Fuzzy incorporated noise compensation technique for autoregressive spectral estimation

Abstract

This thesis deals with the problem of autoregressive (AR) spectral estimation from a finite set of noisy observations without a priori knowledge of additive noise power. For single channel case 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. This method is highly accurate and is particularly suitable for cases where the system of unknown equations are strongly nonlinear at low SNRand uniqueness of solution from LOYW equations cannot be guaranteed. 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. An extension of the above method for the estimation of multichannel autoregressive power spectrum from a finite set of noisy observations is also proposed. In this case the method is based on the Yule-Walker equations and estimates the autoregressive parameters from a finite set of measured data and then the power spectrum. An inverse filtering technique is used to estimate the observation noise variance and AR parameters simultaneously. Two different algorithms are proposed to estimate the noise variances of all channels. First al- . gorithm is based on the gradient search technique of solving nonlinear equations and the second one is based on fuzzy incorporated iterative search.