Third-order cumulants based methods for continuous-time errors-in-variables model identification

In this paper, the problem of identifying stochastic linear continuous-time systems from noisy input/output data is addressed. The input of the system is assumed to have a skewed probability density function, whereas the noises contaminating the data are assumed to be symmetrically distributed. The third-order cumulants of the input/output data are then (asymptotically) insensitive to the noises, that can be coloured and/or mutually correlated. Using this noise-cancellation property two computationally simple estimators are proposed. The usefulness of the proposed algorithms is assessed through a numerical simulation.     

Noisy texture classification: A higher-order statistics approach

In this paper, a novel texture classification scheme using higher-order statistics (HOS) functions as discriminating features is proposed. It is well known that such statistical parameters are insensitive to additive Gaussian noise. In particular, third-order statistical parameters, i.e. third-order cumulants and bispectrum, are insensitive to any symmetrically distributed noise, and also exhibit the capability of better characterizing non-Gaussian signals. By exploiting these HOS properties, it is possible to devise a robust method for classifying textures affected by noise with different distributions and even with very low signal-to-noise ratios.     

基于正交分解的递推子空间闭环辨识方法

为实现闭环系统在线辨识,提出递推正交分解闭环子空间辨识方法(RORT)。首先,根据闭环系统状态空间模型和数据间投影关系,构建确定-随机模型,并利用GIVENS变换实现投影向量的递推QR分解;然后,引入带遗忘因子的辨识算法,构建广义能观测矩阵的递推更新形式,以减少子空间辨识算法中QR分解和SVD分解的计算量;最后,针对某型号陀螺仪闭环系统进行实验。实验结果表明, RORT法的辨识拟合度高于91%,能够对陀螺仪闭环系统模型参数进行在线监测。     

递推子空间模型辨识算法的研究与仿真

为了很好的解决在线辨识系统模型问题，在对子空间模型辨识研究的基础上，结合递推最小二乘算法和子空问状态辨识方法。推导了子空间状态辨识的递推算法。该算法不仅解决了在线辨识问题，而且算法简单，计算方便，很好地克服了在线辨识时子空间矩阵维数的变化问题。经仿真研究表明，该递推算法克服了一次完成算法在大批量数据运算时，耗时大，专用内存多的缺点，而且对于测量和过程均有噪声干扰的多输入多输出系统，有很好的辨识效果，有较为广阔的应用前景。     

Improved closed-loop subspace identification with prior information

It has been proven that combining open-loop subspace identification with prior information can promote the accuracy of obtaining state-space models. In this study, prior information is exploited to improve the accuracy of closed-loop subspace identification. The proposed approach initially removes the correlation between future input and past innovation, a significant obstacle in closed-loop subspace identification method. Then, each row of the extended subspace matrix equation is considered an optimal multi-step ahead predictor and prior information is expressed in the form of equality constraints. The constrained least squares method is used to obtain improved results, so that the accuracy of the closed-loop subspace can be enhanced. Simulation examples are provided to demonstrate the effectiveness of the proposed algorithm.     

Closed-loop data-driven simulation

Closed-loop data-driven simulation refers to the problem of finding the set of all responses of a closed-loop system to a given reference signal directly from an input/output trajectory of the plant and a representation of the controller. Conditions under which the problem has a solution are given and an algorithm for computing the solution is presented. The problem formulation and its solution are in the spirit of the deterministic subspace identification algorithms, i.e. in the theoretical analysis of the method, the data is assumed exact (noise free). The results have applications in data-driven control, e.g. testing controller's performance directly from closed-loop data of the plant in feedback with possibly different controller.     

非最小相位FIR系统的自适应辨识

提出了一种基于线性代数方程组约束和梯度法的非最小相位FIR系统的自适应辨 识算法.选用的线性方程组具有列满秩的系数矩阵,保证了系统参数的唯一可识别性.由于只 采用高阶累量,故能够抑制任何高斯有色噪声的影响.重点讨论了梯度法中步长的选择,提出 了收敛速度最快的变步长.仿真实验的结果证实了算法的有效性.     

