Two-stage estimator for dynamic stochastic systems subject to unknown inputs and random bias

The purpose of this paper is to give an optimal solution of a two-stage estimator for discrete-time stochastic systems subject to unknown inputs, random biases or any disturbances evolving in accordance with a dynamic state equation. The proposed two-stage Kalman filter is based on the use of the maximum likelihood descriptor Kalman filter developed by Nikoukhah et al. applied here for state estimation of dynamic systems subject to unknown inputs. Necessary and sufficient conditions for convergence and stability of the proposed two-stage Kalman estimator are established.