Optimal estimation in distributed systems described by the Green function

The paper is concerned with estimation of a time stationary field from measurements of quantities which are related with that field through linear integral operators with known Green functions. The problem is treated for the cases of scalar, vector finite dimensional and vector infinite dimensional (solid image) observation. In all these cases sets of partial integro-differential equations are obtained which are algorithms for optimal field estimation. Difference schemes of transformed algorithms may have a low dimension in computer implementation. For some particular cases general approximate formulae of estimation accuracy are obtained. Specific applications of the resultant algorithms are obtained.