Auxiliary Model Identification Idea Research Articles

Auxiliary Model-Based Recursive Generalized Least Squares Algorithm for Multivariate Output-Error Autoregressive Systems Using the Data Filtering

This paper focuses on the parameter estimation problem of multivariate output-error autoregressive systems. Based on the data filtering technique and the auxiliary model identification idea, we derive a filtering-based auxiliary model recursive generalized least squares algorithm. The key is to filter the input–output data and to derive two identification models, one of which includes the system parameters and the other contains the noise parameters. Compared with the auxiliary model-based recursive generalized least squares algorithm, the proposed algorithm requires less computational burden and can generate more accurate parameter estimates. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithm.

Auxiliary Model Based Least Squares Iterative Algorithms for Parameter Estimation of Bilinear Systems Using Interval-Varying Measurements

This paper focuses on the parameter estimation of a class of bilinear systems, for which the input-output representation is derived by eliminating the state variables in the systems. Based on the obtained identification model and the hierarchical identification principle, a hierarchical auxiliary model based least squares iterative algorithm is derived, to improve the computation efficiency and the parameter estimation accuracy by using the auxiliary model identification idea and the interval-varying input-output data. For comparison, an auxiliary model based least squares iterative algorithm is presented. The simulation results show that the proposed algorithm has better performance in estimating the parameters of bilinear systems.

The data filtering based generalized stochastic gradient parameter estimation algorithms for multivariate output-error autoregressive systems using the auxiliary model

Parameter estimation has wide applications in one-dimensional and multidimensional signal processing and filtering. This paper focuses on the parameter estimation problem of multivariate output-error autoregressive systems. Based on the data filtering technique and the auxiliary model identification idea, we derive a filtering based auxiliary model generalized stochastic gradient algorithm. The key is to choose an appropriate filter to filter the input-output data and to study a novel method to get the system model parameters and noise model parameters respectively. By employing the multi-innovation identification theory, a filtering based auxiliary model multi-innovation generalized stochastic gradient algorithm is proposed. Compared with the auxiliary model generalized stochastic gradient algorithm, the proposed algorithms can generate more accurate parameter estimates. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithms.

Recursive and Iterative Least Squares Parameter Estimation Algorithms for Multiple-Input–Output-Error Systems with Autoregressive Noise

This paper considers the parameter estimation of a multiple-input–output-error system with autoregressive noise. In order to solve the problem of the information vector containing unknown inner variables, an auxiliary model-based recursive generalized least squares algorithm and a least squares-based iterative algorithm are proposed according to the auxiliary model identification idea and the iterative search principle. The simulation results indicate that the least squares-based iterative algorithm can generate more accurate parameter estimates than the auxiliary model-based recursive generalized least squares algorithm. Two examples are given to test the proposed algorithms.

Coupled stochastic gradient identification algorithms for multivariate output-error systems using the auxiliary model

This paper considers the gradient based identification problem of a multivariate output-error system. By using the auxiliary model identification idea and the coupling identification concept, an auxiliary model based stochastic gradient (AM-SG) algorithm and a coupled AM-SG algorithm are presented. The results indicate that the parameter estimation errors converge to zero under the persistent excitation conditions. The simulation examples confirm the theoretical results.

Parameter estimation algorithms for Hammerstein time‐delay systems based on the orthogonal matching pursuit scheme

This study focuses on the parameter estimation of Hammerstein non-linear systems with unknown time-delay and coloured noise. By means of the compressed sensing recovery theory and the auxiliary model identification idea, an orthogonal matching pursuit based iterative algorithm is proposed for estimating the system parameters and the time delay. The proposed algorithms can give highly accurate parameter estimates from a small number of observations. Two simulation examples are provided to test the proposed algorithms.

Parameter estimation for pseudo‐linear systems using the auxiliary model and the decomposition technique

This study focuses on the parameter identification problems of pseudo-linear systems. The main goal is to present recursive least squares (RLS) estimation methods based on the auxiliary model identification idea and the decomposition technique. First, an auxiliary model-based RLS algorithm is given as a comparison. Second, to improve the computation efficiency, a decomposition-based RLS algorithm is presented. Then for the system identification with missing data, an interval-varying RLS algorithm is derived for estimating the system parameters. Furthermore, this study uses the decomposition technique to reduce the computational cost in the interval-varying RLS algorithm and introduces the forgetting factors to track the time-varying parameters. The simulation results show that the proposed algorithms can work well.

