Articles: Department of Mathematics, Computing & Information Technology
http://repository.embuni.ac.ke/handle/123456789/611
Journal articles for Mathematics, Computing & Information TechnologyThu, 23 Jan 2020 23:57:14 GMT2020-01-23T23:57:14ZCrame´R-Rao Bound of Direction Finding using Uniform Circular Array And 2-Circle Concentric Uniform Array
http://repository.embuni.ac.ke/handle/embuni/2208
Crame´R-Rao Bound of Direction Finding using Uniform Circular Array And 2-Circle Concentric Uniform Array
Musyoka, David
Source direction-of-arrival estimation problem has received much attention in recent years
following its significant role in array-signal processing and wide range of applications such
as radar, wireless communication, sonar, seismology among others. Direction finding has
been solved by several techniques such as Maximum likelihood estimator, MUltiple Signal
Classification, Estimation of Parameters via Rotational Invariance Technique and Cram´er-
Rao bound using array of sensors in both uniformly-spaced and non-uniformly-spaced.
The sensors have further been arranged in different geometric patterns ranging from onedimension
to three-dimensional. However, little effort has been made in direction finding
using concentric planar arrays with fixed centers at the Cartesian origin. In this study, a
new planar sensor-array geometry (the 2-circle concentric uniform array geometry) centered
at the Cartesian origin, that maximizes the array’s spatial aperture mainly for bivariate
azimuth-polar resolution of direction-of-arrival estimation problem was proposed. The
proposed geometry provides almost invariant azimuth angle coverage and offers the advantage
of full rotational symmetry (circular invariance) while maintaining an inter-sensor
spacing not exceeding half wavelength (for non-ambiguity with respect to the Cartesian
direction cosines) among other advantages. The study adopted Cram´er-Rao bound technique
of direction finding via a uniform circular array (single ring array) and the proposed
geometry to estimate the bivariate azimuth-polar angles-of-arrival. Both the array manifolds
and the Cram´er-Rao bounds for the uniform circular array and that of the proposed
array grid were derived. Further, a better-accurate performance in direction finding of the
proposed array grid over that of the single ring array grid was analytically verified under
different constraints of investigation. It was found that the proposed sensor-array geometry
has better estimation accuracy than a single ring array and the 2-circle concentric uniform
array geometry would have the best estimation accuracy for minimal number of sensors
hence reducing the hardware cost. The study therefore recommends that the 2-circle concentric
uniform array geometry should be used for direction finding with minimal number
of sensors and with an inter-sensor spacing not exceeding half a wavelength as opposed to
a uniform circular array geometry.
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Sun, 01 Sep 2019 00:00:00 GMThttp://repository.embuni.ac.ke/handle/embuni/22082019-09-01T00:00:00ZA Classification Model for Water Quality analysis Using Decision Tree
http://repository.embuni.ac.ke/handle/embuni/2203
A Classification Model for Water Quality analysis Using Decision Tree
Gakii, Consolata; Jepkoech, Jennifer
A classification algorithm is used to assign predefined classes to test instances
for evaluation) or future instances to an application). This study presents a Classification
model using decision tree for the purpose of analyzing water quality data from different
counties in Kenya. The water quality is very important in ensuring citizens get to drink clean
water. Application of decision tree as a data mining method to predict clean water based on
the water quality parameters can ease the work of the laboratory technologist by predicting
which water samples should proceed to the next step of analysis. The secondary data from
Kenya Water institute was used for creation of this model. The data model was implemented
in WEKA software. Classification using decision tree was applied to classify /predict the clean
and not clean water. The analysis of water Alkalinity,pH level and conductivity can play a
major role in assessing water quality. Five decision tree classifiers which are J48, LMT,
Random forest, Hoeffding tree and Decision Stump were used to build the model and the
accuracy compared. J48 decision tree had the highest accuracy of 94% with Decision Stump
having the lowest accuracy of 83%.
Sat, 01 Jun 2019 00:00:00 GMThttp://repository.embuni.ac.ke/handle/embuni/22032019-06-01T00:00:00ZCramer-Rao Bound of Direction Finding Using a Uniform Hexagonal Array
http://repository.embuni.ac.ke/handle/embuni/2202
Cramer-Rao Bound of Direction Finding Using a Uniform Hexagonal Array
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.
Sat, 01 Jun 2019 00:00:00 GMThttp://repository.embuni.ac.ke/handle/embuni/22022019-06-01T00:00:00ZA uniform circular array of isotropic sensors that stochastically dislocate in three dimensions—The hybrid Cramér-Rao bound of direction-of-arrival estimation
http://repository.embuni.ac.ke/handle/embuni/2200
A uniform circular array of isotropic sensors that stochastically dislocate in three dimensions—The hybrid Cramér-Rao bound of direction-of-arrival estimation
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.
Mon, 01 Jul 2019 00:00:00 GMThttp://repository.embuni.ac.ke/handle/embuni/22002019-07-01T00:00:00Z