Statistical signal processing for acoustic direction finding and for roadway sound-level distribution modeling

Abstract

This thesis presents two investigations in two parts: I. Azimuth-elevation bivariate direction finding using a higher-order "figure-8" sensor and an isotropic sensor. A "p-u probe" (a.k.a. a "p-v probe") comprises one pressure-sensor (which is isotropic) and one uni-axial particle-velocity sensor (which has a "figure-8" bi-directional spatial directivity). This p-u probe may be generalized, by allowing the figure-8 bi-directional sensor to have a higher order of directivity. This "higher-order p-v probe" has not previously been investigated anywhere in the open literature (to the best knowledge of the present authors). For such a sensing system, this work is first (1) to develop closed-form eigen-based signal-processing algorithms for azimuth-elevation direction finding; (2) to analytically derive the associated Cramer-Rao lower bounds (CRB), which is expressed explicitly in terms of the two constituent sensors' spatial geometry and in terms of the figure-8 sensor's directivity order; (3) to verify (via Monte Carlo simulations) the proposed direction-of-arrival estimators' efficacy and closeness to the Cramer-Rao lower bounds. Here, the two constituent sensors of higher-order p-v probe may be spatially displaced. II. Leptokurtic probability density modeling of roadway sound-levels measured at different floors of a high-rise building. The tails of roadway sound-level distributions decay slower than the tails of the Gaussian distribution. This highlights the need to instead use leptokurtic distributions in modeling. To gain new insights into the roadway sound-level distribution, this work is first in the open literature (1) to try out a wide range of well-known leptokurtic probability-density functions of two, three and four parameters, and ranks their goodness-of-fit to sound-pressure-level data measured at a high-rise building in Hong Kong, overlooking the roadway vehicular traffic; (2) to check if a probability density (scalar) metric (i.e. variance, skewness, excess-kurtosis, third central-moment, fourth central moment, fourth cumulant, and peakedness) is a "sufficient statistic" to explain the goodness-of-fit ranks of a candidate probability density function; (3) to analyze the statistical distributions of roadway sound-level data empirically-measured at different days and different vertical locations of a high-rise building.