Data filtering based least squares iterative algorithm for parameter identification of output error autoregressive systems

This letter derives a data filtering based least squares iterative identification algorithm for output error autoregressive systems. The basic idea is to use the data filtering technique to transform the original identification model to an equation error model and to estimate the parameters of this model. The proposed algorithm is more efficient and can produce more accurate parameter estimation than the existing least squares iterative algorithm.     

A new noise-compensated estimation scheme for multichannel autoregressive signals from noisy observations

In many engineering applications concerning the recovery of signals from noisy observations, a common approach consists in adopting autoregressive (AR) models. This paper is concerned with not only the estimation of multichannel autoregressive (MAR) model parameters but also the recovery of signals. A new noise compensated parameter estimation scheme is introduced in this paper. It contains an advanced least square vector (ALSV) algorithm which not only keeps the advantage of blindly estimating the MAR parameters and the variance-covariance matrix of observation noises, but also aims at ensuring the variance-covariance matrix to be symmetric in each iterative procedure. Moreover, the estimation of variance-covariance matrix of input noise is proposed, and then we form an optimal filtering to recover the signals. In the numerical simulations, the estimation performance of the ALSV estimation algorithm significantly outperforms that of other existed methods. Moreover, the optimal filtering based on the ALSV algorithm leads to more accurate recovery of the true signals.     

Autoregressive spectral analysis when observations are missing

A new missing data algorithm ARFIL gives good results in spectral estimation. The log likelihood of a multivariate Gaussian random variable can always be written as a sum of conditional log likelihoods. For a complete set of autoregressive AR(p) data the best predictor in the likelihood requires only p previous observations. If observations are missing, the best AR predictor in the likelihood will in general include all previous observations. Using only those observations that fall within a finite time interval will approximate this likelihood. The resulting non-linear estimation algorithm requires no user provided starting values. In various simulations, the spectral accuracy of robust maximum likelihood methods was much better than the accuracy of other spectral estimates for randomly missing data.     

自回归滤波器的研究

该文主要介绍了现代谱估计中常用到的自回归（AR）谱估计.利用Levinson-Durbin算法可以推导出在已知输出自相关序列的情况下确定预测误差滤波器系数,即AR模型的系数.AR模型的阶次选择是个关键问题,阶次太低会导致平滑的谱估计值,而阶次太高又会引起伪峰并且会产生一般的统计不稳定性.文章中采用了应用比较广泛的最终预测误差（FPE）准则和阿凯克信息论准则（AIC）,最终确定AR模型的阶数.并通过激励高斯白噪声仿真得到海洋混响的输出波形图.     

Adaptive sequential segmentation of piecewise stationary time series

The problem of adaptive segmentation of time series with abrupt changes in the spectral characteristics is addressed. Such time series have been encountered in various fields of time series analysis such as speech processing, biomedical signal processing, image analysis and failure detection. Mathematically, these time series often can be modeled by zero mean gaussian distributed autoregressive (AR) processes, where the parameters of the process, including the gain factor, remain constant for certain time intervals and then jump abruptly to new values. Identification of such processes requires adaptive segmentation: the times of parameter jumps have to be estimated thoroughly to constitute boundaries of “homogeneous” segments which can be described by stationary AR processes. In this paper, a new effective method for sequential adaptive segmentation is proposed, which is based on parallel application of two sequential parameter estimation procedures. The detection of a parameter change as well as the estimation of the accurate position of a segment boundary is effectively performed by a sequence of suitable generalized likelihood ratio (GLR) tests. Flow charts as well as a block diagram of the algorithm are presented. The adjustment of the three control parameters of the procedure (the AR model order, a threshold for the GLR test and the length of a “test window”) is discussed with respect to various performance features. The results of simulation experiments are presented which demonstrate the good detection properties of the algorithm and in particular an excellent ability to allocate the segment boundaries even within a sequence of short segments. As an application to biomedical signals, the analysis of human electroencephalograms (EEG) is considered and an example is shown.     

应用阶数自学习自回归隐马尔可夫模型对控制过程异常数据的在线检测

针对过程工业中强噪声环境下实时采集的控制过程海量数据难以在线精确检测的问题,提出了基于阶数自学习自回归隐马尔可夫模型(ARHMM)的工业控制过程异常数据在线检测方法.该算法采用自同归(AR)模型对时间序列进行拟合,利用隐马尔科夫模型(HMM)作为数据检测的工具,避免了传统检测方法中需要预先设定检测阈值的问题,并将传统的...     

A smoothness priors long AR model method for spectral estimation

A new smoothness priors long AR model method approach is taken to the short data span spectral estimation problem. An autoregressive (AR) model that is relatively long compared to the data length is considered. The smoothness priors are in the form of the integrated squared derivatives of the AR model whitening filter. A smoothness tradeoff parameter or Bayesian hyperparameter balances the tradeoff between the infidelity of the AR model to the data and the infidelity of the model to the smoothness constraint. The critical computation of the likelihood of the hyperparameters of the Bayesian model is realized by a constrained least squares computation. Numerical examples are shown. The results of simulation studies using entropy comparison evaluations of the Bayesian and minimum AIC-AR methods of spectral estimation are also shown.     