Novel recursive least squares identification for a class of nonlinear multiple-input single-output systems using the filtering technique

In this article, we consider the identification problem of a class of nonlinear multiple-input single-output output-error autoregressive systems. First, a recursive generalized least squares algorithm using the auxiliary model identification idea is developed. Then, using the filtering technique, the identification model is decomposed into a filtered sub-identification model and a noise sub-identification model. For solving the difficulties that the filter is unknown and the information vectors contain the unknown variables, the interactive estimation theory and the the idea of replacing the unknown variables with their corresponding estimates are employed: the recursive least squares method is again used for identifying the system and noise model parameters, and the parameter estimates of the noise model are used to construct the estimated filter. Finally, a nonlinear example is given to verify the effectiveness of the algorithms, and the simulation results show that the recursive least squares algorithm using the filtering technique can produce more accurate parameter estimates under larger noise variances.

Data Filtering Based Recursive and Iterative Least Squares Algorithms for Parameter Estimation of Multi-Input Output Systems

This paper discusses the parameter estimation problems of multi-input output-error autoregressive (OEAR) systems. By combining the auxiliary model identification idea and the data filtering technique, a data filtering based recursive generalized least squares (F-RGLS) identification algorithm and a data filtering based iterative least squares (F-LSI) identification algorithm are derived. Compared with the F-RGLS algorithm, the proposed F-LSI algorithm is more effective and can generate more accurate parameter estimates. The simulation results confirm this conclusion.

The auxiliary model based hierarchical gradient algorithms and convergence analysis using the filtering technique

On the basis of the auxiliary model identification idea, this paper studies the filtering based parameter estimation issues for a class of multivariable control systems with colored noise. An auxiliary model based hierarchical stochastic gradient (AM-HSG) algorithm is given for comparison and a data filtering AM-HSG identification algorithm is derived by using the data filtering technique. Its main key is to decompose a multivariable system into two subsystems and to coordinate the associate items between two subsystem identification algorithms. The convergence analysis indicates that the parameter estimates given by the presented algorithms converge to the true values under proper conditions by using the stochastic process theory. The simulation results show that the proposed hierarchical stochastic gradient estimation algorithms are effective.

The recursive least squares identification algorithm for a class of Wiener nonlinear systems

Many physical systems can be modeled by a Wiener nonlinear model, which consists of a linear dynamic system followed by a nonlinear static function. This work is concerned with the identification of Wiener systems whose output nonlinear function is assumed to be continuous and invertible. A recursive least squares algorithm is presented based on the auxiliary model identification idea. To solve the difficulty of the information vector including the unmeasurable variables, the unknown terms in the information vector are replaced with their estimates, which are computed through the preceding parameter estimates. Finally, an example is given to support the proposed method.

Iterative identification algorithms for input nonlinear output error autoregressive systems

This paper focuses on the parameter estimation problems of input nonlinear output error autoregressive systems. Based on the key variables separation technique and the auxiliary model identification idea, the output of the system is expressed as a linear combination of all the system parameters, the unknown inner variables in the information vector are replaced with the outputs of the auxiliary model and a gradient based and a least squares based iterative identification algorithms are derived. Simulation example is provided to illustrate the effectiveness of the proposed algorithms.

An auxiliary model based least squares algorithm for a dual-rate state space system with time-delay using the data filtering

For dual-rate state space systems with time-delay, this paper combines the auxiliary model identification idea with the filtering technique, transforms the state space model into the identification model with different input and output sampling rates, and presents a filtering and auxiliary model based recursive least squares identification algorithm with finite measurement input–output data. Compared with the auxiliary model based recursive least squares algorithm, the proposed algorithm can generate more accurate parameter estimates and has a higher computational efficiency because the dimensions of its covariance matrices become small.

