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