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

Wei Xing Zheng

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.