On optimum distributed-parameter filter design for correlated measurement noise

The problem of designing an optimum filter for a general class of linear distributed-parameter systems with correlated in time and space measurement noise is studied. The input stochastic disturbance is assumed to be white in time, but it is allowed to have any correlation in space. The filter is designed by making use of a learning theorem which gives the mean value and covariance matrix of a conditional distributed-parameter random variable "X1(D) given X2(D)" where X1(D) = {X1(x):x??D} and X2(D) = {X2(x):x??D} are Gaussian variables with known mean values and covariance matrices. A numerical example is computed to illustrate the theory. The results of the paper may find applications in all areas where the information to be processed is distributed in space.