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。     

Higher order cumulants-based least squares for nonminimum-phasesystems identification

A third-order cumulants based adaptive recursive least-squares (CRLS) algorithm for the identification of time-invariant nonminimum phase systems, as well as time-variant nonminimum phase systems, has been successfully developed. As higher order cumulants preserve both the magnitude and the phase information of received signals, they have been considered as powerful signal processing tools for nonminimum phase systems. In this paper, the development of the CRLS algorithm is described and examined. A cost function based on the third-order cumulant and the third-order cross cumulant is defined for the development of the CRLS system identification algorithm. The CRLS algorithm is then applied to different moving average (MA) and autoregressive moving average (ARMA) models. In the case of identifying the parameters of an MA model, a direct application of the CRLS algorithm is adequate. When dealing with an ARMA model, the poles and the zeros are estimated separately. In estimating the zeros of the ARMA model, the construction of a residual time-series sequence for the MA part is required. Simulation results indicate that the CRLS algorithm is capable of identifying nonminimum phase and time-varying systems. In addition, because of the third-order cumulant properties, the CRLS algorithm can suppress Gaussian noise and is capable of providing an unbiased estimate in a noisy environment     

Adaptive identification of nonminimum phase ARMA models usinghigher order cumulants alone

An adaptive identification algorithm for causal nonminimum phase ARMA models in additive colored Gaussian noise is proposed. The algorithm utilizes higher order cumulants of the observed signal alone. It estimates the AR and MA parameters successively in each iteration without computing the residual time series. The steepest descent method is used for parameter updating     

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.     

Semiblind identification of nonminimum-phase ARMA models via orderrecursion with higher order cumulants

This paper develops a novel identification methodology for nonminimum-phase autoregressive moving average (ARMA) models of which the models' orders are not given. It is based on the third-order statistics of the given noisy output observations and assumed input random sequences. The semiblind identification approach is thereby named. By the order-recursive technique, the model orders and parameters can be determined simultaneously by minimizing well-defined cost functions. At each updated order, the AR and MA parameters are estimated without computing the residual time series (RTS), with the result of decreasing the computational complexity and memory consumption. Effects of the AR estimation error on the MA parameters estimation are also reduced. Theoretical statements and simulations results, together with practical application to the train vibration signals' modeling, illustrate that the method provides accurate estimates of unknown linear models, despite the output measurements being corrupted by arbitrary Gaussian noises of unknown pdf     

A cumulant matrix subspace algorithm for blind single FIR channelidentification

Blind identification of discrete-time single-user FIR channels with nonminimum phase is studied here. Exploiting higher order cumulants of output signals of unknown channels, a new closed-form solution to the FIR channel impulse response is derived. The algorithm is simple and fast. It relies only on nullspace decomposition of some cumulant matrices. This method neither involves the difficult task of iterative global minimization of nonunimodal cost functions, nor does it require overparametrization, which poses consistency difficulties. It can be used either as the final channel estimate or as a good initial point in nonlinear cumulant matching techniques. The application of this identification method is broad and not limited to the use of any fixed-order cumulants. Its application in identifying data communication systems shows great potential and promise     

非最小相位ARMA模型的一种自适应辨识算法

本文提出了一种加性有色高斯噪声中因果非最小相位ARMA模型的自适应辨识算法。模型输入假定为非高斯独立同分布随机过程。算法只利用了观测信号的高阶统计量。在每次迭代中,先估计AR参数,再估计MA参数,但不用计算残差序列。在参数递推中采用了随机梯度法。仿真实验证实了本文算法的有效性。     

Linear bispectrum of signals and identification of nonminimum phaseFIR systems driven by colored input

