State and fault estimation of linear stochastic discrete time systems

This paper studies the problem of simultaneously estimating the state and the fault of linear stochastic discrete-time varying systems with 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 systems. We study the case when the direct feedthrough matrix of the fault has full rank. This paper extends previous work by considering that the noises affect the state and measurement output are correlated. A numerical example is given in order to illustrate the performance of the proposed filter.