Medium Inhomogeneities and Instabilities: Effects on Spatial and Temporal Processing

Linear time-invariant space-variant filters and the parabolic equation approximation

“…. Also note that the transfer function derived in this section is written as the product of two functions, one deterministic and the other random which agrees with the assumed transfer function expression of Laval and Labasque [36] and with the general practice of representing a field in a random medium as the product of a deterministic and a random function [43]. Note that the form of eq.…”

“…Some work has been done in treating the ocean medium as a linear, time-variant, space-variant, random filter by Laval [9,35] and Laval and Labasque [36]. However, the notation used to incorporate the space-variant property is ad hoc, i.e., spatial variables are simply included in the arguments of the impulse response and transfer functions, for example, rather than having evolved from a systematic and consistent notation based upon linear, time-varying, space-varying systems theory.…”

“…However, the notation used to incorporate the space-variant property is ad hoc, i.e., spatial variables are simply included in the arguments of the impulse response and transfer functions, for example, rather than having evolved from a systematic and consistent notation based upon linear, time-varying, space-varying systems theory. In addition, Laval and Labasque [36] assume functional forms for the ocean transfer function instead of deriving them. Middleton [37,38] also studied underwater acoustic propagation in a random, inhomogeneous ocean, but did not concern himself directly with the derivation of random, time-variant, space-variant ocean transfer functions.…”

Source localization in a shallow-water channel with a rough surface

“…The knowledge of ν allows one to obtain the optimum robust matrixD(θ θ θ) according to (3) and, as a consequence, estimate the source position of interest…”

“…In such a situation, matching can be performed only in a statistical sense. As a result, the knowledge of the spatial signal correlation matrix along the array aperture is of the uppermost importance to optimize the signal processing techniques and, therefore, to decrease a coherence-induced degradation of the array processor performance (see, e.g., [3]- [9]). However, the complete information about a stochastic underwater channel is rarely available under most practical scenarios and effective estimation algorithms must be developed to improve robustness against statistical mismatch.…”