The identification of non-minimum-phase finite-impulse-response (FIR) systems driven by third-order stationary colored signals that are not linear processes is addressed. Modeling the linear part of the bispectrum of a signal is discussed. The bispectrum of a signal is decomposed into two multiplicative factors. The linear bispectrum is defined as the factor of the bispectrum that can exactly be modeled using a third-order white-noise-driven linear shift-invariant (LSI) system. The linear bispectrum of the output of the unknown LSI system is represented using an ARMA (autoregressive moving average) model, where the MA parameters correspond to the unknown FIR system impulse response coefficients, and the AR parameters model the linear bispectrum of the input signal. An algorithm for identifying the MA and AR parameters is given. How the proposed method is different from fitting an ARMA model directly to the bicumulants or the bispectrum of the system output is discussed. The method is applied to blur identification     

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     

Noncausal nonminimum phase ARMA modeling of non-Gaussian processes

A method is presented for the estimation of the parameters of a noncausal nonminimum phase ARMA model for non-Gaussian random processes. Using certain higher order cepstra slices, the Fourier phases of two intermediate sequences (h_min(n) and h_max(n)) can be computed, where h_min(n) is composed of the minimum phase parts of the AR and MA models, and h_max(n) of the corresponding maximum phase parts. Under the condition that there are no zero-pole cancellations in the ARMA model, these two sequences can be estimated from their phases only, and lead to the reconstruction of the AR and MA parameters, within a scalar and a time shift. The AR and MA orders do not have to be estimated separately, but they are by product of the parameter estimation procedure. Through simulations it is shown that, unlike existing methods, the estimation procedure is fairly robust if a small order mismatch occurs. Since the robustness of the method in the presence of additive noise depends on the accuracy of the estimated phases of h_min(n) and h_max(n), the phase errors due to finite length data are studied and their statistics are derived     

A Least-Squares-Based Algorithm for Identification of Non-Gaussian ARMA Models

A new recursive method for estimating the parameters of autoregressive moving average (ARMA) models is presented in this paper. The recursive linear identification method is developed using higher-order statistics of the observed output data and is based on a least-squares solution. Namely, a matrix consisting of third-order statistics (or cumulants) of the observed output data is constructed so that it almost possesses a full rank structure. The signal is embedded in a Gaussian noise that may be colored. The system is driven by a zero-mean independent and identically distributed non-Gaussian process. The excitation signal is unobserved. Simulation results are given to illustrate the performance of the proposed algorithm with respect to existing well-known methods.     

FIR system identification based on subspaces of a higher ordercumulant matrix

A new linear algebraic approach for identification of a nonminimum phase FIR system of known order using only higher order (>2) cumulants of the output process is proposed. It is first shown that a matrix formed from a set of cumulants of arbitrary order can be expressed as a product of structured matrices. The subspaces of this matrix are then used to obtain the parameters of the FIR system using a set of linear equations. Theoretical analysis and numerical simulation studies are presented to characterize the performance of the proposed methods     

非高斯有色噪声中的正弦信号频率估计

本文研究非高斯ＡＲＭＡ有色噪声中的正弦信号频率估计问题。利用自相关函数和三阶累积量相结合，提出了一种先估计噪声模型ＡＲ参数，然后对观测值进行预滤波，最后估计信号模型参数的新方法，模拟实验结果表明，新方法具有良好的频率估计性能。     

基于倒谱的非最小相位FIR系统自适应辨识

本文介绍了一种在高阶谱一维切片的基础上利用倒谱进行非最小相位FIR系统自适应辨识的算法。这一算法具有计算量小，不需要预先假定系统阶次的特点，而且能够自适应地分别辨识出非最小相位FIR系统的最小相位部分和最大相位部分的冲激响应，同时，系统阶次可以在自适应过程中确定。另外由于本算法利用观测信号的高阶级计量进行系统辨识，所以很好地抑制了高斯有色噪声对辨识结果的影响。数值仿真结果证明了本算法的有效性。     

