To Örebro University

We survey the problem of estimation of linear functionals which depend on the unknown values of a homogeneous random field ξ (k, j) in the perforated region K from observations of correlated random fields ξ (k, j)+ η (k, j) at points (x, y)∈ Z2< K is investigated. The formulas for calculating the mean square errors and the spectral characteristics of the optimal linear estimate of the functionals are obtained in the case when the spectral density of the fields is precisely known. We consider the formulas that determine the least favourable spectral densities and the minimax (robust) spectral characteristics in the case when the spectral densities are not exactly known, while the class of admissible spectral densities is given.