This paper discovers rules-of-thumb on how the estimation precision for an incident source's azimuth-polar direction-of-arrival (ϕ,θ) depends on the number (L) of identical isotropic sensors spaced uniformly on an open sphere of radius R. This estimation's corresponding Cramér–Rao bounds (CRB) are found to follow these elegantly simple approximations, useful for array design: (i) For the azimuth arrival angle: 2π(R/λ)(σs/σn)2LMCRB(ϕ) sin(θ)≈(Le1/14)−1+3→L→∞3, ∀(ϕ,θ); and (ii) for the polar arrival angle: 2π(R/λ)(σs/σn)2LMCRB(θ)≈3−(Le6/7)−1→L→∞3, ∀(ϕ,θ). Here, M denotes the number of snapshots, λ refers to the incident signal's wavelength, and (σs/σn)2 symbolizes the signal-to-noise power ratio.
Directional sensors, if collocated but perpendicularly oriented among themselves, would facilitate signal processing to uncouple the azimuth-polar direction from the time-frequency dimension-in addition to the physical advantage of spatial compactness. One such acoustical sensing unit is the well-known "tri-axial velocity sensor" (also known as the "gradient sensor," the "velocity-sensor triad," the "acoustic vector sensor," and the "vector hydrophone"), which comprises three identical figure-8 sensors of the first directivity-order, collocated spatially but oriented perpendicularly of each other. The directivity of the figure-8 sensors is hypothetically raised to a higher order in this analytical investigation with an innocent hope to sharpen the overall triad's directionality and steerability. Against this wishful aspiration, this paper rigorously analyzes how the directivity-order would affect the triad's "spatial-matched-filter" beam's directional steering capability, revealing which directivity-order(s) would allow the beam-pattern of full maneuverability toward any azimuthal direction and which directivity-order(s) cannot. V
In modern applications such as robotics, autonomous vehicles, and speaker localization, the computational power for sound source localization applications can be limited when other functionalities get more complex. In such application fields, there is a need to maintain high localization accuracy for several sound sources while reducing computational complexity. The array manifold interpolation (AMI) method applied with the Multiple Signal Classification (MUSIC) algorithm enables sound source localization of multiple sources with high accuracy. However, the computational complexity has so far been relatively high. This paper presents a modified AMI for uniform circular array (UCA) that offers reduced computational complexity compared to the original AMI. The complexity reduction is based on the proposed UCA-specific focusing matrix which eliminates the calculation of the Bessel function. The simulation comparison is done with the existing methods of iMUSIC, the Weighted Squared Test of Orthogonality of Projected Subspaces (WS-TOPS), and the original AMI. The experiment result under different scenarios shows that the proposed algorithm outperforms the original AMI method in terms of estimation accuracy and up to a 30% reduction in computation time. An advantage offered by this proposed method is the ability to implement wideband array processing on low-end microprocessors.
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