Estimation Problems for Periodically Correlated Isotropic Random Fields

摘要: Spectral theory of isotropic random fields in Euclidean space developed by M. I. Yadrenko is exploited to find a solution the problem optimal linear estimation functional $$ A\zeta ={\sum\limits_{t=0}^{\infty}}\,\,\,{\int_{S_n}} \,\,a(t,x)\zeta (t,x)\,m_n(dx) $$ which depends on unknown values periodically correlated (cyclostationary with period T) respect time sphere S n E field ζ(t, x), t ∈ Z, x ∈ S . Estimates are based observations x) + θ(t, x) at points (t, t = − 1, − 2, ..., , where θ(t, an uncorrelated field. Formulas for computing value mean-square error and spectral characteristic estimate functional Aζ obtained. The least favourable densities minimax (robust) characteristics estimates determined some special classes densities.