Table of Contents
ISRN Signal Processing
Volume 2011 (2011), Article ID 138683, 10 pages
http://dx.doi.org/10.5402/2011/138683
Research Article

Linear Estimation of Stationary Autoregressive Processes

1Engineering Department, Persian Gulf University, Davvas, 75169-13798 Bushehr Port, Iran
2Advanced Communication Research Center, Sharif University of Technology, P.O. Box 11356-11155, Tehran, Iran

Received 1 December 2010; Accepted 12 January 2011

Academic Editors: K. M. Prabhu and A. Tefas

Copyright © 2011 Reza Dianat and Farokh Marvasti. 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.

Abstract

Consider a sequence of an π‘š th-order Autoregressive (AR) stationary discrete-time process and assume that at least π‘š βˆ’ 1 consecutive neighboring samples of an unknown sample are available. It is not important that the neighbors are from one side or are from both the left and right sides. In this paper, we find explicit solutions for the optimal linear estimation of the unknown sample in terms of the neighbors. We write the estimation errors as the linear combination of innovation noises. We also calculate the corresponding mean square errors (MSE). To the best of our knowledge, there is no explicit solution for this problem. The known solutions are the implicit ones through orthogonality equations. Also, there are no explicit solutions when fewer than π‘š βˆ’ 1 samples are available. The order of the process ( π‘š ) and the feedback coefficients are assumed to be known.