Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates
Estimating the parameters of the autoregressive (AR) random process is a problem that has been well-studied. In many applications, only noisy measurements of AR process are available. The effect of the additive noise is that the system can be modeled as an AR model with colored noise, even when the...
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doaj-1f43df0dd84f44cf81071af50198e7ec2020-11-25T03:36:06ZengMDPI AGEntropy1099-43002020-05-012257257210.3390/e22050572Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance UpdatesTodd K. Moon0Jacob H. Gunther1Electrical and Computer Engineering Department, Utah State University, Logan, UT 84332, USAElectrical and Computer Engineering Department, Utah State University, Logan, UT 84332, USAEstimating the parameters of the autoregressive (AR) random process is a problem that has been well-studied. In many applications, only noisy measurements of AR process are available. The effect of the additive noise is that the system can be modeled as an AR model with colored noise, even when the measurement noise is white, where the correlation matrix depends on the AR parameters. Because of the correlation, it is expedient to compute using multiple stacked observations. Performing a weighted least-squares estimation of the AR parameters using an inverse covariance weighting can provide significantly better parameter estimates, with improvement increasing with the stack depth. The estimation algorithm is essentially a vector RLS adaptive filter, with time-varying covariance matrix. Different ways of estimating the unknown covariance are presented, as well as a method to estimate the variances of the AR and observation noise. The notation is extended to vector autoregressive (VAR) processes. Simulation results demonstrate performance improvements in coefficient error and in spectrum estimation.https://www.mdpi.com/1099-4300/22/5/572autoregressive model estimationspectrum estimationVector AR modelRLS algorithm |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Todd K. Moon Jacob H. Gunther |
spellingShingle |
Todd K. Moon Jacob H. Gunther Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates Entropy autoregressive model estimation spectrum estimation Vector AR model RLS algorithm |
author_facet |
Todd K. Moon Jacob H. Gunther |
author_sort |
Todd K. Moon |
title |
Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates |
title_short |
Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates |
title_full |
Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates |
title_fullStr |
Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates |
title_full_unstemmed |
Estimation of Autoregressive Parameters from Noisy Observations Using Iterated Covariance Updates |
title_sort |
estimation of autoregressive parameters from noisy observations using iterated covariance updates |
publisher |
MDPI AG |
series |
Entropy |
issn |
1099-4300 |
publishDate |
2020-05-01 |
description |
Estimating the parameters of the autoregressive (AR) random process is a problem that has been well-studied. In many applications, only noisy measurements of AR process are available. The effect of the additive noise is that the system can be modeled as an AR model with colored noise, even when the measurement noise is white, where the correlation matrix depends on the AR parameters. Because of the correlation, it is expedient to compute using multiple stacked observations. Performing a weighted least-squares estimation of the AR parameters using an inverse covariance weighting can provide significantly better parameter estimates, with improvement increasing with the stack depth. The estimation algorithm is essentially a vector RLS adaptive filter, with time-varying covariance matrix. Different ways of estimating the unknown covariance are presented, as well as a method to estimate the variances of the AR and observation noise. The notation is extended to vector autoregressive (VAR) processes. Simulation results demonstrate performance improvements in coefficient error and in spectrum estimation. |
topic |
autoregressive model estimation spectrum estimation Vector AR model RLS algorithm |
url |
https://www.mdpi.com/1099-4300/22/5/572 |
work_keys_str_mv |
AT toddkmoon estimationofautoregressiveparametersfromnoisyobservationsusingiteratedcovarianceupdates AT jacobhgunther estimationofautoregressiveparametersfromnoisyobservationsusingiteratedcovarianceupdates |
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1724551067921809408 |