Unbiased minimum-variance filtering for delayed input reconstruction

The unknown inputs in a dynamical system may represent unknown external drivers, input uncertainty, state uncertainty, or instrument faults and thus unknown-input reconstruction has several important applications. In this paper, we consider delayed state estimation and input reconstruction. That is, we develop filters that recursively use current measurements to estimate past states and reconstruct past inputs. By introducing this delay, recursive input reconstruction is viable for a potentially broader class of systems.