Quantifying non-linear effects in acoustic source localization

Abstract

Whenever acoustic source localization is considered, the assumed central hypothesis is the linearity of the acoustic wave. This hypothesis allows direct and inverse problems to be solved faster using the linearized Euler Equations or ray-tracing, for example. However, when considering high amplitude waves - acoustic shockwaves generated from a sniper shot, for instance - such simplification induces errors in the localization process. In the literature, acoustic source localization results relying on the linear hypothesis are considered to be acceptable without knowing how much error is made. This paper focuses on quantifying the errors due to non-linear effects on the source localization when the linear hypothesis is assumed. The proposed methodology consists of quantifying the accuracy of the sound source position by solving the Euler equations with a spectral difference scheme of order 3 for different configurations. First, a reference case in the linear regime is carefully computed. Then, the wave topologies are modified to resemble typical acoustical shockwaves: cylindrical N-wave signals from direct propagation and wall interaction are considered. The assessment is performed on multiple wave strengths and reflection angles to get a wide range of configurations from which errors due to the non-linear reflection will be thoroughly analysed.