Functional Analytic Approach to a Classical Problem of Filtering Theory

Abstract

Filtering theory has been developed out of systematic study of one particularly important type of analytical representation namely, the representation in terms of past innovations. We present a model for the expected value the signal given the fast of the observations upto the present time where the noise is a standard Brownian motion process. The classical result of Benes and its generalization is studied through square integrable functions of Hilbert space. The innovation equivalence theorem leads to the convergence of adaptive process of the signal. Illustration is given one dimensional random process with uncorrelated increments. The computational part employs mat lab coding and the output shows the estimation of signal from the observation.