Filtering-Based Parameter Identification Methods for Multivariable Stochastic Systems

Huafeng Xia,Feiyan Chen

doi:10.3390/math8122254

Abstract

This paper presents an adaptive filtering-based maximum likelihood multi-innovation extended stochastic gradient algorithm to identify multivariable equation-error systems with colored noises. The data filtering and model decomposition techniques are used to simplify the structure of the considered system, in which a predefined filter is utilized to filter the observed data, and the multivariable system is turned into several subsystems whose parameters appear in the vectors. By introducing the multi-innovation identification theory to the stochastic gradient method, this study produces improved performances. The simulation numerical results indicate that the proposed algorithm can generate more accurate parameter estimates than the filtering-based maximum likelihood recursive extended stochastic gradient algorithm.

Highlights

System identification is the theory and methods of establishing the mathematical models of dynamical systems [1,2,3,4,5] and some identification approaches have been proposed for scalar systems and multivariable systems [6,7,8,9,10,11]
The present study aims to investigate a more efficient algorithm based on the maximum likelihood principle, the negative gradient search, the data filtering, and the multi-innovation identification theory
A filtering and maximum likelihood-based recursive least-squares algorithm is available for multivariable systems with complex structures and colored noises [32], there remains a need for enhancing the parameter estimation accuracy with computational efficiency

Summary

Introduction

System identification is the theory and methods of establishing the mathematical models of dynamical systems [1,2,3,4,5] and some identification approaches have been proposed for scalar systems and multivariable systems [6,7,8,9,10,11]. The present study aims to investigate a more efficient algorithm based on the maximum likelihood principle, the negative gradient search, the data filtering, and the multi-innovation identification theory. A filtering and maximum likelihood-based recursive least-squares algorithm is available for multivariable systems with complex structures and colored noises [32], there remains a need for enhancing the parameter estimation accuracy with computational efficiency. Motivated by these considerations, this paper has the following contributions:. A filtering-based multivariable maximum likelihood multi-innovation extended stochastic gradient (F-M-ML-MIESG) algorithm is proposed for improved parameter estimation accuracy while retaining desired computational performance.

The System Description and Identification Model

The F-M-ML-RESG Algorithm

Consider the following

Conclusions