Estimates of Periodically Correlated Isotropic Random Fields

the long version

We propose results of the investigation of the problem of the mean square optimal estimation of linear functionals which depend on the unknown values of periodically correlated isotropic random fields. Estimates are based on observations of the fields with a noise. Formulas for computing the value of the mean-square errors and the spectral characteristics of the optimal linear estimates of functionals are derived in the case of spectral certainty, where the spectral densities of the fields are exactly known. Formulas that determine the least favorable spectral densities and the minimax-robust spectral characteristics of the optimal estimates of functionals are proposed in the case of spectral uncertainty, where the spectral densities are not exactly known while some sets of admissible spectral densities are specified.