Three-stage recursive least squares parameter estimation for controlled autoregressive autoregressive systems

A three-stage recursive least squares parameter estimation algorithm is derived for controlled autoregressive autoregressive (CARAR) systems. The basic idea is to decompose a CARAR system into three subsystems, one of which contains one parameter vector, and to identify the parameters of each subsystem one by one. Compared with the recursive generalized least squares algorithm, the dimensions of the involved covariance matrices in each subsystem become small and thus the proposed algorithm has a high computational efficiency. Finally, we verify the proposed algorithm with a simulation example.     

Least squares based iterative parameter estimation algorithm for multivariable controlled ARMA system modelling with finite measurement data

Difficulties of identification for multivariable controlled autoregressive moving average (ARMA) systems lie in that there exist unknown noise terms in the information vector, and the iterative identification can be used for the system with unknown terms in the information vector. By means of the hierarchical identification principle, those noise terms in the information vector are replaced with the estimated residuals and a least squares based iterative algorithm is proposed for multivariable controlled ARMA systems. The simulation results indicate that the proposed algorithm is effective.     

Maximum likelihood least squares identification for systems with autoregressive moving average noise

Maximum likelihood methods are important for system modeling and parameter estimation. This paper derives a recursive maximum likelihood least squares identification algorithm for systems with autoregressive moving average noises, based on the maximum likelihood principle. In this derivation, we prove that the maximum of the likelihood function is equivalent to minimizing the least squares cost function. The proposed algorithm is different from the corresponding generalized extended least squares algorithm. The simulation test shows that the proposed algorithm has a higher estimation accuracy than the recursive generalized extended least squares algorithm.     

Innovations algorithm asymptotics for periodically stationary time series with heavy tails

The innovations algorithm can be used to obtain parameter estimates for periodically stationary time series models. In this paper we compute the asymptotic distribution for these estimates in the case where the underlying noise sequence has infinite fourth moment but finite second moment. In this case, the sample covariances on which the innovations algorithm are based are known to be asymptotically stable. The asymptotic results developed here are useful to determine which model parameters are significant. In the process, we also compute the asymptotic distributions of least squares estimates of parameters in an autoregressive model.     

Improved estimation in a non-Gaussian parametric regression

The paper considers the problem of estimating the parameters in a continuous time regression model with a non-Gaussian noise of pulse type. The vector of unknown parameters is assumed to belong to a compact set. The noise is specified by the Ornstein–Uhlenbeck process driven by the mixture of a Brownian motion and a compound Poisson process. Improved estimates for the unknown regression parameters, based on a special modification of the James–Stein procedure with smaller quadratic risk than the usual least squares estimates, are proposed. The developed estimation scheme is applied for the improved parameter estimation in the discrete time regression with the autoregressive noise depending on unknown nuisance parameters.     

Switching Control of Nonlinear Systems Based on the Quasi-ARX Model and the SVR Algorithm北大核心CSCD

该文基于改进的含有外部输入项的准线性自回归(准ARX)径向基函数(RBF)网络模型和支持向量回归(SVR)算法,提出了一种非线性切换控制方法.改进的准ARX模型非线性部分采用RBF网络.控制系统设计过程分为三个部分:首先,利用聚类方法确定模型的非线性参数;然后,采用线性SVR算法来解决控制系统的鲁棒性问题;接下来,基于控制误差给出切换判定函数,确定切换律给出控制序列.最后通过数值仿真验证了该方法的有效性.     

Parameter and state estimation algorithm for single-input single-output linear systems using the canonical state space models

This paper presents a new parameter and state estimation algorithm for single-input single-output systems based on canonical state space models from the given input–output data. Difficulties of identification for state space models lie in that there exist unknown noise terms in the formation vector and unknown state variables. By means of the hierarchical identification principle, those noise terms in the information vector are replaced with the estimated residuals and a new least squares algorithm is proposed for parameter estimation and the system states are computed by using the estimated parameters. Finally, an example is provided.     

