Direction of Arrival Estimation in the Spherical Harmonic Domain Using Subspace Pseudointensity Vectors

Abstract

Abstract-Direction of Arrival (DOA) estimation is a fundamental problem in acoustic signal processing. It is used in a diverse range of applications, including spatial filtering, speech dereverberation, source separation and diarization. Intensity vector-based DOA estimation is attractive, especially for spherical sensor arrays, because it is computationally efficient. Two such methods are presented which operate on a spherical harmonic decomposition of a sound field observed using a spherical microphone array. The first uses Pseudo-Intensity Vectors (PIVs) and works well in acoustic environments where only one sound source is active at any time. The second uses Subspace Pseudo-Intensity Vectors (SSPIVs) and is targeted at environments where multiple simultaneous sources and significant levels of reverberation make the problem more challenging. Analytical models are used to quantify the effects of an interfering source, diffuse noise and sensor noise on PIVs and SSPIVs. The accuracy of DOA estimation using PIVs and SSPIVs is compared against the state-of-the-art in simulations including realistic reverberation and noise for single and multiple, stationary and moving sources. Finally, robust performance of the proposed methods is demonstrated using speech recordings in real acoustic environments.

Augmented Intensity Vectors for Direction of Arrival Estimation in the Spherical Harmonic Domain

“…In [37] authors extend the concept of PIVs by taking advantage of higher order SHs and frequency smoothing to enhance the accuracy of DOAs. In the TF domain, the covariance matrix of the observed eigenbeams is given as…”

“…Note that only the directions of the intensity vectors are used and not their vector length. As shown in [37] in case of multiple arriving plane-waves in a TF bin, it is possible to have an erroneous resulting intensity vector with direction in between of or away from the sources and a norm higher than the intensity vector norm in the presence of a single source depending on the relative amplitude and phase of the impinging plane waves. In order to avoid the accuracy-loss effect of the erroneous intensity vector with high norm, the norms are ignored and only the cardinality of the quantized directions are considered in the histogram.…”

“…Statistical DOA estimation methods using directional sparsity of sound sources have also been proposed in [31], [32]. (4) Intensity-based methods [33] determine the direction and the magnitude of the flow of sound energy within a narrow frequency band [17], [34], [35], [16], [36], [37]. Pseudointensity vector (PIV) [17] methods use sound field information with low spatial resolution.…”

“…PIVs are computationally efficient and have been shown in [17] to offer good localization accuracy for a single source in the absence of strong reflections. In common with most localization algorithms however, localization accuracy is reduced as the level of reverberation, the sensor noise or the number of sources increase [16], [38], [37]. An extension of PIV is Subspace PIV (SSPIV) [37] where the low order (≤ 1) spatial information of signal subspace is used to enhance the accuracy of PIV DOA estimates.…”

Multiple DOA estimation based on estimation consistency and spherical harmonic multiple signal classification

“…In case of multiple speech sources, MUSIC is not always preferred as the number of simultaneously active sources is not consistent due to sparseness of speech. (2) Single-Source (SS)-based DOA estimation: a common approach is to assume W-disjoint orthogonality [4] whereby at each TF bin it is assumed that only a single source is active. In practice, many TF bins contain significant contributions from waves arriving from multiple directions, either due to overlapping sources or reflections.…”