### Journals Information

**
Mathematics and Statistics Vol. 2(4), pp. 162 - 171 DOI: 10.13189/ms.2014.020402 Reprint (PDF) (137Kb) **

## Filtering Problems for Periodically Correlated Isotropic Random Fields

**Iryna Dubovets’ka ^{1}, Oleksandr Masyutka ^{2}, Mikhail Moklyachuk ^{1}^{,*}**

^{1}Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine

^{2}Department of Mathematics and Theoretical Radiophysics, Taras Shevchenko National University of Kyiv, Kyiv 01601, Ukraine

**ABSTRACT**

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

**KEYWORDS**

Random Field, Filtering, Robust Estimate, Mean Square Error, Least Favorable Spectral Densities, Minimax Spectral Characteristic

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Iryna Dubovets’ka , Oleksandr Masyutka , Mikhail Moklyachuk , "Filtering Problems for Periodically Correlated Isotropic Random Fields," Mathematics and Statistics, Vol. 2, No. 4, pp. 162 - 171, 2014. DOI: 10.13189/ms.2014.020402.

(b). APA Format:

Iryna Dubovets’ka , Oleksandr Masyutka , Mikhail Moklyachuk (2014). Filtering Problems for Periodically Correlated Isotropic Random Fields. Mathematics and Statistics, 2(4), 162 - 171. DOI: 10.13189/ms.2014.020402.