Fast direction-of-arrival estimation algorithm for multiple wideband acoustic sources using multiple open spherical arrays

The orthonormal propagator method (OPM) is extended to the spherical harmonic (SH) domain using multiple open spherical microphone arrays (SMAs). Compared with the multiple signal classification method (MUSIC), the computational loads of the OPM can be lower (by one or two orders), because the OPM does not require eigendecomposition of the cross spectral matrix (CSM) of the received sensor signals. Moreover, multiple open SMAs have wider frequency ranges of operation because their large radii reduce their lower frequency bounds and their small radii increase their higher frequency bounds. In this work, the performances of the OPM using both the spherical Fourier transform (SFT) components in the SH domain (SH-SFT-OPM) and the cross spectral matrix of the SFT components in the SH domain (SH-CSM-OPM) are analyzed theoretically and then evaluated in terms of their root-mean-square errors under various signal-to-noise ratio (SNR) conditions and direction-of-arrival estimation snapshots. The performance results are then compared with those of the SH-MUSIC. The simulation results confirm that the SH-CSM-OPM performs similarly to the SH-MUSIC, even for low SNRs, and that the computational complexity of the SH-SFT-OPM is significantly lower than that of the SH-MUSIC.