is based on a parameter estimation technique known as the rec ursive maximum likelihood (RML) method. The recursive spectral estimation algorithm is presented and its asymptotic properties are discussed. Simulation results are presented to illustrate the performance of the estimator for various types of data.     

Maximum likelihood estimation of the parameters of nonminimum phaseand noncausal ARMA models

The well-known prediction-error-based maximum likelihood (PEML) method can only handle minimum phase ARMA models. This paper presents a new method known as the back-filtering-based maximum likelihood (BFML) method, which can handle nonminimum phase and noncausal ARMA models. The BFML method is identical to the PEML method in the case of a minimum phase ARMA model, and it turns out that the BFML method incorporates a noncausal ARMA filter with poles outside the unit circle for estimation of the parameters of a causal, nonminimum phase ARMA model     

Comments, with reply, on 'ARMA spectral estimation of time series with missing observations' by B. Porat and B. Friedlander

A variant to a recently proposed autoregressive moving average (ARMA) spectrum estimation technique for time series with gapped data is suggested. It is based on the partial fraction expansion of the power spectrum and exhibits some computational and operational advantages.     

ARMA system identification based on second-order cyclostationarity

Previous work has presented novel techniques that exploit cyclostationarity for channel identification in data communication systems. The present authors investigate the identifiability of linear time-invariant (LTI) ARMA systems based on second-order cyclic statistics. They present a parametric and a nonparametric method. The parametric method directly identifies the zeros and poles of ARMA channels with a mixed phase. The nonparametric method estimates the channel phase based on the cyclic spectra alone. They analyze the phase estimation error of the nonparametric method for finite dimensional ARMA channels. For specific, finite dimensional ARMA channels, an improved method is given, which combines the parametric method with the nonparametric method. Computer simulation illustrates the effectiveness of the methods in identifying ARMA system impulse responses     

Adaptive prediction of an arma lattice

In the letter, based on a modification of a well-known approximate likelihood estimation technique, a one-step-ahead prediction method using an ARMA lattice structure is obtained.     

Computation of the exact cramer-rao lower bound for 2-D ARMA parameter Estimation-I: the quarter-plane case

A closed-form expression for computing the exact Cramer-Rao lower bound (CRLB) on unbiased estimates of the parameters of a two-dimensional (2-D) autoregressive moving average (ARMA) model is developed. The formulation is based on a matrix representation of 2-D homogeneous Gaussian random process that is generated uniformly from the related 2-D ARMA model. The formulas derived for the exact Fisher information matrix (FIM) are an explicit function of the 2-D ARMA parameters and are valid for real-valued homogeneous quarter-plane (QP) 2-D ARMA random fields, where data are propagated using only the past values. It is noteworthy that our approach is practical especially for quantifying the accuracy of 2-D ARMA parameter estimates realized with short data records. Computer simulations display the behavior of the derived CRLB expression for some QP causal 2-D ARMA processes, as a function of the number of data points. The extension of this algorithm for the nonsymmetric half-plane (NSHP) case will be presented in a subsequent paper.     

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     

Two-dimensional harmonic retrieval and its time-domain analysistechnique

The two-dimensional harmonic retrieval is examined in theory by confirming that the 2-D sinusoids in white noise are modeled as a special 2-D autoregressive moving average (ARMA) process whose AR parameters are identical to the MA ones. A new analysis technique for resolving 2-D sinusoids in white noise is proposed     

基于零极点预测模型的码激励线性预测语音编码算法

针对传统码激励线性预测（Code Excited Linear Predictive，CELP）语音编码器在预测模型和参数估计方面的不足，提出了一种基于零极点预测模型的CELP语音编码新算法。该算法采用零极点预测模型来更准确地描述语音信号的短时相关性，并采用梯度法来同时对零极点模型的参数和激励码本增益进行联合优化求解。实验结果表明所提语音编码算法可显著降低CELP编码器合成语音的归一化均方误差，有效提高合成语音的质量。     

A new recursive pseudo least squares algorithm for ARMA filteringand modeling. I

This study is based on the observation that if the bootstrapping is combined with different parameterizations of the ARMA (autoregressive moving average) process, then different linearized problems are obtained for the underlying nonlinear ARMA modeling problem. In this part, a specific parameterization termed the predictor space representation for an ARMA process, which decouples the estimation for the AR and the MA parameters, is used. A vector space formalism for the given data case is then defined, and the least-squares ARMA filtering problem is interpreted in terms of projection operations on some linear spaces. A new projection operator update formula, which is particularly suited for the underlying problem, is then used in conjunction with the vector space formalism to develop a computationally efficient pseudo-least-squares algorithm for ARMA filtering. It is noted that these recursions can be put in the form of a filter structure     

基于ARMA模型的电力系统负荷预测方法研究

采用加权最小二乘法参数估计方法，得到应用于电力系统日负荷预测和月负荷预测的ARMA模型，实验预测结果表明，用ARMA模型进行电力负荷预测是非常有铲的。尤其是采用加权最小二乘估计的ARMA模型，预测精度更高。     

A new algorithm for linear and nonlinear ARMA model parameter estimation using affine geometry

A linear and nonlinear autoregressive (AR) moving average (MA) (ARMA) identification algorithm is developed for modeling time series data. The new algorithm is based on the concepts of affine geometry in which the salient feature of the algorithm is to remove the linearly dependent ARMA vectors from the pool of candidate ARMA vectors. For noiseless time series data with a priori incorrect model-order selection, computer simulations show that accurate linear and nonlinear ARMA model parameters can be obtained with the new algorithm. Many algorithms, including the fast orthogonal search (FOS) algorithm, are not able to obtain correct parameter estimates in every case, even with noiseless time series data, because their model-order search criteria are suboptimal. For data contaminated with noise, computer simulations show that the new algorithm performs better than the FOS algorithm for MA processes, and similarly to the FOS algorithm for ARMA processes. However, the computational time to obtain the parameter estimates with the new algorithm is faster than with FOS. Application of the new algorithm to experimentally obtained renal blood flow and pressure data show that the new algorithm is reliable in obtaining physiologically understandable transfer function relations between blood pressure and flow signals.     

An analog architecture on parameter estimation of ARMA models

An analog architecture that is suitable for parameter estimation of autoregressive moving average (ARMA) models is proposed. The convergence theorem that connects this architecture with ARMA parameter estimation is presented. Simulation results indicate that its convergence takes only a few microseconds. Hence, this architecture can lead to online implementations