Array processing estimation of non-linearly superimposed acoustic waves

Acoustic pressure waves are non-linearly superimposed when a periodic gas flow is perturbing the propagating medium, as it arises in car exhaust systems. In such an environment, the application of standard beamforming techniques to the estimation of the forward and backward waves needs a previous reformulation to establish a linear superposition model. In this paper a new linearization method for the superposition of waves is proposed and compared to the classical assumption of linear pressure superposition. Moreover, a new problem formulation including the noise corruption of source waves is presented. In both new and classical linear contexts, three different beamformers-delay-and-sum (DS), linearly constrained minimum variance (LCMV) and minimum mean squared error (MMSE)-have been applied to numerical data generated by a thermodynamics modeling software. Results have shown that the new linearization method improves the backward wave estimation error in almost 3 dB for typical experiment conditions (few sensors and moderate signal-to-noise ratio)