Conventional equivalent source method always models the reflective waves from boundaries with one-layer equivalent sources,but how to select the optimized distances of the equivalent sources is always difficult.A multilayer equivalent source method(MESM) is proposed to approximate the desired sound field by multiple layer equivalent sources under the assumption that the equivalent sources are sparsely distributed on the external boundary of the space.First,the details of the proposed method are derived.Secondly,the proposed MESM is validated using numerical simulations in a rectangular cavity and measured data from a cabin.The numerical simulation shows that a lower error of 5-10 dB can be achieved by MESM than ESM for frequency higher than 600 Hz and a higher error of 5 dB for frequency lower than 200 Hz.A higher performance can also be achieved by the experimental data.Next,MESM is also investigated through numerical simulations against different conditions.It turns out that the elapsed time by MESM would be about two times the elapsed of ESM.However,a high reconstructive accuracy for the frequency higher than 600 Hz can be obtained if the sound field in an enclosed space is computed using more sensors,with a random distribution of microphones and a lower absorption coefficient.In addition,the performance of sound field reconstruction will almost be unaffected by the layer number and the number of the equivalent sources in each layer.
