Affiliation:
1. National Technical University of Ukraine
2. Taras Shevchenko National University of Kyiv
Abstract
The problem of optimal linear estimation of functionals depending on the unknown values of a random fieldζ(t,x), which is mean-square continuous periodically correlated with respect to time argumenttє R and isotropic on the unit sphere Sn with respect to spatial argumentxєSn. Estimates are based on observations of the fieldζ(t,x) +Θ(t,x) at points (t,x) :t< 0;xєSn, whereΘ(t,x) is an uncorrelated withζ(t,x) random field, which is mean-square continuous periodically correlated with respect to time argumenttє R and isotropic on the sphereSnwith respect to spatial argumentxєSn. Formulas for calculating the mean square errors and the spectral characteristics of the optimal linear estimate 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 favourable spectral densities and the minimax (robust) spectral characteristics are proposed in the case where the spectral densities are not exactly known while a class of admissible spectral densities is given.
Subject
General Environmental Science
Reference51 articles.
1. P. Adshead, W. Hu, Fast computation of first-order feature-bispectrum corrections, Phys. Rev. D. 85(10) (2012) 103531.
2. J. Antoni, Cyclostationarity by examples, Mechanical Systems and Signal Processing. 23(4) (2009) 987-1036.
3. J.G. Bartlett, The standard cosmological model and CMB anisotropies, New Astron. Rev. 43(2) (1999) 83-109.
4. N. Cressie, C.K. Wikle, Statistics for spatio-temporal data, Wiley Series in Probability and Statistics, John Wiley & Sons, (2011).
5. I.I. Dubovets'ka, O. Yu. Masyutka, M.P. Moklyachuk, Filtering problems for periodically correlated isotropic random fields, Mathematics and Statistics. 2(4) (2014) 162-171.