Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 591639, 24 pages
Research Article

Robust Filtering for State and Fault Estimation of Linear Stochastic Systems with Unknown Disturbance

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

Received 16 February 2010; Revised 24 August 2010; Accepted 27 September 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 robust filter structure to solve the simultaneous state and fault estimation problem of linear stochastic discrete-time systems with unknown disturbance. The method is based on the assumption that the fault and the unknown disturbance affect both the system state and the output, and no prior knowledge about their dynamical evolution is available. By making use of an optimal three-stage Kalman filtering method, an augmented fault and unknown disturbance models, an augmented robust three-stage Kalman filter (ARThSKF) is developed. The unbiasedness conditions and minimum-variance property of the proposed filter are provided. An illustrative example is given to apply this filter and to compare it with the existing literature results.