On the problem of robust filtering of homogeneous random fields. (English. Russian original) Zbl 0834.62094

Moklyachuk, M. P.; Tatarinov, S. V.

Theory Probab. Math. Stat. 46, 103-110 (1993); translation from Teor. Jmovirn. Mat. Stat. 46, 104-114 (1992).

Summary: The problem of optimal linear estimation of the transform \[ A\xi= \int_0^\infty \int_0^\infty a(t,s) \xi(-t, -s)dt ds \] of a homogeneous random field \(\xi (t,s)\) with spectral density \(f(\lambda, \mu)\) is considered in the case of given observations \(\xi (t, s)+ \eta (t, s)\) of the field for \(t,s\leq 0\), where \(\eta (t, s)\) is a random field, uncorrelated with \(\xi (t, s)\), having the density \(g( \lambda, \mu)\). The least favorable spectral densities \(f_0 (\lambda, \mu)\) and \(g_0 (\lambda, \mu)\) and robust (minimax) spectral characteristics of the optimal estimator of the transform \(A\xi\) are found for various classes of spectral densities \({\mathcal D}_f\) and \({\mathcal D}_g\).

MSC:

62M20	Inference from stochastic processes and prediction
62M40	Random fields; image analysis
60G60	Random fields
62M15	Inference from stochastic processes and spectral analysis

Keywords:

robust filtering; optimal linear estimation; homogeneous random field; spectral density; least favorable spectral densities