EM algorithm-based identification of a class of nonlinear Wiener systems with missing output data

This paper is concerned with the problem of parameter estimation for nonlinear Wiener systems in the stochastic framework. Based on the expectation–maximization (EM) algorithm in dealing with the incomplete data, it is applied to estimate the parameters of nonlinear Wiener models considering the randomly missing outputs. By means of the EM approach, the parameters and the missing outputs can be estimated simultaneously. To obtain the noise-free output in the linear subsystem of the Wiener model, the auxiliary model identification idea is adopted here. The simulation results indicate the effectiveness of the proposed approach for identification of a class of nonlinear Wiener models.

Recursive least squares parameter identification algorithms for systems with colored noise using the filtering technique and the auxilary model

This paper focuses on the parameter estimation problems of output error autoregressive systems and output error autoregressive moving average systems (i.e., the Box–Jenkins systems). Two recursive least squares parameter estimation algorithms are proposed by using the data filtering technique and the auxiliary model identification idea. The key is to use a linear filter to filter the input–output data. The proposed algorithms can identify the parameters of the system models and the noise models interactively and can generate more accurate parameter estimates than the auxiliary model based recursive least squares algorithms. Two examples are given to test the proposed algorithms.

A Fast and Efficient Parameter Estimation Algorithm for Generalized Output Error Models

One kind of the colored noise interference systems is generalized output error model (OEARMA). This paper presents a two-stage recursive least squares algorithm for OEARMA. Aiming at the OEARMA, this paper puts forward a two-stage recursive least squares algorithm. The basic idea of the algorithm is to combinie the auxiliary model identification idea and the decomposition technique to decompose a system into two subsystems. Each subsystem contains a parameter vector. With auxiliary model-based recursive extended least squares theory, an unknown intermediate variable output instead of the auxiliary model identification model vector, instead of unmeasurable noise terms in the information vector with the estimated residuals, which can use recursive identification idea to estimated all the parameters of the system, the algorithm has a high computational efficiency. The example of simulation states the effectiveness of the proposed algorithm.

Recursive least squares estimation algorithm applied to a class of linear-in-parameters output error moving average systems

Abstract This letter deals with the identification problem of a class of linear-in-parameters output error moving average systems. The difficulty of identification is that there exist some unknown variables in the information vector. By means of the auxiliary model identification idea, an auxiliary model based recursive least squares algorithm is developed for identifying the parameters of the proposed system. The simulation results confirm the conclusion.

Auxiliary model based least squares parameter estimation algorithm for feedback nonlinear systems using the hierarchical identification principle

This paper presents a decomposition based least squares estimation algorithm for a feedback nonlinear system with an output error model for the open-loop part by using the auxiliary model identification idea and the hierarchical identification principle and by decomposing a system into two subsystems. Compared with the auxiliary model based recursive least squares algorithm, the proposed algorithm has a smaller computational burden. The simulation results indicate that the proposed algorithm can estimate the parameters of feedback nonlinear systems effectively.

An Auxiliary-Model-Based Stochastic Gradient Algorithm for Dual-Rate Sampled-Data Box–Jenkins Systems

This paper presents an identification algorithm for Box–Jenkins systems by combining the auxiliary model identification idea and the gradient search principle. The proposed algorithm can estimate all unknown parameters of the Box–Jenkins systems. Furthermore, to improve the convergence rate of the stochastic gradient algorithm, a modified stochastic gradient algorithm is given. The simulation results indicate that the proposed algorithm can work well.

Hierarchical Least Squares Estimation Algorithm for Hammerstein–Wiener Systems

This letter focuses on identification problems of a Hammerstein-Wiener system with an output error linear element embedded between two static nonlinear elements. A hierarchical least squares algorithm is presented for the Hammerstein-Wiener system by using the auxiliary model identification idea and the hierarchical identification principle. The major contributions of the present study are that the identification model is formulated by using the auxiliary model identification idea (the estimate of the unknown internal variable is replaced with the output of an auxiliary model) and that the bilinear parameter vectors in the identification model are estimated by using the hierarchical identification principle. The proposed hierarchical identification approach is computationally more efficient than the existing over-parametrization method.