A mapping result between Wiener theory and Kalman filtering for nonstationary processes

A connection between Wiener theory and Kalman filtering is presented for discrete nonstationary finite-dimensional processes. A time-varying realization of input-output relation by matrix fraction description (MFD) form and the observer state-space form in operator notation are used to derive the innovation filters of the nonstationary processes and to express the Kalman gain in terms of Wiener theory. The results generalize the stationary case.