Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 343586, 17 pages
Research Article

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

1Electrical Engineering Department, ESSTT-C3S, 5 Avenue Taha Hussein, BP 56, 1008 Tunis, Tunisia
2Electrical Engineering Department, CRAN (CNRS UMR 7039), 2 Avenue de la forêt de Haye, 54516 Vandœuvre-les-Nancy Cedex, France

Received 5 October 2009; Revised 2 January 2010; Accepted 11 January 2010

Academic Editor: J. Rodellar

Copyright © 2010 Fayçal Ben Hmida et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.