Data Filtering Based Recursive Least Squares Algorithm for Two-Input Single-Output Systems with Moving Average Noises

Xianling Lu,Wei Zhou,Wenlin Shi

doi:10.1155/2014/694053

Abstract

This paper studies identification problems of two-input single-output controlled autoregressive moving average systems by using an estimated noise transfer function to filter the input-output data. Through data filtering, we obtain two simple identification models, one containing the parameters of the system model and the other containing the parameters of the noise model. Furthermore, we deduce a data filtering based recursive least squares method for estimating the parameters of these two identification models, respectively, by replacing the unmeasurable variables in the information vectors with their estimates. The proposed algorithm has high computational efficiency because the dimensions of its covariance matrices become small. The simulation results indicate that the proposed algorithm is effective.

Highlights

Studies on identification methods have been active in recent years [1,2,3]
This paper studies identification problems of two-input single-output controlled autoregressive moving average systems by using an estimated noise transfer function to filter the input-output data
Xie et al studied recursive least squares parameter estimation methods for nonuniformly sampled systems based on data filtering [11]; Wang et al discussed filtering based recursive least squares algorithm for Hammerstein nonlinear FIR-MA systems [12]; Wang proposed a filtering and auxiliary model-based recursive least squares identification algorithm for output error moving average systems [15]; Shi and Fang developed a recursive algorithm for parameter estimation by modifying the Kalman filterbased algorithm after designing a missing output estimator [16]; and Wang et al derived a hierarchical generalized stochastic gradient algorithm and a filtering based hierarchical stochastic gradient algorithm to estimate the parameter vectors and parameter matrix of the multivariable colored noise systems by using the hierarchical identification principle [17]

Summary

Introduction

Studies on identification methods have been active in recent years [1,2,3]. The recursive least squares algorithm is a popular and important identification method for many different systems [4,5,6]. Hu proposed an iterative and recursive least squares estimation algorithm for moving average systems [10]. Li proposed parameter estimation for Hammerstein controlled autoregressive moving average systems based on the Newton iteration [22]. Yao and Ding derived a two-stage least squares based iterative identification algorithm for controlled autoregressive moving average (CARMA) systems; the basic idea is to decompose a CARMA system into two subsystems and to identify each subsystem, respectively [23]. This paper considers the identification problems of two-input singleoutput controlled autoregressive moving average systems by using input-output data filtering and derives a data filtering.

Data Filtering Based Recursive Least Squares Algorithm

The RELS Algorithm

Example

Conclusions