  This paper considers the simultaneous state and unknown input estimation for
continuous-discrete stochastic systems. Two types of approaches (with and
without modeling of unknown inputs) which can address this issue are
investigated. A novel continuous recursive four-step Kalman filter is proposed
and its asymptotic stability condition is established. A novel one-step unknown
input Kalman filter is proposed and has guaranteed stability when the number of
unknown inputs is equal to that of the measurements. The design of unknown
input Kalman filters and observers is unified. Furthermore, an adaptive
augmented Kalman filter which requires the modeling of unknown inputs is
introduced. The estimation error covariance of the recursive four-step Kalman
filter and the adaptive augmented Kalman filter is analyzed and compared.
Finally, simulation results demonstrate the effectiveness of the proposed
approaches.
