Minimax filtering of homogeneous random fields with white noise |
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Authors: | M P Moklyachuk S V Tatarinov |
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Institution: | 1. Kiev University, Ukraine
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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 . |
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