Estimation of the parameters of autoregressive signals from colored noise-corrupted measurements

Abstract

This paper is concerned with identification of autoregressive (AR) model parameters using observations corrupted with colored noise. A novel formulation of an auxiliary least-squares estimator is introduced so that the autocovariance functions of the colored observation noise can be estimated in a straightforward manner. With this, the colored-noise-induced estimation bias can be removed to yield the unbiased estimate of the AR parameters. The performance of the proposed unbiased estimation algorithm is illustrated by simulation results. The presented work greatly extends the author's previous methods that were developed for identification of AR signals observed in white noise.