Higher-order figure-8 microphones/hydrophones collocated as a perpendicular triad—Their “spatial-matched-filter” beam steering

Abstract

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

Quantitative Analysis Method and Correction Algorithm Based on Directivity Beam Pattern for Mismatches between Sensitive Units of Acoustic Dyadic Sensors

“…According to the Taylor series expansion theory of sound pressure [4], complete sound field information includes sound pressure (scalar, zero-order spatial partial derivative), sound pressure gradient or acoustic particle velocity (vector, first-order spatial partial derivative), second-order sound pressure gradient or particle velocity gradient (dyadic, second-order spatial partial derivative) and higher order information. Additionally, the higher the order of the measured sound field information, the higher the directivity of the acoustic detection system [5][6][7][8][9][10][11], so as to meet the application requirements.…”

“…Therefore, we define the difference between the ratio of the ideal cosine squared beam pattern and the ratio of the beam pattern with amplitude mismatch 𝜇 as the Beam Width Increase (BWI) of an ADS. Using Equation (11), the BWI can be written as follows:…”

“…It means that the second term on the right side of Equation ( 15) is equal to 1.25, which is the ratio of the ideal cosine beam pattern. Look back to Equation (11), when µ = 0, the two exponential terms in the normalized directivity function become one, and the magnitude of the function becomes directly proportional to the cosine function of the incident angle θ (L λ). In other words, in this case, the directivity of order two with a cosine squared shape of an ADS has degenerated into the directivity of order one with a cosine shape.…”

Vector Sensor Steering-Dependent Performance in an Underwater Acoustic Communication Field Experiment

“…It is notorious and expected that most of the literature on vector sensors addresses the direction-finding issues since a compact collocated device can improve the gain of an ordinary pressure sensor or enhance the gain of a pressure array [ 7 , 8 , 9 , 10 ]. Much work has been carried out regarding direction of arrival (DoA) estimation using vector sensors, either by additive or multiplicative channel combining methods [ 7 , 11 , 12 , 13 ], exploiting signal and noise subspace domains [ 14 ], higher-order array manifold [ 15 ], or artificial intelligence [ 16 ]. Although researchers have deeply investigated DoA methods, the use of this information for UWAC is still little explored.…”