Further results on 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-fitted 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-fitted model roots using a root matching technique that utilizes the results obtained from the second approach. This method is highly accurate and is particularly suitable for cases where the system of unknown equations are strongly nonlinear at low SNR and uniqueness of solution from the LOYW equations cannot be guaranteed. In addition, 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. Several numerical examples are presented to evaluate the performance of the proposed scheme in this paper.
spectral estimation additive noise fuzzy logic autoregressive system iterative method