An improved functional beamforming algorithm for far-field multi-sound source localization based on Hilbert curve

Abstract

In view of the mismatch problem between the sound sources and searching grid points (non-ideal case), an improved functional beamforming (FBF) algorithm based on the Hilbert curve, so-called HFBF, for far-field localization of multi-sound sources is presented in this paper. In contrast with the traditional FBF, the HFBF may generate the searching grids on a sound source plane and optimize them by reducing the searching plane size, adjusting the function order and the focusing vector direction, so as to improve the efficiency of grid searching and the estimation accuracy of sound source parameters. A computational procedure of the HFBF is proposed and applied to identify two independent sound sources. In terms of the locating error and the estimated error of sound pressure level (SPL), the performances of four algorithms are compared by simulations and experiments. The results suggest that the accuracies of the location coordinates and the estimated SPL values are significantly improved by the Hilbert-based grid searching. The conclusions can be drawn that, for multi-source localization, the HFBF can somewhat break through the Rayleigh limit. If the exponent value is selected properly, the estimated SPL error of the HFBF can be less than 0.1 dB. The HFBF has a larger range of available exponent values, which is negatively correlated with the frequency of a sound source. Generally speaking, in the non-ideal cases, the proposed HFBF is more accurate and effective than the FBF. It can be applied to a large-scale space, such as aircraft, train, traffic environment, etc., for far-field localization of multi-sound sources in engineering.