Unbiased Minimum-Variance Filter for State and Fault Estimation of Linear Time-Varying Systems with Unknown Disturbances

Fayçal Ben Hmida,Karim Khémiri,Moncef Gossa,José Ragot

doi:10.1155/2010/343586

Abstract

This paper presents a new recursive filter to joint fault and state estimation of a linear time-varying discrete systems in the presence of unknown disturbances. The method is based on the assumption that no prior knowledge about the dynamical evolution of the fault and the disturbance is available. As the fault affects both the state and the output, but the disturbance affects only the state system. Initially, we study the particular case when the direct feedthrough matrix of the fault has full rank. In the second case, we propose an extension of the previous case by considering the direct feedthrough matrix of the fault with an arbitrary rank. The resulting filter is optimal in the sense of the unbiased minimum-variance (UMV) criteria. A numerical example is given in order to illustrate the proposed method.

Highlights

This paper presents a new recursive filter to joint fault and state estimation of a linear timevarying discrete systems in the presence of unknown disturbances
We propose an extension of the previous case by considering the direct feedthrough matrix of the fault with an arbitrary rank
This paper is concerned with the problem of joint fault and state estimation of linear timevarying discrete-time stochastic systems in the presence of unknown disturbances

Summary

Introduction

This paper is concerned with the problem of joint fault and state estimation of linear timevarying discrete-time stochastic systems in the presence of unknown disturbances. Gillijns and Moor have treated the problem of estimating the state in the presence of unknown inputs which affect the system model They developed a recursive filter which is optimal in the sense of minimumvariance. This filter has been extended by the same authors for joint input and state estimation to linear discrete-time systems with direct feedthrough where the state and the unknown input estimation are interconnected. We develop a new recursive filter to joint fault and state estimation for linear stochastic, discrete-time, and time-varying systems in the presence of unknown disturbances.

Statement of the Problem

Filter Design

Extended UMV Fault and State Estimation

Summary of Filter Equations

An Illustrative Example

Conclusion