多维滑动和（MA）模型参数的自适应估计

本文利用AR模型LS梯格滤波的有关公式给出了实时辨识多维MA模型参数的递推算法,该算法建立在对模型噪声和观测的自协方差阵和互协方差阵的矩估计基础上,由一个N阶反馈形式的梯格滤波器构成,可关于时间和阶次双重递推,该算法计算量为O(N)的量级,并具备梯格滤波固有的良好数值及结构特性。     

Dynamic models for nonstationary signal segmentation.

This paper investigates Hidden Markov Models (HMMs) in which the observations are generated from an autoregressive (AR) model. The overall model performs nonstationary spectral analysis and automatically segments a time series into discrete dynamic regimes. Because learning in HMMs is sensitive to initial conditions, we initialize the HMM model with parameters derived from a cluster analysis of Kalman filter coefficients. An important aspect of the Kalman filter implementation is that the state noise is estimated on-line. This allows for an initial estimation of AR parameters for each of the different dynamic regimes. These estimates are then fine-tuned with the HMM model. The method is demonstrated on a number of synthetic problems and on electroencephalogram data.     

Autoregressive and adaptive estimation with an application to hurricane track prediction

The key result of this paper is that following a change in a parameter of AR (p), an autoregressive process of order p, the innovations sequence of the Kalman filter parameters will follow an autoregressive moving-average model in addition to a transient function. Furthermore, it is also shown that the first p values of the innovations' sample autocorrelation can be used to form a sufficient statistic to detect if at least one of the parameters in the AR (p) model did change at an unknown point in time. Following a parameter change detection process, improved estimates and noise statistics can be determined and implemented to modify the Kalman filter. The revised model will thus be more consistent with the most recent process behaviour. To motivate the reader, a simulation exercise was conducted to validate the on-line change detector and adaptive estimation algorithm. The proposed algorithm was used to predict hurricane movements with real data provided by the National Hurricane Center.     

AR模型压力变送器响应时间测量方法

压力变送器响应时间传统检测方法是将待测变送器送入试验室进行离线检测。电厂压力变送器无法进行实时性检测。压力变送器在役期响应时间原位测量对保证电厂系统的可靠性与安全性非常重要。基于电厂正常工作期的压力变送器噪声信号,研究一种压力变送器噪声时域信号自回归(AR)模型分析的响应时间测量方法。通过最终测量误差(FPE)和阿凯克信息论(AIC)准则判断模型收敛阶数,Yuler-walker算法估计参数。模型参数确定后,计算模型脉冲响应,积分得斜坡响应并求得模型的响应时间。通过仿真验证模型算法,在实验室条件下通过外加气动噪声,对3款压力变送器试验,并与传统斜坡法测试结果进行对比。结果表明,3款压力变送器测试结果与斜坡法误差均小于7%,该研究对国内电厂压力变送器原位测试装置的研发有重要意义。     

High-resolution time–frequency representation of EEG data using multi-scale wavelets

An efficient time-varying autoregressive (TVAR) modelling scheme that expands the time-varying parameters onto the multi-scale wavelet basis functions is presented for modelling nonstationary signals and with applications to time–frequency analysis (TFA) of electroencephalogram (EEG) signals. In the new parametric modelling framework, the time-dependent parameters of the TVAR model are locally represented by using a novel multi-scale wavelet decomposition scheme, which can allow the capability to capture the smooth trends as well as track the abrupt changes of time-varying parameters simultaneously. A forward orthogonal least square (FOLS) algorithm aided by mutual information criteria are then applied for sparse model term selection and parameter estimation. Two simulation examples illustrate that the performance of the proposed multi-scale wavelet basis functions outperforms the only single-scale wavelet basis functions or Kalman filter algorithm for many nonstationary processes. Furthermore, an application of the proposed method to a real EEG signal demonstrates the new approach can provide highly time-dependent spectral resolution capability.     

只估计AR参数的ARMA(p,q)谱估计的新算法

本文提出一种估计自回归AR参数的新算法.新算法采用递推Householder变换算法. 文中给出了ARMA(4,4)仿真计算例子及两个正弦加白噪声的仿真计算结果,并与最小二乘 法的计算结果进行了比较.结果表明新算法在分辨率和估计质量方面均优于最小二乘法和已 有的谱估计方法,也说明用提高算法稳定性的方法可解决负谱问题和提高谱估计质量.     

Combining GA and iterative MVDR for DOA estimation in space-time CDMA systems

This paper deals with direction-of-arrival (DOA) estimation of minimum variance distortionless response (MVDR) approach based on iterative searching technique for space-time code-division multiple access (CDMA) systems. It has been shown that the iterative searching technique is more likely to converge to a local maximum, causing errors in DOA estimation. In conjunction with a genetic algorithm for selecting initial search angle, an efficient approach is presented to achieve the advantages of iterative DOA estimation with fast convergence and less computational load over existing conventional spectral searching MVDR estimator. Simulation results are provided for illustrating the effectiveness of the proposed approach.     

