The classical Kalman filter (KF) provides a practical and efficient way for state estimation. It is, however, not applicable when the external excitations applied to the structures are unknown. Moreover, it is known the classical KF is only suitable for linear systems and can't handle the nonlinear cases. The aim of this paper is to extend the classical KF approach to circumvent the aforementioned limitations for the joint estimation of structural states and the unknown inputs. On the basis of the scheme of the classical KF, analytical recursive solution of an improved KF approach is derived a...
