Browsing by Author "Lin, Tsair-Chuan"

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    Direction Finding with the Sensors' Gains Suffering Bayesian Uncertainty — Hybrid CRB and MAP Estimation
    (IEEE, 2016-08) Yue, Ivan Wu; Kitavi, Dominic M.; Lin, Tsair-Chuan; Wong, Kainam Thomas
    The paper analyzes how a sensor array's direction-finding accuracy may be degraded by any stochastic uncertainty in the sensors' complex value gains, modeled here as complex value Gaussian random variables. This analysis is via the derivation of the hybrid Cramer-Rao bound (HCRB) of the azimuth-elevation direction-of-arrival estimates. This HCRB is analytically shown to be inversely proportional to a multiplicative factor equal to one plus the variance of the sensors' gain uncertainty. This finding applies to any array grid geometry. The maximum a posteriori (MAP) estimator corresponding to this uncertain gain data model is also derived. Monte Carlo simulations demonstrate that this estimator approaches the lower bound derived.
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    Hybrid Cram er-Rao bound of direction finding, using a triad of cardioid sensors that are perpendicularly oriented and spatially collocated
    (Acoustical Society of America, 2019-07) Kitavi, Dominic M.; Wong, Kainam Thomas; Lin, Tsair-Chuan; Wu, Yue Ivan
    Cardioid microphones/hydrophones are highly directional acoustical sensors, which enjoy easy availability via numerous commercial vendors for professional use. Collocating three such cardioids in orthogonal orientation to each other, the resulting triad would be sharply directional yet physically compact, while decoupling the incident signal’s time-frequency dimensions from its azimuth-elevation directional dimensions, thereby simplifying signal-processing computations. This paper studies such a cardioid triad’s azimuth-elevation direction-of-arrival estimation accuracy, which is characterized here by the hybrid Cram er-Rao bound. This analysis allows the cardioidicity index (a) to be stochastically uncertain, applies to any cardioidic order (k), and is valid for any real-valued incident signal regardless of the signal’s time-frequency structure.
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    A uniform circular array of isotropic sensors that stochastically dislocate in three dimensions—The hybrid Cramer-Rao bound of direction-of-arrival estimation
    (Acoustical Society of America, 2019-07) Wong, Kainam Thomas; Ndiku, Morris Zakayo; Kitavi, Dominic M.; Lin, Tsair-Chuan
    An array’s constituent sensors could be spatially dislocated from their nominal positions. This paper investigates how such sensor dislocation would degrade a uniform circular array (UCA) of isotropic sensors (like pressure sensors) in their direction-finding precision. This paper analytically derives this direction finding’s hybrid Cram er-Rao bound (HCRB) in a closed form that is expressed explicitly in terms of the sensors’ dislocation parameters. In the open literature on UCA direction finding, this paper is the first to be three-dimensional in modeling the sensors’ dislocation. Perhaps unexpectedly to some readers, sensor dislocation could improve and not necessarily degrade the HCRB; these opposing effects depend on the dislocation variances, the incident source’s arrival angle, and the signal-to-noise power ratio—all analyzed rigorously in this paper. Interesting insights are thereby obtained: (a) The HCRB is enhanced for the impinging source’s polar arrival angle as the sensors become more dislocated along the impinging wavefront due to aperture enlargement over the stochastic dislocation’s probability space. (b) Likewise, the HCRB is improved for the azimuth arrival angle as the sensors become more dislocated on the circular array’s plane, also due to aperture enlargement. (c) In contrast, sensor dislocation along the incident signal’s propagation direction can only worsen the HRCBs due to nuisance-parameter effects in the Fisher information. (d) Sensor dislocation orthogonal to the array plane must degrade the HCRB for the azimuth arrival angle but could improve the HCRB for the polar arrival angle.
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    A uniform circular array of isotropic sensors that stochastically dislocate in three dimensions—The hybrid Cramér-Rao bound of direction-of-arrival estimation
    (2019-07) Wong, Kainam Thomas; Morris, Zakayo Ndiku; Kitavi, Dominic M.; Lin, Tsair-Chuan
    An array’s constituent sensors could be spatially dislocated from their nominal positions. This paper investigates how such sensor dislocation would degrade a uniform circular array (UCA) of isotropic sensors (like pressure sensors) in their direction-finding precision. This paper analytically derives this direction finding’s hybrid Cram er-Rao bound (HCRB) in a closed form that is expressed explicitly in terms of the sensors’ dislocation parameters. In the open literature on UCA direction finding, this paper is the first to be three-dimensional in modeling the sensors’ dislocation. Perhaps unexpectedly to some readers, sensor dislocation could improve and not necessarily degrade the HCRB; these opposing effects depend on the dislocation variances, the incident source’s arrival angle, and the signal-to-noise power ratio—all analyzed rigorously in this paper. Interesting insights are thereby obtained: (a) The HCRB is enhanced for the impinging source’s polar arrival angle as the sensors become more dislocated along the impinging wavefront due to aperture enlargement over the stochastic dislocation’s probability space. (b) Likewise, the HCRB is improved for the azimuth arrival angle as the sensors become more dislocated on the circular array’s plane, also due to aperture enlargement. (c) In contrast, sensor dislocation along the incident signal’s propagation direction can only worsen the HRCBs due to nuisance-parameter effects in the Fisher information. (d) Sensor dislocation orthogonal to the array plane must degrade the HCRB for the azimuth arrival angle but could improve the HCRB for the polar arrival angle.