Consistency of the extended gradient identification algorithm for multi-input multi-output systems with moving average noises

The consistency of identification algorithms for systems with colored noises is a main topic in system identification. This paper focuses on the extended stochastic gradient (ESG) identification algorithm for the multivariable linear systems with moving average noises. By integrating the noise regression terms and the noise model parameters into the information matrix and the parameter vector, and based on the gradient search principle, the ESG algorithm is presented. The unknown noise terms in the information matrix are replaced with their estimates. The convergence analysis shows that the parameter estimation error converges to zero under a persistent excitation condition. Two simulation examples are given to illustrate the effectiveness of the algorithm.     

连续时间模型的闭环子空间辨识

本文对直接使用采样数据进行连续系统的闭环子空间辨识问题进行了研究．将线性滤波方法与基于主 元分析的子空间辨识相结合,利用参考输入或者外部激励信号的高阶滤波变换的正交投影变量作为辅助变量,提出 了一种新的连续时间系统闭环子空间辨识算法．数值仿真表明了与其他算法相比,本文提出的算法具有很好的辨识 效果．     

有色噪声背景下的正交子空间辨识

针对传统子空间辨识中存在的有色噪声干扰问题,本文提出一种正交子空间辨识方法.首先,根据子空间辨识算法机制构建含有色噪声的扩展状态空间模型.然后,结合有色噪声的相关性分析,研究了传统子空间辨识方法的有偏性问题,并重新设计了投影向量和正交投影方式,用以消除有色噪声干扰.最后,对投影后的数据矩阵进行奇异值分解,获取广义能观测矩阵,进而求得系统的状态空间模型参数.仿真结果表明该方法在有色噪声干扰下是一致无偏的,并且具有渐进二阶统计特性.结合陀螺仪的具体实验结果表明,该算法在实际应用中具有比传统子空间辨识法更高的辨识精度.     

Maximum likelihood identification of noisy input-output models

This work deals with the identification of errors-in-variables models corrupted by white and uncorrelated Gaussian noises. By introducing an auxiliary process, it is possible to obtain a maximum likelihood solution of this identification problem, by means of a two-step iterative algorithm. This approach allows also to estimate, as a byproduct, the noise-free input and output sequences. Moreover, an analytic expression of the finite Cràmer-Rao lower bound is derived. The method does not require any particular assumption on the input process, however, the ratio of the noise variances is assumed as known. The effectiveness of the proposed algorithm has been verified by means of Monte Carlo simulations.     

Consistency of noise covariance estimation in joint input–output closed-loop subspace identification with application in LQG benchmarking

The LQG trade-off curve has been used as a benchmark for control loop performance assessment. The subspace approach to estimating the LQG benchmark has been proposed in the literature which requires certain intermediate matrices in subspace identification as well as the covariance matrix of the noise. It is shown in this paper that many existing closed-loop identification methods do not give a consistent estimate of the noise covariance matrix. As a result, we propose an alternative subspace formulation for the joint input–output closed-loop identification for which the consistency of the required subspace matrices and noise covariance is guaranteed. Simulation studies and experimental results are provided to demonstrate the utility of the proposed method.     

Higher-Order-Statistics-Based Radial Basis Function Networks for Signal Enhancement

In this paper, a higher-order-statistics (HOS)-based radial basis function (RBF) network for signal enhancement is introduced. In the proposed scheme, higher order cumulants of the reference signal were used as the input of HOS-based RBF. An HOS-based supervised learning algorithm, with mean square error obtained from higher order cumulants of the desired input and the system output as the learning criterion, was used to adapt weights. The motivation is that the HOS can effectively suppress Gaussian and symmetrically distributed non-Gaussian noise. The influence of a Gaussian noise on the input of HOS-based RBF and the HOS-based learning algorithm can be mitigated. Simulated results indicate that HOS-based RBF can provide better performance for signal enhancement under different noise levels, and its performance is insensitive to the selection of learning rates. Moreover, the efficiency of HOS-based RBF under the nonstationary Gaussian noise is stable     

Identification of linear systems using input-output cumulants

A new identification method is proposed for estimating the parameters of a discrete-time linear dynamic system excited by non-gaussian inputs using kth order (k > 2) cumulants of input and output signals contaminated by additive (possibly coloured) gaussian noise. The parameter estimates obtained by this method are proved to be consistent under weak conditions. This method has an on-line algorithm for computing the parameter estimates, just like the least-squares method. A simulation example is included to demonstrate the effectiveness of this method.     

