Parameter estimation of autoregressive signals in presence of colored AR(1) noise as a quadratic eigenvalue problem

In this paper, we consider the problem of parameter estimation of autoregressive (AR) signals from observations corrupted with colored AR(1) noise. The proposed method is based on Yule-Walker equations. We express these equations as a quadratic eigenvalue problem and then the parameters of the signal and noise are estimated by solving this eigenvalue problem. We also apply the proposed method to the problem of sinusoidal frequency estimation in colored noise. The performance of the proposed algorithm is evaluated by computer simulation examples.