Unbiased identification of autoregressive signals observed in colored noise

Autoregressive (AR) modeling has played an important role in many signal processing applications. This paper is concerned with identification of 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 method that was developed for identification of AR signals observed in white noise.