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Measurement of echo reduction for passive-material samples using sparse Bayesian learning and least squares estimation.

Echo reduction (ER) for passive materials is important for the evaluation of sound absorption performance. In a limited space, due to the strong interference of multipath signals, it is difficult to separate and extract the directed and reflected signals of the sample from the measured signal to accurately calculate the ER, especially at low frequencies. A method combining sparse Bayesian learning (SBL) and the least squares estimation (LSE) is proposed to extract the directed and normal reflected signals of the sample from the received signal. First, owing to the high resolution of SBL in time delays estimation, the set of multipath time delays is estimated. Then, the LSE is utilized to evaluate the amplitudes of multipath signals with estimated time delays as a priori information. With combination processing, the resolution of time delay estimation is enhanced, the dimension of the LSE is reduced, and the accuracy of the amplitude estimation for the directed and normal reflected signals, as well as the ER evaluation, is improved. The proposed method is validated through simulations and experiments in a cylindrical tank.