Mathematical Problems in Engineering
Volume 2003 (2003), Issue 3, Pages 93-101
Study of a least-squares-based algorithm for
autoregressive signals subject to white noise
School of Quantitative Methods and Mathematical Sciences (QMMS), University of Western Sydney, Penrith South DC, NSW 1797, Australia
Received 16 October 2002
Copyright © 2003 Wei Xing Zheng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A simple algorithm is developed for unbiased parameter
identification of autoregressive (AR) signals subject to white
measurement noise. It is shown that the corrupting noise
variance, which determines the bias in the standard least-squares
(LS) parameter estimator, can be estimated by simply using the
expected LS errors when the ratio between the driving noise
variance and the corrupting noise variance is known or obtainable
in some way. Then an LS-based algorithm is established via the
principle of bias compensation. Compared with the other LS-based
algorithms recently developed, the introduced algorithm requires
fewer computations and has a simpler algorithmic structure.
Moreover, it can produce better AR parameter estimates whenever a
reasonable guess of the noise variance ratio is available.