Applied stochastic Eigen-analysis

The 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.

Department dc:contributor.department

Joint Program in Applied Ocean Physics and Engineering

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2006

Author dc:creator

• Nadakuditi, Rajesh Rao

Advisor dc:contributor.advisor

• Alan Edelman.

• Electrical Engineering and Computer Science.
• /Woods Hole Oceanographic Institution. Joint Program in Applied Ocean Science and Engineering.
• Woods Hole Oceanographic Institution.

Statement dc:rights

• M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/38538

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/38538