Output Error Autoregressive Systems Research Articles

Maximum likelihood interval-varying recursive least squares identification for output-error autoregressive systems with scarce measurements

The identification problem of output-error autoregressive (OEAR) systems with scarce measurements is considered in this paper. In order to overcome the massive absence of outputs, an interval-varying recursive identification algorithm is proposed through changing the sampling interval and skipping the missing outputs. Based on the maximum likelihood principle, a maximum likelihood interval-varying recursive least squares algorithm is proposed. The effectiveness of the proposed algorithm is tested by a numerical simulation example, and an application example about the heading motion control of underwater vehicle.

Neuro-fuzzy based identification of Hammerstein OEAR systems

This paper considers the parameter identification of neuro-fuzzy based Hammerstein output error auto-regressive (OEAR) systems by combining multiple signal source separation principle and auxiliary model identification idea. The unmeasurable internal variable is replaced by the correlation function of input and output data, then correlation analysis method is adopted to identify the parameters of linear part. In order to solve the parameter identification of the nonlinear part and the noise model, this paper presents a recursive generalized least squares algorithm based on auxiliary model. The convergence analysis in stochastic process theory shows that the parameter estimation error converges to zero under the persistent excitation condition. Examples results indicate that the proposed algorithm has significant advantages of good recognition accuracy to noise disturbance.

Auxiliary model based recursive generalized least squares identification algorithm for multivariate output-error autoregressive systems using the decomposition technique

This paper focuses on the parameter estimation problem of multivariate output-error autoregressive systems. Based on the decomposition technique and the auxiliary model identification idea, we derive a decomposition based auxiliary model recursive generalized least squares algorithm. The key is to divide the system into two fictitious subsystems, the one including a parameter vector and the other including a parameter matrix, and to estimate the two subsystems using the recursive least squares method, respectively. Compared with the auxiliary model based recursive generalized least squares algorithm, the proposed algorithm has less computational burden. Finally, an illustrative example is provided to verify the effectiveness of the proposed algorithms.

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.

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.

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.

Filtering-Based Multistage Recursive Identification Algorithm for an Input Nonlinear Output-Error Autoregressive System by Using the Key Term Separation Technique

This paper derives a data filtering-based two-stage stochastic gradient algorithm and a data filtering-based multistage recursive least-squares algorithm for input nonlinear output-error autoregressive systems (i.e., Hammerstein systems). The output of the system is expressed as a linear combination of all system parameters based on the key term separation technique. The basic idea of the proposed algorithm is to filter the input---output data and to separate the parameter vector into several vectors and to interactively identify each parameter vector. The data filtering-based two-stage stochastic gradient algorithm has higher convergence rate than the stochastic gradient algorithm. Compared with the recursive generalized least-squares algorithm, the dimensions of the involved covariance matrices in the data filtering-based multistage recursive least-squares algorithm become small, and thus the data filtering-based multistage recursive least-squares algorithm has a higher computational efficiency. The numerical simulation results indicate that the proposed algorithms are effective.

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.

Parameter estimation for nonlinear systems by using the data filtering and the multi-innovation identification theory

For Hammerstein output-error autoregressive systems, a decomposition based multi-innovation stochastic gradient (D-MISG) identification algorithm and a data filtering based multi-innovation stochastic gradient (F-MISG) identification algorithm are derived by means of the key-term separation principle and the multi-innovation identification theory. The D-MISG algorithm uses the decomposition technique to transform a Hammerstein system into two subsystems and requires less computational cost, and the F-MISG algorithm uses a linear filter to filter the input-output data and has a higher estimation accuracy for larger innovation lengths. The simulation results show that the proposed two algorithm can give satisfactory parameter estimates.

Data Filtering-Based Multi-innovation Stochastic Gradient Algorithm for Nonlinear Output Error Autoregressive Systems

This paper discusses the parameter estimation problems of nonlinear output error autoregressive systems and presents a data filtering-based multi-innovation stochastic gradient algorithm for improving the parameter estimation accuracy of the stochastic gradient algorithm by combining the multi-innovation identification theory and the data filtering technique. The proposed algorithm is effective and can generate highly accurate parameter estimates compared with the multi-innovation stochastic gradient algorithm. The simulation results confirm this conclusion.

Auxiliary model based recursive and iterative least squares algorithm for autoregressive output error autoregressive systems

This paper considers the stochastic systems described by the autoregressive output error autoregressive (AR-OEAR) models. The AR-OEAR model is a special output error model which has an extra autoregressive term of the output signal. Basing on the auxiliary model idea, the recursive method and the iterative principle, the auxiliary model based recursive and iterative least squares algorithms are proposed to estimate the parameters of the autoregressive output error autoregressive system which contains the autoregressive output error system model and the autoregressive noise model, respectively. The simulation results indicate that the proposed algorithms can work well.

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.

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.

Auxiliary model based recursive generalized least squares parameter estimation for Hammerstein OEAR systems

This paper deals with the parameter identification problem of Hammerstein output error auto-regressive (OEAR) systems with different nonlinearities by combining the key-term separation principle and the auxiliary model identification idea. The basic idea is, by using the key-term separation principle, to present auxiliary model based recursive generalized least squares algorithms in terms of the auxiliary model idea. The proposed algorithm can obtain the system model parameter estimates and the noise model parameter estimates, and can be extended to other nonlinear systems.