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.
