Methods of Signal Processing

Optimum Linear Estimates for the Regression Coefficients of Isotropic Random Fields

M. I. Yadrenko


Abstract: Isotropic random fields (fields whose correlation functions are invariant under rotations about a fixed point) are discussed. Linear unbiased estimates optimum in the sense of minimizing the mean-square error are given for the regression coefficients when the random field is observed on a sphere. It turns out, in particular, that the optimum unbiased estimate of an unknown expectation coincides with the average over the sphere. Optimum nonlinear estimates for random regression coefficients are investigated.

UDC: 519.25

Received: 30.08.1971
Revised: 22.01.1973

 English version: Problems of Information Transmission, 1973, 9:3, 228–237

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