Abstract

  The synthesis of coupled systems including linear propagation media and nonlinear lumped subsystems is investigated. The resulting coupled system is expected to exhibit improved dynamic behavior. Such improvements are sought after by designing exclusively the lumped nonlinear subsystem and not by modifying the propagation medium. The lumped subsystem can be static or dynamic as well as passive or active. The design method is based on the Volterra-Wiener theory of nonlinear systems combined with the Linear Fractional Transformation employed for the analysis of uncertain linear systems. Although the techniques are applicable to a variety of practical engineering and physical systems, this work addresses acoustic source localization. Indeed, a moving acoustic source can be considered to nonlinearly modify the characteristics of a carrier acoustic wave. Such an acoustic carrier might be a monochromatic or polychromatic tone as well as other broadband signals such as band-limited white or colored noise. The sound source position signal is propagated through a nonlinear operator and then, under noise-free environment assumptions, determines the sound pressure level at the receiver location. In this paper, the proposed method is applied to the simplified case of a one-dimensional acoustic cavity defined by totally reflective barriers. Furthermore, the lossless wave equation is assumed to govern the sound pressure level in the homogeneous domain of interest. However, even in this simple scenario, only the additional assumptions of negligible source velocity and acceleration allow the derivation of an expression for the sound pressure level containing exclusively source displacement. In this context, simulation data series or analytical solutions, approximate or exact, are post-processed in order to determine the Volterra kernels, which effectively are a convenient extension of the impulse response concept in the nonlinear case, of the operator connecting source displacement to sound pressure level at the receiver. The outcome is Linear Time Invariant models depicting the dominant sound propagation dynamics. Then the synthesis stage is based on the properties of interconnected nonlinear systems that are described in the Volterra-Wiener framework. By using such properties, the signal processing algorithm for the estimation of the acoustic source position based on the received sound pressure level is finally developed.

Keywords: Linear Systems; Frequency; Acoustic Pressure

References

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Citation

Citation: Nikolaos I Xiros. “Underwater Acoustic Localization Using Nonlinear Processing”. Acta Scientific Computer Sciences 2.2 (2020): 02-09.

Copyright

Copyright: © 2020 Nikolaos I Xiros. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.