• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.18 no.3
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• pp.83-92
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• 2018

This paper uses the Apollonius Circle technique to estimate the position of a target that generates a specific signal by using a drone, which is rapidly becoming a rapidly expanding industry. The existing direction finding method is performed through the vehicle on the ground or installed the antenna at a high position to detect the position of the target. However, the conventional direction finding method is difficult to configure the reception environment of the LOS signal, It is difficult. However, the direction finding using the drone is easy to construct and measure the LOS signal receiving environment using the drone flying at high altitude. In this study, we use the 3D 800MHz Path-Loss Model to reconstruct the signal by using the measurement data of the ground direction finding, reconstruct the signal by using the 3-D 800MHz Path-Loss Model, and use the Apollonius Circle method to estimate the position of the target. A simulation was performed to estimate the position of the target. Simulation was performed to determine the target position estimation performance by configuring the ground direction finding and the dron direction finding.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.5
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• pp.2029-2043
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• 2018

In this paper, we propose a novel inter-cell handover approach from a new perspective in dense Heterogeneous and Small Cell Networks (HetSNets). We first devise a cell selection mechanism to choose a proper candidate small cell for the UEs that tend to implement inter-small cell handover (ICH). By exploiting the property of a typical non-concentric circle, i.e., circle of Apollonius, we then propose a novel analytical method for modeling inter-cell handover regions and present mathematical derivation to prove that the inter-small cell handover issues fit the property of the circle of Apollonius. We design an inter-cell handover algorithm (ICHA) by means of our proposed handover model to dynamically configure hysteresis margin and properly implement handover decision in terms of UE's mobility. Simulation results demonstrate that the proposed ICHA yields lower call drop rate and radio link failure rate than the conventional methods and hence achieve high Handover Performance Indicator (HPI).

• The Journal of the Acoustical Society of Korea
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• v.26 no.8
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• pp.415-425
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• 2007

This paper proposes a method of underwater source localization using the wideband interference patterns matching. By matching two interference patterns in the spectrogram, it is estimated a ratio of the range from source to sensor5, and then this ratio is applied to the Apollonius circle. The Apollonius circle is defined as the locus of all points whose distances from two fixed points are in a constant value so that it is possible to represent the locus of potential source location. The Apollonius circle alone, however still keeps the ambiguity against the correct source location. Therefore another equation is necessary to estimate the unique locus of the source location. By estimating time differences of signal arrivals between source and sensors, the hyperbola equation is used to get the cross point of the two equations, where the point being assumed to be the source position. Simulations are performed to get performances of the proposed algorithm. