| dc.description |
The main contributions of this thesis are the development and
application of four computationally efficient solutions for
least-squares-based (LS-based) minimum variance spectral estimation
(MVSE). They are: (1) fast computational solution for the 1-D
covariance LS-based MVSE, (2) fast computational solution for the
1-D modified covariance LS-based MVSE, (3) fast computational
solution for the 2-D covariance LS-based MVSE, and (4) fast
computational solution for the 2-D modified covariance LS-based
MVSE. The four fast computational solutions not only significantly
reduce computational complexity and save memory from array to vector
sizing proportionalities, but they also inherit improved-feature
details from the corresponding direct methods of 1-D and 2-D
LS-based MVSEs. The two 2-D fast computational solutions numerically
produce the same results as the corresponding 1-D fast solutions
when the estimation order in one of the two dimensions is set to
zero.
MVSEs are high-resolution spectral estimators which have been used
extensively in the sensor community (for example, radar, sonar,
communication signal localization, and seismic velocity
discrimination) for extracting and resolving more features from
limited data collection apertures than traditional Fourier-based
techniques. Least-squares-based MVSEs are especially applicable in
the case that the autocorrelation is unknown and only 1-D or 2-D
finite data acquisitions are available. However, LS-based minimum
variance (MV) spectral estimators require intensive computational
burdens which limit their operational use. This thesis proposes 1-D
and 2-D fast computational solutions. The basis for the fast
solutions is the exploitation of the special structures of the
various inverse matrix relationships, which express the inverse of
autocorrelation matrices (or autocorrelation-like
quadratic-data-matrix product matrices in the case of the
least-squares algorithms) in terms of the parametric autoregressive
(AR) or linear prediction (LP) parameters. The fast algorithms also
have the serendipitous feature that all lower-order solutions are
obtained by the fast computational solutions without additional
computations, unlike the non-fast approaches. This is useful
especially when the correct order is unknown, requiring that a range
of orders to be evaluated to determine the order that produces the
best result using one algorithmic execution of a fast algorithm. |
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