Abstract
The purpose of this paper is to present a filtering technique for distributed parameter systems with random coefficients. Two kinds of systems are considered. One is modeled by a partial differential equation of parabolic type and the other by that of hyperbolic type. In the both systems, the statistics of random coefficients are assumed to be white Gaussian.
Based on the concept of stochastic eigenvalue problems, properties of the solution processes to the system equations are first discussed. Then, the Radon-Nikodym derivative is given which plays an important role to derive the filtering equation. Under the criterion of the minimal variance estimate, a precise form of the filter dynamics is derived, reflecting the nonlinearity due to the existence of random coefficients.
The latter half of this paper is devoted to describe an approximated filter dynamics by the Gaussian assumption, and to show results of digital simulation experiments.