An asymptotically efficient ARMA estimator based on sample covariances

An asymptotically efficient autoregressive moving-average (ARMA) spectral estimator is presented, based on the sample covariances of observed time series. The estimate of the autoregressive (AR) part is shown to be identical to the optimal instrumental variable (IV) estimator in [7] although derived here using a different approach. The moving-average (MA) spectral parameter estimate is new.     

Hierarchical Newton and least squares iterative estimation algorithm for dynamic systems by transfer functions based on the impulse responses

This paper develops a parameter estimation algorithm for linear continuous-time systems based on the hierarchical principle and the parameter decomposition strategy. Although the linear continuous-time system is a linear system, its output response is a highly nonlinear function with respect to the system parameters. In order to propose a direct estimation algorithm, a criterion function is constructed between the response output and the observation output by means of the discrete sampled data. Then a scheme by combining the Newton iteration and the least squares iteration is builded to minimise the criterion function and derive the parameter estimation algorithm. In light of the different features between the system parameters and the output function, two sub-algorithms are derived by using the parameter decomposition. In order to remove the associate terms between the two sub-algorithms, a Newton and least squares iterative algorithm is deduced to identify system parameters. Compared with the Newton iterative estimation algorithm without the parameter decomposition, the complexity of the hierarchical Newton and least squares iterative estimation algorithm is reduced because the dimension of the Hessian matrix is lessened after the parameter decomposition. The experimental results show that the proposed algorithm has good performance.     

强跟踪平方根容积卡尔曼滤波和 自回归模型融合的故障预测

为了解决非线性系统中不可测量参数的预测问题,提出一种带有次优渐消因子的强跟踪平方根容积卡尔曼滤波(STSCKF)和自回归(AR)模型相结合的故障预测方法.利用AR模型时间序列预测法预测未来时刻的测量值,将预测的测量值作为STSCKF的测量变量,从而将预测问题转化为滤波估计问题.STSCKF通过在预测误差方差阵的均方根中引入渐消因子调节滤波过程中的增益矩阵,克服了故障参数变化函数未知情况下普通SCKF跟踪故障参数缓慢甚至失效的局限性,使得STSCKF能较好地预测故障参数的发展趋势.连续搅拌反应釜(CSTR)仿真结果表明,STSCKF的预测精度高于普通SCKF和强跟踪无迹卡尔曼滤波(STUKF),验证了方法的有效性.     

Maximum likelihood parameter estimation algorithm for controlled autoregressive autoregressive models

A maximum likelihood parameter estimation algorithm is derived for controlled autoregressive autoregressive (CARAR) models based on the maximum likelihood principle. In this derivation, we use an estimated noise transfer function to filter the input–output data. The simulation results show that the proposed estimation algorithm can effectively estimate the parameters of such class of CARAR systems and give more accurate parameter estimates than the recursive generalized least-squares algorithm.     

A genetic algorithm approach to the spectral estimation of time series with noise and missed observations

This study considers the problem of estimating the autoregressive moving average (ARMA) power spectral density when measurements are corrupted by noise and by missed observations. The missed observations model is based on a probabilistic structure. Unlike conventional cases of missed observation in parameter estimation problems, the variance of noise is unavailable, that is the time points of missed observations are unknown, and the probability of missing data needs to be estimated. In this situation, spectral estimation is more difficult to solve and becomes a highly nonlinear optimization problem with many local minima. In this paper, we use the genetic algorithm (GA) method to achieve a global optimal solution with a fast convergence rate for this spectral estimation problem. From the simulation results, we have determined that the performance is significantly improved if the probability of data loss is considered in the spectral estimation problem.     

Time-varying parametric system multiresolution identification by wavelets

In this paper, the problem of time-varying parametric system identification by wavelets is discussed. Employing wavelet operator matrix representation, we propose a new multiresolution least squares (MLS) algorithm for time-varying AR (ARX) system identification and a multiresolution least mean squares (MLMS) algorithm for the refinement of parameter estimation. These techniques can achieve the optimal tradeoff between the over-fitted solution and the poorly represented identification. The main features of time-varying model parameters are extracted in a multiresolution way, which can be used to represent the smooth trends as well as track the rapidly changing components of time-varying parameters simultaneously and adaptively. Further, a noisy time-varying AR (ARX) model can also be identified by combining the total least squares algorithm with the MLS algorithm. Based on the proposed AR (ARX) model parameter estimation algorithm, a novel identification scheme for time-varying ARMA (ARMAX) system is presented. A higher-order time-varying AR (ARX) model is used to approximate the time-varying ARMA (ARMAX) system and thus obtain an initial parameter estimation. Then an iterative algorithm is applied to obtain the consistent and efficient estimates of the ARMA (ARMAX) system parameters. This ARMA (ARMAX) identification algorithm requires linear operations only and thus greatly saves the computational load. In order to determine the time-varying model order, some modified AIC and MDL criterions are developed based on the proposed wavelet identification schemes. Simulation results verify that our methods can track the rapidly changing of time-varying system parameters and attain the best balance between parsimonious modelling and accurate identification.