Design of normalized fractional adaptive algorithms for parameter estimation of control autoregressive autoregressive systems

In this paper, strength of fractional adaptive signal processing is exploited for parameter identification of control autoregressive autoregressive (CARAR) systems using normalized version of fractional least mean square (FLMS) and its recently introduced modification of type 1 and 2. The adaptation performance of the proposed normalized FLMS methods is compared with standard counterparts for CARAR identification model by taking different noise levels as well as fractional orders. The results of the statistical analyses are used to validate the consistency of the proposed normalized fractional adaptive methodologies in terms of convergence, accuracy and robustness. The reliability and effectiveness of the design schemes is further validated through consistently approaching the desired identification parameters based on performance metrics of mean square error, variance account for and Nash–Sutcliffe efficiency.     

Quantile regression for linear models with autoregressive errors using EM algorithm

In this paper, we consider the quantile linear regression models with autoregressive errors. By incorporating the expectation–maximization algorithm into the considered model, the iterative weighted least square estimators for quantile regression parameters and autoregressive parameters are derived. Finally, the proposed procedure is illustrated by simulations and a real data example.     

Hierarchical least squares based iterative estimation algorithm for multivariable Box-Jenkins-like systems using the auxiliary model

This paper presents a hierarchical least squares iterative algorithm to estimate the parameters of multivariable Box-Jenkins-like systems by combining the hierarchical identification principle and the auxiliary model identification idea. The key is to decompose a multivariable systems into two subsystems by using the hierarchical identification principle. As there exist the unmeasurable noise-free outputs and noise terms in the information vector, the solution is using the auxiliary model identification idea to replace the unmeasurable variables with the outputs of the auxiliary model and the estimated residuals. A numerical example is given to show the performance of the proposed algorithm.     

A Combinatorial Approach to Piecewise Linear Time Series Analysis

Over recent years, several nonlinear time series models have been proposed in the literature. One model that has found a large number of successful applications is the threshold autoregressive model (TAR). The TAR model is a piecewise linear process whose central idea is to change the parameters of a linear autoregressive model according to the value of an observable variable, called the threshold variable. If this variable is a lagged value of the time series, the model is called a self-exciting threshold autoregressive (SETAR) model. In this article, we propose a heuristic to estimate a more general SETAR model, where the thresholds are multivariate. We formulate the task of finding multivariate thresholds as a combinatorial optimization problem. We develop an algorithm based on a greedy randomized adaptive search procedure (GRASP) to solve the problem. GRASP is an iterative randomized sampling technique that has been shown to quickly produce good quality solutions for a wide variety of optimization problems. The proposed model performs well on both simulated and real data.     

Identification of nonlinear system using extreme learning machine based Hammerstein model

In this paper, a new method for nonlinear system identification via extreme learning machine neural network based Hammerstein model (ELM-Hammerstein) is proposed. The ELM-Hammerstein model consists of static ELM neural network followed by a linear dynamic subsystem. The identification of nonlinear system is achieved by determining the structure of ELM-Hammerstein model and estimating its parameters. Lipschitz quotient criterion is adopted to determine the structure of ELM-Hammerstein model from input–output data. A generalized ELM algorithm is proposed to estimate the parameters of ELM-Hammerstein model, where the parameters of linear dynamic part and the output weights of ELM neural network are estimated simultaneously. The proposed method can obtain more accurate identification results with less computation complexity. Three simulation examples demonstrate its effectiveness.     

The growth curve model with an autoregressive covariance structure

The growth curve model with an autoregressive covariance structure is considered. An iterative algorithm for finding the MLE's of the parameters in the model is presented, based on the modified likelihood equations. Asymptotic distributions of the MLE's are obtained when the sample size is large. A likelihood ratio statistic for testing the autoregressive covariance structure is presented.     

