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Identification of autoregressive models in the presence of additive noise
Author(s) -
Diversi Roberto,
Guidorzi Roberto,
Soverini Umberto
Publication year - 2008
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.989
Subject(s) - autoregressive model , autocorrelation , noise (video) , white noise , algorithm , computer science , system identification , monte carlo method , mathematics , statistics , data modeling , artificial intelligence , image (mathematics) , database
A common approach in modeling signals in many engineering applications consists in adopting autoregressive (AR) models, consisting in filters with transfer functions having a unitary numerator, driven by white noise. Despite their wide application, these models do not take into account the possible presence of errors on the observations and cannot prove accurate when these errors are significant. AR plus noise models constitute an extension of AR models that consider also the presence of an observation noise. This paper describes a new algorithm for the identification of AR plus noise models that is characterized by a very good compromise between accuracy and efficiency. This algorithm, taking advantage of both low and high‐order Yule–Walker equations, also guarantees the positive definiteness of the autocorrelation matrix of the estimated process and allows to estimate the equation error and observation noise variances. It is also shown how the proposed procedure can be used for estimating the order of the AR model. The new algorithm is compared with some traditional algorithms by means of Monte Carlo simulations. Copyright © 2007 John Wiley & Sons, Ltd.