Order-recursive blind identification of linear models using mixedcumulants

The problem of determining the AR order and parameters of a nonminimum phase ARMA model from observations of the system output is considered. The model is driven by a sequence of random variables which is assumed unobservable. A novel identification algorithm based on the second- and third-order cumulants of the output sequences is introduced. It performs order-recursively by minimising a well defined cost function. Strong convergence and consistency of the algorithm are proved and the weight of the cost function is balanced between the second-order and the third-order cumulants of output sequences. The influence of the weight on the estimation accuracy is also evaluated. Theoretical analyses and numerical simulations show that the proposed algorithm is satisfactory for both order and parameter identification of an AR model which is subordinate to a nonminimum phase ARMA model     

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.     

基于非线性时间序列的预测模型检验与优化的研究

 模型的适用性检验和参数优化是系统建模的最关键环节,对于预测模型的适用性检验,常采用残差方差图、最小信息准则和AIC准则等方法,存在计算量大、准确性低、模型不唯一等缺点.本文给出采用自相关系数和偏自相关系数的拖尾先对ARIMA模型检验,再对其进行F适用性检验,克服了由于观测样本的长度是有限的,偏相关的估计存在误差,拖尾时不能为ARMA定阶的缺陷,并采用具有超线性收敛性等诸多优点的变尺度法对模型参数进行了优化,得到了较为精确的、单一AIRMA 模型,该方法可应用于网络流量模型的适用性检验和模型优化,为网络流量的预测、异常检测和服务器负载预测的应用奠定了坚实的基础.     

High-order ar estimation method of ARMA power spectrum

In this paper, the high-order AR estimation method of ARMA power spectrum and the whitened-noise decision order criterion of AR order are presented. It is indicated that the quality of high-order AR estimation is related to the ill-condition problem and the algorithmic stability of numerical calculation in the paper. The latter can be solved well by using the recurrence algorithm of Householder transform in the solution of high-order AR parameter estimation.     

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

For pt.I see ibid., vol.40, no.11, p.2766-74 (Nov. 1992). A recursive algorithm for ARMA (autoregressive moving average) filtering has been developed in a companion paper. These recursions are seen to have a lattice-like filter structure. The ARMA parameters, however, are not directly available from the coefficients of this filter. The problem of identification of the ARMA model from the coefficients of this filter is addressed here. Two new update relations for certain pseudoinverses are derived and used to obtain a recursive least squares algorithm for AR parameter estimation. Two methods for the estimation of the MA parameters are also presented. Numerical results demonstrate the usefulness of the proposed algorithms     

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.     

调幅信号的参数循环累量估计

本文利用循环累量讨论讽调幅混合相位信号的参数估计方法。首先给出了调幅信号的基于任意阶循环累量的参数方程。对于调幅混合相位ＡＲ，ＭＡ和ＡＲＭＡ模型，提出了相应的参数估计方法。模拟实验表明了本文方法的有效性。     

A NEW METHOD OF BISPECTRAL ESTIMATION FOR TRANSIENT SIGNAL

Estimation of model parameter for transient signal is very important in many aspects. This paper presents a new Markov ARMA model Q-slice estimation algorithm for transient signal based on bispectrum. Simulation results show that this new method has some special features, such as higher estimation precision, lower amount of calculation, higher fitting effect even in lower signal-to-noise ratio (SNR) situation.     

Adaptive Processing of Digital Broadband Seismic Data

The main purpose of this paper is to develop a step-wise approach to recursive parameter estimation for time-invariant autoregressive moving average (ARMA) models used to track slowly time variant-seismic noise. In these steps computational complexity is balanced against estimation accuracy. By updating with every new data sample, the recursions are well adapted to on-line implementation. They are designed to be insensitive to spurious additive glitches in the data. Assuming that the ARMA parameters vary slowly with time, the estimated parameters contain information about the long time behavior of the modeled process compared with the time duration of additive transient signals. In seismological applications these transients are thought to be earthquake signals. The estimated ARMA parameters are used a) for the design of robust prediction error filters with arbitrary prediction distance to reduce the microseismic noise while passing the earthquake signal widely undisturbed, and b) for automatic detection of earthquake signals. A three-step scheme for the detection of weak earthquake signals is developed: The first step is to clean the data from glitches (for example data transmission errors) by replacing these with predicted values. The second step involves conventional recursive bandpass filtering to focus upon relevant frequency bands. In the third step a detection variable is computed from the difference of time consecutive ARMA parameter vectors for the bandpass filtered traces.     

瞬态信号双谱估计的一种新方法

瞬态信号的模型参数估计在许多领域占据相当重要的地位。本文利用高阶矩的性质,提出一种Q-slice马尔可夫ARMA模型双谱估计算法。仿真结果表明,该方法估计精度高,计算量小,即使在低信噪比的情况下,对瞬态信号也有较好的拟合效果.     

