Browsing by Author "Wong, Kainam Thomas"

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    A Centrosymmetric Array Comprising a Horizontal Uniform Circular Subarray and a Vertical Uniform Linear Subarray—Its Design in Reference to Its Direction-Finding Cramér–Rao Bound.
    (IEEE, 2021-06) Lin, Yang; Wong, Kainam Thomas; Zakayo, Ndiku Morris
    Azimuthal centrosymmetry in an array grid is typically associated with arrays that are circular, concentric, cylindrical, spherical, or hemispherical. However, a recently proposed alternative combines an azimuthal circular array with a linear vertical array. For this elegantly simple new array grid's use in the direction-of-arrival estimation, this article advances array-design insights to meet a given estimation-precision threshold, by examining the tradeoff between the azimuth-angle Cramér-Rao bound vis-a-vis the polar-angle Cramér-Rao bound in a proposed two-step design procedure.
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    Comparing the “Rim” Versus the “Filled” Rectangular Array Grids—Their Direction-Finding Cramér-Rao Bounds
    (IEEE, 2018) Zakayo, Ndiku Morris; Wong, Kainam Thomas
    A rectangular array of sensors is often used in direction finding, due to the geometric regularity in its spatial rectangular grid. The sensor positions may be confined to the rectangle's perimeter (as in a “rim” array), or may span over the rectangle's entire interior as well (as in a “filled” array). This paper compares these two array grids by their precision in direction finding, by pioneering Cramér-Rao bound expressions for both array grids above, in closed forms and explicitly in terms of the array parameters.
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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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    The hybrid Cramer-Rao bound of direction finding by a uniform circular array of isotropic sensors that suffer stochastic dislocations
    (Acoustical Society of America, 2017-11-15) Zakayo, N. Morris; Wong, Kainam Thomas; Kitavi, Dominic M.; Tsair-Chuan, Lin
    Consider azimuth-elevation direction finding by a uniform circular array of isotropic sensors. In the real world, the sensors may dislocate from their nominal positions. These dislocations could be modeled as random variables having an a priori known distribution. This paper investigates how the dislocations would affect azimuth-elevation direction finding by deriving the corresponding hybrid Cramer-Rao bounds. Maximum a posteriori estimators are derived and Monte Carlo simulations are conducted to validate the derived hybrid Cramer-Rao bounds
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    An L-shaped Array with Non-Orthogonal Axes – Its Cramer-Rao Bound for Direction Finding
    (IEEE, 2017-08) Kitavi, Dominic M.; Wong, Kainam Thomas; Hung, Chun-Chiu
    If a nominally L-shaped sensor-array's two legs are not exactly perpendicular, its azimuth-polar direction-of-arrival estimation would be degraded. This paper quantifies this degradation via a deterministic Cramér-Rao bound analysis of the direction-finding error variance.
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    A Lower Bound of Estimation Error of an Emitter's Direction-of-Arrival / Polarization, for a Collocated Triad of Orthogonal Dipoles/Loops That Fail Randomly
    (2017-04) Kitavi, Dominic M.; Wong, Kainam Thomas; Zou, Mengxi; Agrawal, Keshav
    For a triad of short dipoles (or of small loops), in perpendicular orientation relative to each other but collocated in space, this study derives a lower bound for their error in direction-of-arrival estimation and polarisation estimation, accounting for the possibility of failure in any individual dipoles (or loops).
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    Three-dimensional dislocations in a uniform linear array's isotropic sensors-Direction finding's hybrid Cramér-Rao bound
    (Acoustical Society of America, 2020-05) Ndiku, Morris, Zakayo; Wong, Kainam Thomas; Wu, Yue Ivan
    The linear array’sone-dimensional spatial geometry is simple but suffices forunivariate direction finding, i.e., isadequate for the estimation of an incident source’s direction-of-arrival relative to the linear array axis. However, thisnominalone-dimensional ideality could be often physically compromised in the real world, as the constituentsensors may dislocatethree-dimensionally from their nominal positions. For example, a towed array is subject toocean-surface waves and to oceanic currents [Tichavsky and Wong (2004). IEEE Trans. Sign. Process.52(1),36–47]. This paper analyzes how a nominally linear array’sone-dimensional direction-finding accuracy would bedegraded by thethree-dimensional random dislocation of the constituent sensors. This analysis derives the hybridCram er-Rao bound (HCRB) of the arrival-angle estimate in a closed form expressed in terms of the sensors’ disloca-tion statistics. Surprisingly, the sensors’ dislocation could improve and not necessarily degrade the HCRB, depend-ing on the dislocation variances but also on the incident source’s arrival angle and the signal-to-noise power ratio
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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.