Three-Dimensional Acoustic Source Mapping with Different Beamforming Steering Vector Formulations

Acoustic source mapping techniques using acoustic sensor arrays and delay-and-sum beamforming techniques suffer from bad spatial resolution at low-aperture-based Helmholtz numbers. This is especially a problem for three-dimensional map grids, when the sensor array is not arranged around the region spanned by the grid but on only one side of it. Then, the spatial resolution of the result map in the direction pointing away from the array is much worse than in the other lateral directions. Consequently, deconvolution techniques need to be applied. Some of the most efficient deconvolution techniques rely on the properties of the spatial beamformer filters used. As these properties are governed by the steering vectors, four different steering vector formulations from the literature are examined, and their theoretical background is discussed. It is found that none of the formulations provide both the correct location and source strength. As a practical example the CLEAN-SC deconvolution methodology is applied to simulated data for a three-source scenario. It is shown that the different steering vector formulations are not equally well suited for three-dimensional application. The two preferred formulations enable the correct estimation of the source location at the cost of a negligible error in the estimated source strength.