Recursive estimation based on an extended observation vector
type: Item
instance of: scholarly article
title: Recursive estimation based on an extended observation vector
zbMATH Open document ID: 0534.93060
author: N. A. Firsov
published in: Automation and Remote Control
publication date: 1983-01-01T00:00:00Z
review text: The author considers the construction of a suboptimal filtering algorithm of assigned order N with a memory of \(\tau\) steps for a partially observable stochastic sequence \(z_ t=(x_ t,y_ t)\) described by the system of difference equations \[ x_ t=a_ 1(t,\epsilon_ t)+b_ 1(t,\epsilon_ t)x_{t-1}+u_ 1(t-1)+d_ 1(t,\epsilon_ t)y_{t-1}, \] \[ y_ t=a_ 2(t,\epsilon_ t)+b_ 2(t,\epsilon_ t)x_{t- 1}+u_ 2(t-1)+d_ 2(t,\epsilon_ t)y_{t-1}, \] where the controls \(u_ 1(t-1)\) and \(u_ 2(t-1)\) are expressed linearly in terms of linear estimates of the unobservable component \(x_ t\) of \(z_ t\) on the basis of realizations of the observable component \(y_ t\) of \(z_ t\) and \(\epsilon_ t\) is a sequence of independent random vectors with independent components whose distribution is assumed to be known. The proposed algorithm gives estimates whose accuracy is higher than that of linear estimates, this being due to the use of polynomial functions of \(y_ t\).
reviewed by: A.Ponomarenko
Mathematics Subject Classification ID: 93E11
Mathematics Subject Classification ID: 62L12
Mathematics Subject Classification ID: 93E25
Mathematics Subject Classification ID: 93E10
Mathematics Subject Classification ID: 62M20
Mathematics Subject Classification ID: 60G35
zbMATH DE Number: 3849109
zbMATH Keywords: polynomial functions of the observable component
zbMATH Keywords: suboptimal filtering algorithm
zbMATH Keywords: partially observable stochastic sequence
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3849109