The equivalent source method has been one of the most commonly used methods for sound source localization. It involves equivalent sources spread over the source plane (or region). The pressure fields from these equivalent sources are usually spherical harmonics. But, the spherical harmonic
fields are derived for the Sommerfeld boundary condition with no reflection or reverberation. Data-driven methods help perform sound source localization in a reverberant environment when no prior information about the surroundings is available. The methods studied are linear regression (LR)
with Adam, linear regression with L-BFGS, multi-layer perceptron (MLP) with one and two hidden layers. The simulations are conducted for two monopoles in rooms with different reverberation times and compared with one norm convex optimization (L1CVX). It is observed that overall, LR with L-BFGS
gave the best results. Also, for low reverberation time, LR with L-BFGS was able to localize the sources better than L1CVX.
In recent times, equivalent source method-based near-field acoustic holography methods have been extensively applied in sound source localization and characterization. The most commonly used equivalent sources are spherical harmonics. In a non-reverberant environment with no reflections, these equivalent sources could be the best choice since spherical harmonics are derived for the Sommerfeld boundary condition. However, these methods are not the best fit for reverberating environments. In such cases, a new relationship can be calculated between the field weights and the measured pressure with enough training examples. The proposed machine learning models include linear regression (LR) with adaptive moment estimation (Adam), LR with limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS), and multi-layer perceptron with one and two hidden layers. These methods are tested for multiple monopoles and vibrating plate simulations in a room with different wall absorption coefficients. The data-driven methods are also studied on loudspeakers numerically and experimentally in a free field environment. The results from these methods are compared with the results of one norm convex optimization (L1CVX). LR with L-BFGS performed the best among all the methods studied and performed better than L1CVX for less absorption coefficient for geometrically separable sources. LR with L-BFGS also has much faster inference times.
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