Asymptotically \(\epsilon\)-optimal nonparametric procedure for nonlinear filtering of stationary sequences with unknown statistical characteristics
type: Item
instance of: scholarly article
title: Asymptotically \(\epsilon\)-optimal nonparametric procedure for nonlinear filtering of stationary sequences with unknown statistical characteristics
zbMATH Open document ID: 0563.93064
author: Alexander V. Dobrovidov
published in: Automation and Remote Control
publication date: 1984-01-01T00:00:00Z
review text: A nonparametric procedure is given for the nonlinear filtering of Markov random sequences which are stationary in the narrow sense, whose state equations and family of finite-dimensional distributions are unknown. Such a procedure is based on a unique realization of the observed process with strong mixing under certain assumptions about the noise distribution in the observations. Asymptotically, i.e., for increasing length of the realization, the performance of this procedure differs by arbitrary \(\epsilon >0\) from optimal nonlinear filtering, which is based on completely known statistical characteristics of unobserved signals. Examples are considered and results of a model experiment are given.
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 60G10
Mathematics Subject Classification ID: 60G20
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 62M20
zbMATH DE Number: 3898737
zbMATH Keywords: unknown characteristics
zbMATH Keywords: nonparametric procedure
zbMATH Keywords: nonlinear filtering
zbMATH Keywords: Markov random sequences
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3898737