Constrained Spectral Conditioning for spatial sound level estimation

Microphone arrays are utilized in aeroacoustic testing to spatially map the sound emitted from an article under study. Whereas a single microphone allows only the total sound level to be estimated at the measurement location, an array permits differentiation between the contributions of distinct components. The accuracy of these spatial sound estimates produced by post-processing the array outputs is continuously being improved. One way of increasing the estimation accuracy is to filter the array outputs before they become inputs to a post-processor. This work presents a constrained method of linear filtering for microphone arrays which minimizes the total signal present on the array channels while preserving the signal from a targeted spatial location. Thus, each single-channel, filtered output for a given targeted location estimates only the signal from that location, even when multiple and/or distributed sources have been measured simultaneously. The method is based on Conditioned Spectral Analysis and modifies the Wiener-Hopf equation in a manner similar to the Generalized Sidelobe Canceller. This modified form of Conditioned Spectral Analysis is embedded within an iterative loop and termed Constrained Spectral Conditioning. Linear constraints are derived which prevent the cancellation of targeted signal due to random statistical error as well as location error in the sensor and/or source positions. The increased spatial mapping accuracy of Constrained Spectral Conditioning is shown for a simulated dataset of point sources which vary in strength. An experimental point source is used to validate the efficacy of the constraints which yield preservation of the targeted signal at the expense of reduced filtering ability. The beamforming results of a cold, supersonic jet demonstrate the qualitative and quantitative improvement obtained when using this technique to map a spatially-distributed, complex, and possibly coherent sound source.