Parameter Estimation Algorithms for Hammerstein–Wiener Systems With Autoregressive Moving Average Noise

Hammerstein–Wiener (H–W) systems are a class of typical nonlinear systems. This paper studies the gradient-based parameter estimation algorithms for H–W nonlinear systems based on the multi-innovation identification theory and the data filtering technique. The proposed methods include a generalized extended stochastic gradient (GESG) algorithm, a multi-innovation GESG (MI-GESG) algorithm, a data filtering based GESG (F-GESG) algorithm and a data filtering based MI-GESG algorithm. Finally, the computational efficiency of the proposed algorithms are analyzed and compared. The simulation example verifies the theoretical results.

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Least-Squares Parameter Estimation Algorithm for a Class of Input Nonlinear Systems

Journal of Applied Mathematics ◽

10.1155/2012/684074 ◽

2012 ◽

Vol 2012 ◽

pp. 1-14 ◽

Cited By ~ 13

Author(s):

Weili Xiong ◽

Wei Fan ◽

Rui Ding

Keyword(s):

Parameter Estimation ◽

Nonlinear Systems ◽

Least Squares ◽

Moving Average ◽

Estimation Algorithm ◽

Autoregressive Moving Average ◽

Parameter Estimates ◽

Persistent Excitation ◽

Estimation Algorithms ◽

Parameter Estimation Algorithm

This paper studies least-squares parameter estimation algorithms for input nonlinear systems, including the input nonlinear controlled autoregressive (IN-CAR) model and the input nonlinear controlled autoregressive autoregressive moving average (IN-CARARMA) model. The basic idea is to obtain linear-in-parameters models by overparameterizing such nonlinear systems and to use the least-squares algorithm to estimate the unknown parameter vectors. It is proved that the parameter estimates consistently converge to their true values under the persistent excitation condition. A simulation example is provided.

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Adaptive Gradient-Based Iterative Algorithm for Multivariable Controlled Autoregressive Moving Average Systems Using the Data Filtering Technique

Complexity ◽

10.1155/2018/9598307 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11 ◽

Cited By ~ 32

Author(s):

Jian Pan ◽

Hao Ma ◽

Xiao Jiang ◽

Wenfang Ding ◽

Feng Ding

Keyword(s):

Moving Average ◽

Measurement Data ◽

Identification Problem ◽

Autoregressive Moving Average ◽

Data Filtering ◽

Moving Average Process ◽

Output Data ◽

Gradient Based ◽

Filtering Technique ◽

Negative Gradient

The identification problem of multivariable controlled autoregressive systems with measurement noise in the form of the moving average process is considered in this paper. The key is to filter the input–output data using the data filtering technique and to decompose the identification model into two subidentification models. By using the negative gradient search, an adaptive data filtering-based gradient iterative (F-GI) algorithm and an F-GI with finite measurement data are proposed for identifying the parameters of multivariable controlled autoregressive moving average systems. In the numerical example, we illustrate the effectiveness of the proposed identification methods.

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