Far field shallow water horizontal wave number estimation given a linear towed array using fast maximum likelihood, matrix pencil and subspace fitting techniques

Kenneth J McPhillips, University of Rhode Island

Abstract

A new algorithm for the estimation of horizontal wave numbers in a far field, range independent, shallow water environment is developed. The algorithm consists of an optimal subspace estimation component along with a maximum likelihood component. Optimal subspace estimators are extended to incorporate the forward/backward method and solutions obtained via this improved formulation are subsequently iteratively refined by maximizing a compressed likelihood function of horizontal wave numbers only. Previously developed "fast" maximum likelihood estimators in conjunction with legacy gradient-based methods as well as a variety of matrix pencil algorithms are shown in this thesis to perform poorly in crowded signal environments. The algorithm proposed in this thesis proves to be an efficient wave number estimation algorithm which works well in difficult crowded signal environments, and it is shown to have significantly improved performance. The proposed algorithm can be employed in a variety of applications including inverse hydrodynamic problems such as waveguide classification, bottom tomography and source localization via methods like matched field processing. ^ The algorithm proposed in this thesis is shown to nearly achieve the Cramer-Rao bounds under both sparse and crowded signal conditions using a relatively short towed array while still maintaining reasonable processing requirements for between 2 and 10 modes. The proposed algorithm is capable of processing multiple data snapshots as well as measurement data from a horizontal array whose depth is varied but whose horizontal range with respect to the source is kept constant. The SNR threshold of the proposed algorithm is shown to be lower than fast maximum likelihood, matrix pencil and standalone optimal subspace based techniques. However, the estimation of a dozen or more closely spaced horizontal wave numbers in a noisy ocean environment given measurements from a towed linear array still remains a challenging estimation problem. ^

Subject Area

Mathematics

Recommended Citation

Kenneth J McPhillips, "Far field shallow water horizontal wave number estimation given a linear towed array using fast maximum likelihood, matrix pencil and subspace fitting techniques" (2007). Dissertations and Master's Theses (Campus Access). Paper AAI3276997.
http://digitalcommons.uri.edu/dissertations/AAI3276997

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