An array of directional sensors (cardioid sensors or figure-8 sensors), diversely orientated but spatially collocated : their beam-patterns

Abstract

This dissertation contains four related investigations: 1. A Triad of Cardioid Sensors in Orthogonal Orientation and Spatial Collocation - Its Spatial-Matched-Filter-Type Beam-Pattern: This work proposes a new confi.guration of acoustic sensors - three cardioid sensors in perpendicular orientation and spatial collocation, in order to increase the mainlobe-to-sidelobe height ratio (possibly to ∞). This study will analyze such a proposed triad's "spatial matched filter" beam-pattern that is independent of the frequency/spectrum of the incident signal. Specifically, this investigation will analytically derive (i) the mainlobe's pointing error in azimuth-elevation, (ii) the mainlobe's two-dimensional beam "width", (iii) the necessary and sufficient conditions for any sidelobe to exist, (iv) the mainlobe-to-sidelobe height ratio, and (v) the array gain. These above characteristics depend on the cardioids' "cardiodicity parameter" and on the beam's nominal "look direction". This work is first in the open literature to propose and to investigate a collocated triad of orthogonally oriented cardioids. The findings show that the proposed cardioid triad can have higher mainlobe-to-sidelobe height ratio and can avoid sidelobes altogether. Its physical compactness makes it portable for mobile deployment, indoor or outdoor. This work has been published in the IEEE Transaction on Signal Processing (authors include the candidate, his chief supervisor and another collaborator). 2. Cardioid Microphones/Hydrophones in a Collocated and Orthogonal Triad - A New Beamformer with No Beam-Pointing Error: Cardioid sensors offer low sidelobes/backlobes, compared to bi-directional sensors (like velocity-sensors). Three cardioid sensors, in orthogonal orientation and in spatial collocation, have recently been proposed in Chapter 1; and such a cardioid-triad's "spatial matched filter" beam-pattern has been analyzed therein. That beam-pattern, unfortunately, suffers pointing error, i.e. the spatial beam's actual peak direction deviates from the nominal "look direction". Instead, this study will propose a new beamformer for the abovementioned cardioidic triad to avoid beam-pointing error. Also analytically derived here is this beam-pattern's lobes' height ratio, beamwidth, directivity, and array gain. This work is under review by the Journal of the Acoustical Society of America (authors include the candidate, his chief supervisor and another collaborator). 3. Two Higher-Order Figure-8 Sensors in Spatial Collocation — Their "Spatial Matched Filter" Beam-Pattern: Higher-order figure-8 sensors have relatively high directivity and are sorted after due to this feature. Collocating directional sensor can be advantageous due to its spatial compactness and the frequency-independence of its array manifold. In this work, the "spatial matched filter" (SMF) beam-pattern of such collocated pair will be analytically studied. Due to real-world manufacturing imperfections, such pair of collocated higher-order figure-8 sensors may not be orthogonal. This work will also investigate how the non-orthogonal orientation affects the beam-pattern pointing assuming the beamformer has no knowledge of the imperfection. It is shown that non-perpendicularity would affect both the overall shape and introduce pointing bias in the spatial-matched-type beampattern of the two collocated higher-order figure-8 sensors. More importantly, this work relates the beamformer's look direction, array's skewed angle and sensor's order to the mis-pointing. 4. Directional Pointing Error in "Spatial Matched Filter" Beamforming at a Tri-Axial Velocity-Sensor due to Non-Orthogonal Axes: The "tri-axial velocity-sensor" has three axes that are nominally perpendicular, but may be non-perpendicular in practice, due to real-world imperfections in manufacturing or wear during operations. This work comprehensively investigates how such non-perpendicularity would affect the tri-axial velocity-sensor's azimuth-elevation beam-pattern in terms of the beam's pointing direction. Closed form expressions were developed for the pointing bias which can be used in offsetting the pointing bias introduced by the non-perpendicularity among the constituent velocity-sensors. This work was presented at the 175th Meeting of the Acoustical Society of America in Minneapolis, Minnesota on May 7, 2018.