An information-based complexity approach to acoustic linear stochastic time-variant systems

Abstract

This thesis describes the formulation of a Computational Signal Processing (CSP) modeling framework for the analysis of underwater acoustic signals used in the search, detection, estimation, and tracking (SDET) operations of moving objects. The underwater acoustic medium where the signals propagate is treated as linear stochastic time-varying system exhibiting double dispersive characteristics, in time and frequency, simultaneously. Acoustic Linear Stochastic (ALS) time-variant systems are characterized utilizing what is known as time-frequency calculus. The interaction of wavefront acoustic pressure fields with underwater moving objects is modeled using what is termed Imaging Sonar and Scattering (ISS) operators. It is demonstrated how the proposed CSP modeling framework, called ALSISS, may be formulated as an aggregate of ALS systems and ISS operators. Furthermore, it is demonstrated how concepts, tools, methods, and rules from the field of Information-Based Complexity (IBC) are utilized to seek approximate solutions to NP-hard problems encountered in the analysis of underwater acoustic signals treated under the ALSISS modeling framework. Error approximation algorithms, formulated as approximate solutions, are implemented using convex optimization techniques. Finally, Kronecker products algebra is used as a mathematical language to formulate new variants of matching pursuit algorithms and to aid in the mapping of these algorithms to parallel computational structures.