Minimax filtering of homogeneous random fields with white noise

Abstract

We consider mean-square optimal linear estimation of the transform

$$A\xi = \sum\limits_{k,j = 0}^\infty {a(k,j)} \xi ( - k, - j)$$

of the homogeneous random field ξ(k, j) with density f(λ, Μ) from the observations ξ(k, j) + η(k, j) with k ≤ 0, j ≤ 0, where η(k, j) is a random field with orthogonal values uncorrelated with ξ(k, j) (white noise). We determine the worst spectral densitiesf ₀(λ, Μ) ∈

and the minimax (robust) spectral characteristics of the optimal estimator of the transform Aξ for various density classes

.