Browsing by Author "Kitavi, Dominic M."
Now showing 1 - 11 of 11
Results Per Page
Sort Options
Item Aperture Maximization with Half-Wavelength Spacing, via a 2-Circle Concentric Array Geometry that is Uniform but Sparse(2019-05) Kinyili, Musyoka; Kitavi, Dominic M.; Ngari, Cyrus G.This paper proposes a new sensor-array geometry (the 2-circle concentric array geometry), that maximizes the array's spatial aperture mainly for bivariate azimuth-polar resolution of direction-of-arrival estimation problem. The proposed geometry provides almost invariant azimuth angle coverage and o ers the advantage of full rotational symmetry (circular invariance) while maintaining an inter-sensor spacing of only an half wavelength (for non-ambiguity with respect to the Cartesian direction cosines). A better-accurate performance in direction nding of the proposed array grid over a single ring array geometry termed as uniform circular array (UCA) is hereby analytically veri ed via Cram er-Rao bound analysis. Further, the authors demonstrate that the proposed sensor-array geometry has better estimation accuracy than a single ring array.Item Cramer-Rao Bound of Direction Finding Using a Uniform Hexagonal Array(2019-06) Ndiritu, Grace Wakarima; Kitavi, Dominic M.; Ngari, Cyrus G.Direction-of-arrival (DOA) estimation is a key area of sensor array processing which is encountered in many important engineering applications. Although various studies have focused on the uniform hexagonal array for direction nding, there is a scanty use of the uniform hexagonal array in conjunction with Cram er-Rao bound for direction nding estimation. The advantage of Cram er- Rao bound based on the uniform hexagonal array: overcome the problem of unwanted radiation in undesired directions. In this paper, the direction-of-arrival estimation of Cram er-Rao bound based on the uniform hexagonal array was studied. The proposed approach concentrated on deriving the array manifold vector for the uniform hexagonal array and Cram er-Rao bound of the uniform hexagonal array. The Cram er-Rao bound based on the uniform hexagonal array was compared with Cram er-Rao bound based on the uniform circular array. The conclusions are as follows. The Cram er-Rao bound of uniform hexagonal array decreases with an increase in the number of sensors. The comparison between the uniform hexagonal array and uniform circular array shows that the Cram er-Rao bound of the uniform hexagonal array was slightly higher as compared to the Cram er-Rao bound of the uniform circular array. The analytical results are supported by graphical representation.Item Cramer-Rao Bound of Direction Finding Using Uniform Arc Arrays(2019) Nyokabi, Veronicah; Kitavi, Dominic M.; Ngari, Cyrus G.Direction-of-Arrival estimation accuracy using arc array geometry is considered in this paper. There is a scanty use of Uniform Arc Array (UAA) in conjunction with Cram er-Rao bound (CRB) for Direction-of-Arrival estimation. This paper proposed to use Uniform Arc Array formed from a considered Uniform Circular Array (UCA) in conjunction with CRB for Direction-of-Arrival estimation. This Uniform Arc Array is obtained by squeezing all sensors on the Uniform Circular Array circumference uniformly onto the Arc Array. Cram er-Rao bounds for the Uniform Arc Array and that of the Uniform Circular Array are derived. Comparison of performance of the Uniform Circular Array and Uniform Arc Array is done. It was observed that Uniform Arc Array has better estimation accuracy as compared to Uniform Circular Array when number of sensors equals four and ve and azimuth angle ranging between π 9 7 and π and also 18 10 9 π and 25 18π. However, UCA and UAA have equal performance when the number of sensors equals three and the azimuth angle ranging between 0 and 2π. UCA has better estimation accuracy as compared to UAA when the number of sensors equals four and ve and the azimuth angle ranging between π 2 and π and also 32 π and 2πItem 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 ThomasThe 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.Item 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 IvanCardioid 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.Item 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, LinConsider 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 boundsItem 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-ChiuIf 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.Item 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, KeshavFor 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).Item Parameterization and Forecasting of Childhood Pneumonia Model Using Least Square Approximation, Lagrange Polynomial and Monte Carlo Simulation(2020-09) Ngari, Cyrus G.; Kitavi, Dominic M.espite a study by [1] proposing a simple model of under five years pneumonia, doubt lingers regarding its reliability, sufficiency and validity. The research question is whether the model is valid for use or not? The objectives of this study were to: incorporate exit rate from under five-year age bracket in the model, use Kenya data to parameterize the model, taking into account the uncertainties and finally to predict the dynamics of pneumonia. The model was rescaled through nondimensionalization. Data was fitted using theory of general solutions of nonlinear Ordinary differential equations, numerical differentiation using Lagrange polynomials and least square approximation method. Uncertainties due to disparities and round off errors were simulated using Monte Carlo simulation. Predictions of dynamics of pneumonia were carried out using MATLAB inbuilt ode solvers. Excel software was used to predict dynamics of discrete ordinary differential equations and to fit data. The basic reproduction number () and effective reproduction number () were obtained as 61 and 7 respectively. Iteration of uncertainties on R was carried out 1000 times by Monte Carlo simulation. The maximum and minimum R were obtained as 90 and 55, respectively. Using MATLAB software and effective reproduction number, the ratio of infective class to the total population and the ratio of class under treatment to the total population will remain constant at 0.095 and 0.2297 respectively for the years 2021, 2022 and 2023. Research result indicted that it is more effective and efficient to use effective reproduction number () than basic reproduction number () in mathematical modelling of Infectious diseases whenever study focuses on proportion of population. On basis of large absolute errors in fitting data to model, findings cast doubt on model formulation and/or observed data.Item 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-ChuanAn 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.Item 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-ChuanAn 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.