基于输出累积量的 ARMA(AR)系统的一致性阶次递推辩识(英文)

本文提出了一种根据系统输出的观测数据对ARMA（AR）系统进行盲识别的新算法。该模型由独立同分布非高斯随机序列驱动，其输出序列中含方差未知的加性高斯噪声。通过求解基于三阶累积量谱的代价函数，该算法以模型阶次递推形式同时辩识ARMA的系统阶次和估计出系统参数。文章给出了该算法一致收敛性的证明，并对两类不同阶次的最小及非最小相位ARMA系统的AR参数及阶次辩识进行了数字仿真，结果令人满意。     

Characterization of video codecs as autoregressive moving averageprocesses and related queueing system performance

A method of characterizing video codec sources in asynchronous transfer mode (ATM) networks as an autoregressive moving average (ARMA) process is described. Measurements of long-term mean and the autocorrelation function of cell interarrival times allow the parameter estimation of the ARMA model. The video source is then described by ARMA model. Furthermore, it is shown that the multiplexed stream of video cells is also an ARMA process. Such a cell stream is then applied to a model of a queuing system to obtain performance measures of the system. Perturbation analysis is then performed on the functional behavior of the queuing system by appropriate perturbation of the model parameters to determine cell waiting time sensitivity due to slight variations of the input process     

Multichannel ARMA processes

Parametric modeling of multichannel time series is accomplished by using higher (than second) order statistics (HOS) of the observed nonGaussian data. Cumulants of vector processes are defined using a Kronecker product formulation, and consistency of their sample estimators is addressed. Identifiability results in connection with the HOS-based parameter estimation of causal and noncausal multivariate ARMA processes are established. Estimates of the parameters of causal ARMA models are obtained as the solution to a set of linear equations, whereas those of noncausal ARMA models are obtained as the solution to a cumulant matching algorithm. Conventional approaches based on second-order statistics can identify a multichannel system only to within post multiplication by a unimodular matrix. HOS-based methods yield solutions that are unique to within post-multiplication by an (extended) permutation matrix; additionally, the multiminimum phase assumption can be relaxed, and the observations may be contaminated with colored Gaussian noise. Frequency-domain methods for nonparametric system identification are discussed briefly. Simulations results validating the multichannel parameter estimation algorithms are provided     

The effect of identifier structure on parameter convergence

The effects of a chosen system structure on the identification of its parameters are considered. In particular, convergence rates are compared for the parameters of three state-space structures: direct form II, parallel, and dual generalized Hessenberg representation structures. It is shown that the chosen structure does influence identification algorithms, and that this influence is measured by examining the information contained in the structural parameters. A conjecture about the relative convergence of the parameters is offered, and evidence in its support is provided. An important result is that identification of the usually identified direct from II parameters (the standard ARMA parameters) does not necessarily yield the fastest parameter convergence for the system being identified     

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     

多跳频信号频率跟踪与二维波达方向实时估计算法

为了实时提取跳频(FH)通信参数以及为通信对抗提供所需信息,该文提出一种多跳频信号频率跟踪和2维波达方向实时估计算法。首先建立跳频信号的L型阵列接收数据模型,并推导证明了自回归滑动平均(ARMA)模型对L型阵列数据的适用性,然后采用粒子滤波思想对阵列流型矩阵和频率进行实时估计。再基于频率估计值建立ARMA模型实时检测跳时刻,并结合流型矩阵估计值实现无需参数配对的2维波达方向(2D-DOA)准确估计。新方法通过设计合理的粒子生成以及权值更新方式,使流型矩阵与频率估计值能够迅速收敛至稳定状态。最后蒙特卡罗仿真结果验证了该算法的有效性。     

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.     

LD2-ARMA identification algorithm

The authors present the LD²-ARMA identifier, a novel algorithm that solves the essentially nonlinear autoregressive moving-averaged (ARMA) identification problem with a linear procedure, in two steps: an order selection algorithm followed by an ARMA parameter estimator. The determination of the AR and MA coefficients involves the solution of two dual systems of linear equations. These systems decouple the estimation of the autoregressive component from the estimation of the moving average component. The selection of the number of poles and of the number of zeros is accomplished by a scheme that minimizes the mismatch of the data to each proposed model. Simulated experiments on the proposed order selection procedure are presented     

Optimal reconstruction of ARMA signals with decimated samples under corrupting noise by use of multirate Kalman filter

A multirate modeling theory of the ARMA stochastic signals is derived from a state-space viewpoint in this work. Its application to the signal reconstruction problem for the recovery of the complete ARMA signal from its noise-corrupted, missing-sample sequence is then developed in detail. The proposed estimation-interpolation problem can be resolved by using the multirate optimal state estimation scheme of this work. Theoretically, the multirate Kalman reconstruction filters derived in this paper produce the minimum variance estimation and interpolation of the original complete, clean ARMA signal. Practically, the numerical examples show that the multirate Kalman reconstruction filters illustrate good estimation/interpolation performances, not only for synthetic ARMA sequences but also for human speech signals.     

噪声背景下正弦信号频率估计:基于约束广义逆的总体最小二乘方法

分析了噪声背景下实谐波过程ARMA模型系数之间的对称性,并以此为约束条件加入到ARMA谱估计方法的求解过程中,从而提出了一种改进的正弦信号频率估计方法。理论分析与计算机仿真表明,对于低信噪比条件下的正弦信号参量估计,这一算法的分辨率与精度都优于MUSIC方法和仅使用总体最小二乘法(SVD-TLS)的ARMA谱估计方法。