Optimal filtering for a class of stochastic distributed systems

Optimal distributed filters are designed for a class of linear Gaussian disturbed distributed-parameter systems. A direct approach, in which the Green's function and covariance matrices are expressed using a complete set of orthonormal basis, is used. Noisy measurements are assumed available at a finite number of fixed points in the space. The filter performance is demonstrated for a particular diffusion process together with the details of the numerical computations.