This paper presents an optimal two-stage estimator for discrete-time stochastic systems subject to disturbances evolving in accordance with a dynamic state equation. The proposed two-stage estimator gives an optimum state estimate expressed as x/sub k/k//sup 1/=x/sub k/k//sup 1/+/spl beta//sub k/k/ x/sub k/k//sup 2/, where x/sub k/k//sup 1/ and x/sub k/k//sup 2/ are computed via two reduced-order filters and where /spl beta//sub k/k/ is the coupling term assuring the optimality of the solution.