Approximation problems with the divergence criterion for Gaussian variables and Gaussian processes

System identification for stationary Gaussian processes includes an approximation problem. Currently, the subspace algorithm for this problem enjoys much attention. This algorithm is based on a transformation of a finite time series to canonical variable form followed by a truncation. There is no proof that this algorithm is the optimal solution to an approximation problem with a specific criterion. In this paper it is shown that the optimal solution to an approximation problem for Gaussian random variables with the divergence criterion is identical to the main step of the subspace algorithm. An approximation problem for stationary Gaussian processes with the divergence criterion is formulated.     

基于子空间方法的精馏塔系统辨识建模研究

子空间辨识方法作为一种有效的针对多输入-多输出系统(MIMO)的辨识建模方法近年来受到广泛的重视.目前主要采用的子空间辨识算法只能适用于白噪声环境,而实际的工业现场数据很多是受到较大有色噪声干扰的.针对问题采用了一种新的子空间辨识算法,利用马尔可夫参数用于处理随机性部分,同时引入辅助变量用以去除噪声的干扰,能够适用于存在较大有色噪声干扰情况下的辨识建模,并可得到对象的无偏模型,建模的精度优于通常所采用的子空间辨识算法.通过对精馏塔仿真模型的辨识结果证明了该方法的可行性和有效性,以及在实际工业过程对象建模中良好的应用前景.     

Orthogonal projection based subspace identification against colored noise

In this paper, a bias-eliminated subspace identification method is proposed for industrial applications subject to colored noise. Based on double orthogonal projections, an identification algorithm is developed to eliminate the influence of colored noise for consistent estimation of the extended observability matrix of the plant state-space model. A shift-invariant approach is then given to retrieve the system matrices from the estimated extended observability matrix. The persistent excitation condition for consistent estimation of the extended observability matrix is analyzed. Moreover, a numerical algorithm is given to compute the estimation error of the estimated extended observability matrix. Two illustrative examples are given to demonstrate the effectiveness and merit of the proposed method.     

On Consistency of Subspace Methods for System Identification

Subspace methods for identification of linear time-invariant dynamical systems typically consist of two main steps. First, a so-called subspace estimate is constructed. This first step usually consists of estimating the range space of the extended observability matrix. Secondly, an estimate of system parameters is obtained, based on the subspace estimate. In this paper, the consistency of a large class of methods for estimating the extended observability matrix is analyzed. Persistence of excitation conditions on the input signal are given which guarantee consistent estimates for systems with only measurement noise. For systems with process noise, it is shown that a persistence of excitation condition on the input is not sufficient. More precisely, an example for which the subspace methods fail to give a consistent estimate of the transfer function is given. This failure occurs even if the input is persistently exciting of any order. It is also shown that this problem can be eliminated if stronger conditions on the input signal are imposed.     

Error analysis of fixed-point prediction with coloured measurement noise

The main purpose of this paper is the error analysis of the fixed-point prediction for the linear continuous-time system with the coloured measurement noise. In the first part of this paper we derive an algorithm for the fixed-point prediction with the coloured measurement, noise from the given system. The remaining part presents the error analysis of the fixed-point prediction due to two causes, one of which is misidentifying the coefficients of the system and the covariances of the noises and the other of simplifying the coloured measurement noise by a white measurement noise. For the above cases two differential equations are obtained which govern the actual covariances regarded as the error quantities.     

Cumulant-based inverse filters for blind deconvolution

Blind deconvolution of linear time-invariant (LTI) systems has received wide attention in various fields such as data communication and image processing. Blind deconvolution is concerned with the estimation of a desired input signal from a given set of measurements. This paper presents a technique for reconstructing the desired input from only the available corrupted data. The estimator is given in terms of an autoregressive moving average (ARMA) innovation model. This technique is based on higher order statistics (HOS) of a non-Gaussian output sequence in the presence of additive Gaussian or non-Gaussian noise. The algorithm solves a set of overdetermined linear equations using third-order cumulants of the given non-Gaussian measurements in the presence of additive Gaussian or non-Gaussian noise. The inverse filter is a finite impulse response (FIR) filter. Simulation results are provided to show the effectiveness of this method and compare it with a recently developed algorithm based on maximizing the magnitude of the kurtosis of estimate of the input excitation.