Adaptive algorithm for noisy autoregressive signals
type: Item
instance of: scholarly article
title: Adaptive algorithm for noisy autoregressive signals
zbMATH Open document ID: 0996.93094
DOI: 10.1155/S1024123X00001472
author: Wei Xing Zheng
published in: Mathematical Problems in Engineering
publication date: 2002-08-20T00:00:00Z
full work available at URL: https://eudml.org/doc/49484
review text: A new form of a direct adaptive improved least-squares (ILS) algorithm is proposed for on-line estimation of autoregressive (AR) signals corrupted by additive white noise. The AR random process \(x(t)\) is defined as \(x(t)= a_{1}x(t-1)+\dots +a_{p}x(t-p)+\nu(t)\), where \(\nu(t)\) is a driving white noise having variance \(\sigma^{2}_{\nu}\), and the noisy measurement of the AR signal is described by \(y(t)=x(t)+w(t),\) where \(w(t)\) is another white noise having variance \(\sigma^{2}_{w}\). The white noises are supposed to be independent. The proposed algorithm is characterized by its direct AR parameter estimation structure. The algorithm itself consists of five steps that include initialization, recursive procedure of calculation of LS-estimates of the vector \(a=(a_1,\dots ,a_p)\), evaluation of covariance estimates, computing the measurement noise variance estimate and finding the AR estimate via LS-estimates and noise variance estimate. The algorithm can give consistent parameter estimates in a very direct manner, it does not involve dealing with an augmented noisy AR model. The new algorithm is demonstrated to outperform the previous ILS based methods in terms of its improved numerical efficiency.
Mathematics Subject Classification ID: 93E24
Mathematics Subject Classification ID: 93E10
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 1569511
zbMATH Keywords: adaptive parameter estimation
zbMATH Keywords: autoregressive signals
zbMATH Keywords: noisy observations
zbMATH Keywords: least-square algorithm
zbMATH Keywords: covariance estimates
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
OpenAlex ID: W2006842586
description: scientific article; zbMATH DE number 1569511