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.