Stochastic Systems

Linear optimal estimation of nonstationary random processes and factorization of correlation operators

O. A. Petrov, V. N. Fomin

Leningrad

Abstract: The problem of developing a linear optimal filter is considered in the framework of the correlation theory. The solution is obtained by factorization of the correlation operator of the observed process in the time domain and so the conventional Kolmogorov — Wiener theory is extended to nonstationary random processes. This leads to an operator method of solving the nonstationary Wiener — Hopf equation which is ideologically kindred with the well-known Wiener — Hopf method of solving integral equations of the convolution type on a semi- axis and the operator of an optimal filter is represented in a uniform way for extrapolation, interpolation, and filtering of nonstationary random processes.

UDC: 519.23.2


Received: 03.02.1987

 English version: Automation and Remote Control, 1988, 49:7, 887–895

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