Unbiased minimum-variance input and state estimation for systems with unknown inputs: A system reformation approach

This paper presents a system reformation based unbiased minimum-variance input and state estimation for systems with unknown inputs which can be reconstructed with a one-step delay. It is shown that, within this new filtering approach the optimal unknown input and state estimation can be simultaneously achieved through the filter developed by Gillijns and De Moor. An illustrative example is given to show the effectiveness of the proposed results. Moreover, under some additional assumptions the proposed system reformation can be easily extended to consider a multi-step delayed input estimation.