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

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.

Novel optimal recursive filter for state and fault estimation of linear stochastic systems with unknown disturbances

“…We consider the numerical example used by Ben Hmida et al (2010). In this simulation, three cases of F y k will be studied:…”

“…This may be achieved by making use of unbiased minimum-variance estimation. The proposed filter can play a significant role in several applications, e.g., the model-based Fault Detection and Isolation (FDI) problem (Ben Hmida et al, 2010;Chen and Patton, 1996;1999) and the Fault Tolerant Control (FTC) problem (Blanke et al, 2006).…”

“…The FDI problem for linear systems without and with unknown disturbances has been thoroughly investigated (Nikoukhah, 1994;Keller, 1998;1999;Keller and Sauter 2011;Jamouli et al, 2003, Chen andPatton, 1996;1999;Ben Hmida et al, 2010). Keller (1999) designed a fullorder Kalman filter under a particular eigenstructure assignment.…”

“…In this paper, we extend the version of Ben Hmida et al (2010) to further propose a new recursive optimal filter structure. The fault affects both the state and output equations where the direct feedthrough matrix has arbitrary rank, whereas the unknown disturbances only affect the state system equation, without any prior information about their dynamical evolution.…”

“…The aim of this paper is to extend the results of Ben Hmida et al (2010) in order to derive a new recursive optimal filter structure to obtain a better fault and state estimation when 0 < rank (F y k ) ≤ p in spite of the presence of the unknown disturbances d k .…”