The Hierarchical Iterative Identification Algorithm for Multi-Input-Output-Error Systems with Autoregressive Noise

Jiling Ding

doi:10.1155/2017/5292894

Abstract

This paper considers the identification problem of multi-input-output-error autoregressive systems. A hierarchical gradient based iterative (H-GI) algorithm and a hierarchical least squares based iterative (H-LSI) algorithm are presented by using the hierarchical identification principle. A gradient based iterative (GI) algorithm and a least squares based iterative (LSI) algorithm are presented for comparison. The simulation results indicate that the H-LSI algorithm can obtain more accurate parameter estimates than the LSI algorithm, and the H-GI algorithm converges faster than the GI algorithm.

Highlights

System identification studies mathematical models of dynamic systems by fitting experimental data to a suitable model structure [1, 2]
A hierarchical gradient based iterative (H-GI) algorithm and a hierarchical least squares based iterative (H-LSI) algorithm are presented by using the hierarchical identification principle
A gradient based iterative (GI) algorithm and a least squares based iterative (LSI) algorithm are presented for comparison

Summary

Introduction

System identification studies mathematical models of dynamic systems by fitting experimental data to a suitable model structure [1, 2]. For the sake of reducing the computational complexity, the hierarchical identification principle is utilized to transform a complex system into several subsystems and to estimate the parameter vector of each subsystem [23, 24], respectively In this literature, Schranz et al proposed a feasible hierarchical identification process for identifying the viscoelastic model of respiratory mechanics [25]. This paper focuses on the parameter estimation for output-error autoregressive (OEAR) systems using the hierarchical identification principle and the iterative identification principle and presents a hierarchical gradient based iterative (H-GI) algorithm and a hierarchical least squares based iterative (H-LSI) algorithm.

The Problem Formulation

The Gradient Based and Least Squares Based Iterative Algorithm

The Hierarchical Gradient Based Iterative Algorithm

The Hierarchical Least Squares Based Iterative Algorithm

Example

Conclusions