Especially in online and real-time applications, the importance of adaptive algorithms is well known in. Autoregressive parameters are important for model identification, prediction, spectral estimation and filtering.Hence, AAR parameters are useful the time-varying (non-stationary) applicationsof modelling, spectral estimation, prediction and filtering. (For stationary AR models see also the TSA toolbox )

This page deals with the adaptive estimation of autoregressive (including ARMA) model parameters. For AAR estimation, Kalman filtering, Recursive Least Squares(RLS) and the Least Mean Squares (LMS) algorithms are usually used.
AAR modelling can be seen as a time-frequency analysis (TFA) method. Hence, the principle of uncertainty between time and frequency domain has to be considered. On the other hand, all AAR algorithms require to select a modelorder p and an update coefficient UC (or forgetting factor). The references [1-3] describe a method, [p,UC] can be found. If the optimum [p,UC] is identified, also the optimal time-frequency resolution of a given signalis obtained.

Download the AAR estimation algorithm for Matlab

Reference(s):

[1] Alois Schlögl (2000)
The electroencephalogram and the adaptive autoregressive model: theory and applications
Shaker Verlag , Aachen, Germany,(ISBN3-8265-7640-3).
short presentation * * Table of Content (*.ps 106kB)

[2] A. Schlögl, S.J. Roberts, G. Pfurtscheller (2000)
A criterion for adaptive autoregressive models.
World Congress on Medical Physics and Biomedical Engineering, Jul. 23-28, 2000, Chicago.
Short Paper pdf(55kb) - - short presentation

[3] A. Schlögl and G. Pfurtscheller (1998)
Considerations on Adaptive Autoregressive Modelling in EEG Analysis,
Proc. of First International Sysmposium on Communication Systemsand Digital Signal Processing CSDSP'98, ISBN 0-86339-7719 Sheffield,UK 6-8. April 1998, pp.367-370.
Abstract (Postscript 41kB) * Paper (Postscript 195kB)

(Click here for more references and applications)

Copyright © 1997-2001 by A. Schloegl