基于主成份分析的递推子空间辨识

研究了多输入多输出系统的状态空间模型的递推子空间辨识问题.针对只有输出量测噪声的线性时不变系统,提出了基于随机逼近-主成份分析(SA-PCA)的估计扩张能观矩阵的递推算法.同时利用递推最小二乘在线估计系统矩阵.最后通过仿真例子说明算法的收敛速度和估计效果.     

Hierarchical multi-innovation stochastic gradient algorithm for Hammerstein nonlinear system modeling

This paper decomposes a Hammerstein nonlinear system into two subsystems, one containing the parameters of the linear dynamical block and the other containing the parameters of the nonlinear static block, and presents a hierarchical multi-innovation stochastic gradient identification algorithm for Hammerstein systems based on the hierarchical identification principle. The proposed algorithm is simple in principle and easy to implement on-line. A simulation example is provided to test the effectiveness of the proposed algorithm.     

Robust Simulation-Based Estimation of ARMA Models

This article proposes a new approach to the robust estimation of a mixed autoregressive and moving average (ARMA) model. It is based on the indirect inference method that originally was proposed for models with an intractable likelihood function. The estimation algorithm proposed is based on an auxiliary autoregressive representation whose parameters are first estimated on the observed time series and then on data simulated from the ARMA model. To simulate data the parameters of the ARMA model have to be set. By varying these we can minimize a distance between the simulation-based and the observation-based auxiliary estimate. The argument of the minimum yields then an estimator for the parameterization of the ARMA model. This simulation-based estimation procedure inherits the properties of the auxiliary model estimator. For instance, robustness is achieved with GM estimators. An essential feature of the introduced estimator, compared to existing robust estimators for ARMA models, is its theoretical tractability that allows us to show consistency and asymptotic normality. Moreover, it is possible to characterize the influence function and the breakdown point of the estimator. In a small sample Monte Carlo study it is found that the new estimator performs fairly well when compared with existing procedures. Furthermore, with two real examples, we also compare the proposed inferential method with two different approaches based on outliers detection.     

Bias compensation methods for stochastic systems with colored noise

For ARX-like systems, this paper derives a bias compensation based recursive least squares identification algorithm by means of the prefilter idea and bias compensation principle. The proposed algorithm can give the unbiased estimates of the system model parameters in the presence of colored noises, and can be on-line implemented. Finally, the advantages of the proposed bias compensation recursive least squares algorithm are shown by simulation tests.     

Real-coded genetic algorithm for system identification and controller tuning

This paper presents an application of real-coded genetic algorithm (RGA) for system identification and controller tuning in process plants. The genetic algorithm is applied sequentially for system identification and controller tuning. First GA is applied to identify the changes in system parameters. Once the process parameters are identified, the optimal controller parameters are identified using GA. In the proposed genetic algorithm, the optimization variables are represented as floating point numbers. Also, cross over and mutation operators that can directly deal with the floating point numbers are used. The proposed approach has been applied for system identification and controller tuning in nonlinear pH process. The simulation results show that the GA based approach is effective in identifying the parameters of the system and the nonlinearity at various operating points in the nonlinear system.     

A NARMAX model-based state-space self-tuning control for nonlinear stochastic hybrid systems

A novel state-space self-tuning control methodology for a nonlinear stochastic hybrid system with stochastic noise/disturbances is proposed in this paper. via the optimal linearization approach, an adjustable NARMAX-based noise model with estimated states can be constructed for the state-space self-tuning control in nonlinear continuous-time stochastic systems. Then, a corresponding adaptive digital control scheme is proposed for continuous-time multivariable nonlinear stochastic systems, which have unknown system parameters, measurement noise/external disturbances, and inaccessible system states. The proposed method enables the development of a digitally implementable advanced control algorithm for nonlinear stochastic hybrid systems.     

关于非线性自回归模型的几何遍历性

本文讨论带噪声的动态系统，即非线性自由回归模型，若原系统不具有任何压缩性质，但是它的某种拓扑共轭变换后的系统满足一定的压缩性质，本文指出，当噪声适当小时，相应的带噪声的动态系统将有唯一的平稳解，而且是几何遍历的。