Remote microphone virtual sensing with nested microphone sub-arrays

This study uses the remote microphone technique to investigate the use of nested sub-arrays that incorporate either pressure or both pressure and pressure gradient information to estimate the pressure at remote locations in a random sound field. The sub-arrays of either pressure sensors or closely spaced microphone pairs are nested to form both uniform linear and circular arrays. The performance of the different configurations is evaluated through both experiments and simulations in terms of the level of estimation error and the spatial extent over which a low estimation error can be achieved. The presented results show that the use of nested arrays of closely spaced microphone pairs outperforms conventional arrays that use pressure alone, both in terms of the estimation error and the size of the estimation zone. Overall, the circular configurations are shown to outperform the equivalent linear configurations. The gains in nominal performance, however, are paid for by an increase in the condition number, which influences the robustness of these arrays to uncertainties. The paper highlights the importance of array topology and the advantages provided by the inclusion of pressure gradient information into the estimation of the pressure at remote locations.