Minimax approach to the estimation problem for homogeneous random fields

The problem of the mean-square optimal estimation of the linear functionals which depend on the unknown values of a multidimensional homogeneous random field from observations of the field with noise is considered.

The minimax (robust) method of estimation is applied in the case where the spectral densities of the fields are not known exactly while some sets of admissible spectral densities are given.

Formulas that determine the least favourable spectral densities and the minimax spectral characteristics are derived for some special sets of admissible densities.