A joint technique for autoregressive spectral estimation from noisy observations

This paper deals with the problem of autoregressive (AR) spectral estimation from a finite set of noisy observations without a priori knowledge of additive noise power. A joint technique is proposed based on the high-order and true-order AR model fitting; to the observed noisy process. The first approach utilizes the uncompensated lattice filter algorithm to estimate the parameters of the over-parameterized AR model and is one-pass. The latter uses the noise compensated low-order Yule-Walker (LOYW) equations to estimate the true-order AR model parameters and is iterative. The desired AR parameters, equivalently the roots, are extracted from the over-parameterized model roots using a root matching technique that utilizes the results obtained from the second approach. In addition, an approach based on fuzzy logic is adopted for calculating the step size adaptively with the cost function to reduce the computational time of the iterative total search technique. Finally, several numerical examples are presented to evaluate the performance of the proposed scheme.