基于累计量辨识非最小相位FIR系统的新方法

该文考虑用带有噪声输出数据的累计量实现对非最小相位PIR系统的参数辨识问题。提出一个新的基于高阶累计量的方法。其特点如下,(1)灵活性:采用了两个任意阶次相邻的输出累计量;(2)线性:方法的表达式相对于未知量为线性。这不同于其它一些已存在的算法。因而,避免了额外的滞后处理,可提高参数估计的准确性。本文在ARMA高斯噪声及三种实际噪声情况下,做了大量的实验。结果表明,本文提出的算法不仅能有效地完成参数估计,而且,在低信噪比下,其估计结果比其它已有的算法更准确。     

New approaches without postprocessing to FIR system identificationusing selected order cumulants

In this paper, we address the problem of identifying the parameters of the nonminimum-phase FIR system from the cumulants of noisy output samples. The system is driven by an unobservable, zero-mean, independent and identically distributed (i.i.d) non-Gaussian signal. The measurement noise may be white Gaussian, colored MA, ARMA Gaussian processes, or even real. For this problem, two novel methods are proposed. The methods are designed by using higher order cumulants with the following advantages. (i) Flexibility: method 1 employs two arbitrary adjacent order cumulants of output, whereas method 2 uses three cumulants of output: two cumulants with arbitrary orders and the other one with an order equal to the summation of the two orders minus one. Because of this flexibility, we can select cumulants with appropriate orders to accommodate different applications. (ii) Linearity: both the formulations in method 1 and method 2 are linear with respect to the unknowns, unlike the existing cumulant-based algorithms. The post-processing is thus avoided. Extensive experiments with ARMA Gaussian and three real noises show that the new algorithms, especially algorithm 1, perform the FIR system identification with higher efficiency and better accuracy as compared with the related algorithms in the literature     

A parametric modeling of ionic channel current fluctuations usingthird-order statistics and its application to estimation of the kineticparameters of single ionic channels

The case where third-order cumulants of stationary ionic-channel current fluctuations (SICFs) are nonzero, and where SICFs are corrupted by an unobservable additive colored Gaussian noise that is independent of SICFs is considered. First, a virtual synthesizer that yields an output whose third-order cumulants are equivalent to those of SICFs on a specific slice is constructed. The synthesizer output is expressed by the sum of N_s-1 first-order differential equation systems, where N_s denotes the number of states of single ionic channels. Next, discretizing the synthesizer output, a discrete autoregressive [AR(N_s-1)] process driven by the sum of N_s-1 moving average (MA(N_s -2)) processes is derived. Then the AR coefficients are explicitly related to the kinetic parameters of single ionic channels, implying that the kinetic parameters can be estimated by identifying the autoregressive moving-average coefficients using the third-order cumulants. In order to assess the validity of the proposed modeling and the accuracy of parameter estimates, Monte Carlo simulation is carried out in which the closed-open and closed-open-blocked schemes are treated as specific examples     

Bispectrum Reconstruction Method of UWB Echoes

Estimation of transient signal in additive noise is very important in radar object detection and recognition. This paper presents a new method for transient signal reconstruction based on bispectrum estimation techniques. The third-order cumulants of the received noisy ultra-wide band echoes are acquired first and an ARMA model is then fitted. The bispectrum of the output signal of the ARMA model will be used to reconstruct the transient signal. Simulation results show that the effect is very good even in lower signal-to-noise (SNR) situation.     

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     

Tutorial on higher-order statistics (spectra) in signal processingand system theory: theoretical results and some applications

A compendium of recent theoretical results associated with using higher-order statistics in signal processing and system theory is provided, and the utility of applying higher-order statistics to practical problems is demonstrated. Most of the results are given for one-dimensional processes, but some extensions to vector processes and multichannel systems are discussed. The topics covered include cumulant-polyspectra formulas; impulse response formulas; autoregressive (AR) coefficients; relationships between second-order and higher-order statistics for linear systems; double C(q,k) formulas for extracting autoregressive moving average (ARMA) coefficients; bicepstral formulas; multichannel formulas; harmonic processes; estimates of cumulants; and applications to identification of various systems, including the identification of systems from just output measurements, identification of AR systems, identification of moving-average systems, and identification of ARMA systems