A new look at parameter estimation of autoregressive signals from noisy observations

Abstract

This paper is concerned with parameter estimation of autoregressive (AR) signals from noisy observations. A set of bilinear equations has been derived for noisy AR signal estimation. An analysis reveals that the derived set of bilinear equations can be efficiently solved by using the separable least-squares method. That is, estimation of the observation noise variance can be conducted separately from that of the AR parameters. Once the observation noise variance has been estimated, an estimate of the AR parameters can be easily obtained without involving any iteration procedure. It is also shown that the estimate of the observation noise variance can be improved by using an overdetermined set of bilinear equations. Numerical results are given to demonstrate the effectiveness of the proposed estimation algorithm.