6 research outputs found
Performance bounds on matched-field methods for source localization and estimation of ocean environmental parameters
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2001Matched-field methods concern estimation of source location and/or ocean environmental
parameters by exploiting full wave modeling of acoustic waveguide propagation.
Typical estimation performance demonstrates two fundamental limitations.
First, sidelobe ambiguities dominate the estimation at low signal-to-noise ratio (SNR),
leading to a threshold performance behavior. Second, most matched-field algorithms
show a strong sensitivity to environmental/system mismatch, introducing some biased
estimates at high SNR.
In this thesis, a quantitative approach for ambiguity analysis is developed so that
different mainlobe and sidelobe error contributions can be compared at different SNR
levels. Two large-error performance bounds, the Weiss-Weinstein bound (WWB)
and Ziv-Zakai bound (ZZB), are derived for the attainable accuracy of matched-field
methods. To include mismatch effects, a modified version of the ZZB is proposed.
Performance analyses are implemented for source localization under a typical shallow
water environment chosen from the Shallow Water Evaluation Cell Experiments
(SWellEX). The performance predictions describe the simulations of the maximum
likelihood estimator (MLE) well, including the mean square error in all SNR regions
as well as the bias at high SNR. The threshold SNR and bias predictions are also
verified by the SWellEX experimental data processing. These developments provide
tools to better understand some fundamental behaviors in matched-field performance
and provide benchmarks to which various ad hoc algorithms can be compared.Financial support for my research was provided by the Office of Naval Research
and the WHOI Education Office
A Nonparametric Approach to Segmentation of Ladar Images
The advent of advanced laser radar (ladar) systems that record full-waveform signal data has inspired numerous inquisitions which aspire to extract additional, previously unavailable, information about the illuminated scene from the collected data. The quality of the information, however, is often related to the limitations of the ladar camera used to collect the data. This research project uses full-waveform analysis of ladar signals, and basic principles of optics, to propose a new formulation for an accepted signal model. A new waveform model taking into account backscatter reflectance is the key to overcoming specific deficiencies of the ladar camera at hand, namely the ability to discern pulse-spreading effects of elongated targets. A concert of non-parametric statistics and familiar image processing methods are used to calculate the orientation angle of the illuminated objects, and the deficiency of the hardware is circumvented. Segmentation of the various ladar images performed as part of the angle estimation, and this is shown to be a new and effective strategy for analyzing the output of the AFIT ladar camera
Applied stochastic eigen-analysis
Submitted in partial fulfillment of the requirements for the degree of
Doctor of Philosophy at the Massachusetts Institute of Technology and the
Woods Hole Oceanographic Institution February 2007The first part of the dissertation investigates the application of the theory of large
random matrices to high-dimensional inference problems when the samples are drawn
from a multivariate normal distribution. A longstanding problem in sensor array processing
is addressed by designing an estimator for the number of signals in white noise
that dramatically outperforms that proposed by Wax and Kailath. This methodology is
extended to develop new parametric techniques for testing and estimation. Unlike techniques
found in the literature, these exhibit robustness to high-dimensionality, sample
size constraints and eigenvector misspecification.
By interpreting the eigenvalues of the sample covariance matrix as an interacting
particle system, the existence of a phase transition phenomenon in the largest (“signal”)
eigenvalue is derived using heuristic arguments. This exposes a fundamental limit on
the identifiability of low-level signals due to sample size constraints when using the
sample eigenvalues alone.
The analysis is extended to address a problem in sensor array processing, posed by
Baggeroer and Cox, on the distribution of the outputs of the Capon-MVDR beamformer
when the sample covariance matrix is diagonally loaded.
The second part of the dissertation investigates the limiting distribution of the
eigenvalues and eigenvectors of a broader class of random matrices. A powerful method
is proposed that expands the reach of the theory beyond the special cases of matrices
with Gaussian entries; this simultaneously establishes a framework for computational
(non-commutative) “free probability” theory.
The class of “algebraic” random matrices is defined and the generators of this class
are specified. Algebraicity of a random matrix sequence is shown to act as a certificate
of the computability of the limiting eigenvalue distribution and, for a subclass, the limiting
conditional “eigenvector distribution.” The limiting moments of algebraic random
matrix sequences, when they exist, are shown to satisfy a finite depth linear recursion
so that they may often be efficiently enumerated in closed form. The method is applied
to predict the deterioration in the quality of the sample eigenvectors of large algebraic
empirical covariance matrices due to sample size constraints.I am grateful to the National Science Foundation for supporting this work via grant
DMS-0411962 and the Office of Naval Research Graduate Traineeship awar