Unbiased minimum-variance state and fault estimation for linear systems with unknown input

This paper extends the existing results on joint input and state estimation to systems with arbitrary fault and unknown inputs. The objective is to derive an optimal filter in the general case where not only fault affect both the systems state and the output, but also the direct feedthrough matrix has arbitrary rank. The paper extends both the results of Bessaoudi and Ben Hmida (2013). [State and fault estimation of linear discrete time systems, (HIS 2013)]. 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. The relationship between the proposed filter and the existing literature results is also addressed. Finally, two numerical examples are given in order to illustrate the proposed method, in particular to solve the estimation of the simultaneous actuator and sensor fault problem and to make a comparison with the existing literature results.