Minimum-variance state estimation for uniform causal functional equations

Recently, a new class of time-domain state space models has been developed (Ref. 11 and 12) to describe layered media systems. When layers are uniform, the resulting state equations are referred to as uniform causal functional equations. In this paper we develop the minimum-variance state estimator for such equations. We are led to a natural form of parallel data processing for practical implementation of our estimator.