Stochastic Systems

Optimal digital filtering of continuous signals in time lag systems

K. Yu. Polyakov

State Marine Technical University of St. Petersburg

Abstract: The problem of the optimal estimation of continuous processes by discrete measurements in the presence of time lag (delay) is considered. On the basis of the theory of parametric transfer functions, an optimal, periodically nonstationary filter is developed, which affords a minimum of the estimation error variance at any instant of time. The comparison is performed of the obtained solution with the optimal stationary filter, which ensures a minimum of the mean (by continuous time) error variance. It is shown that in the problem of estimation of the Markov process of the first order, a simpler stationary filter with the fixer of order zero is insignificantly inferior to the optimal filter.

PACS: 02.30.Yy

Presented by the member of Editorial Board: B. T. Polyak

Received: 30.05.2005

 English version: Automation and Remote Control, 2008, 69:5, 858–873

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