Generalized two-stage Kalman estimator

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(k/k)(1) = x(k/k)(-1) + beta(k/k)x(k/k)(2), where x(k/k)(-1) and x(k/k)(2) are computed via two reduced-order filters and where beta(k/k) is the coupling term assuring the optimality of the solution.