Parameter Estimation Algorithms for Hammerstein Finite Impulse Response Moving Average Systems Using the Data Filtering Theory

Yan Ji,Jinde Cao

doi:10.3390/math10030438

Abstract

This paper considers the parameter estimation problems of Hammerstein finite impulse response moving average (FIR–MA) systems. Based on the matrix transformation and the hierarchical identification principle, the Hammerstein FIR–MA system is recast into two models, and a decomposition-based recursive least-squares algorithm is deduced for estimating the parameters of these two models. In order to further improve the accuracy of the parameter estimation, a multi-innovation hierarchical least-squares algorithm based on the data filtering theory proposed. Finally, a simulation example demonstrates the effectiveness of the proposed scheme.

Highlights

The idetification methods have been very mature for multivariable linear systems [1,2].many systems in practical applications and industrial control are nonlinear multivariable systems [3,4]
This paper studies the parameter estimation problems of two-input two-output Hammerstein finite impulse response moving average (FIR–MA) systems
Based on the decomposition technique, we decomposed the Hammerstein system into two models, each of which is expressed as a regression form in the parameters of the nonlinear part or in the parameters of the linear part, and we propose a hierarchical least-squares algorithm

Summary

Introduction

The idetification methods have been very mature for multivariable linear systems [1,2]. Wang and Ding presented a novel recursive least-squares algorithm for multiple-input multiple-output (MIMO) systems with autoregressive moving average noise, employing the auxiliary model and the data filtering technique [9]. This paper studies the parameter estimation problems of two-input two-output Hammerstein finite impulse response moving average (FIR–MA) systems. Based on the decomposition technique, we decomposed the Hammerstein system into two models, each of which is expressed as a regression form in the parameters of the nonlinear part or in the parameters of the linear part, and we propose a hierarchical least-squares algorithm. By applying the data filtering technique, the input–output data are filtered, and a filtering-based hierarchical least-squares algorithm is presented for Hammerstein finite impulse response moving average systems to improve the accuracy of parameter estimation.

System Description and Identification Model

The Hierarchical Least-Squares Algorithm

The Convergence Analysis of the Hierarchical Least-Squares Algorithm

The Filtering Based Recursive Least-Squares Algorithm

Examples

Conclusions