The analytical passive time reversal method (APTRM) is a powerful technique for sound source localization. In that technique, it generally requires that the frequency response function relating the measurement point to the focusing point should be known in advance. However, inside an enclosure of arbitrary shape, there is no theoretical formulation of this frequency response function, and using the APTRM with the free-field Green's function might lead to inaccurate localization of sound sources. This paper proposes a method combining the APTRM with the equivalent source method (ESM) to locate sound sources in an enclosure of arbitrary shape. In this method, the frequency response function relating the measurement point to the focusing point inside the enclosure is first calculated numerically using the ESM, and then the APTRM with this numerical frequency response function is used to realize the localization of sound sources. Numerical simulations in a rectangular enclosure and an enclosure of arbitrary shape as well as an experiment in a rectangular wooden cabinet are performed to verify the validity of the proposed method. The results demonstrate that the frequency response function in an enclosure can be accurately calculated using the ESM; based on measurements with a spherical array composed of 48 microphones, the proposed method can effectively locate the sound sources in enclosures of different shapes and work stably under the situation of low signal-to-noise ratio.

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