Weiner and Kalman filters for systems with random parameters

A linear stationary optimal filtering problem is considered in which the plant dynamics and noise covariances are incompletely known. Unknown plant parameters in the plant model, such as gains and time constants, are treated as random variables with specified means and variances. Generalized Wiener and Kalman-Bucy filters are derived on the basis of transfer-function matrix or state-space representations of the plant, respectively. An application of the generalized filter to the linear quadratic optimal control of plants with unknown disturbances is also described and a certainty equivalence principle is shown to apply.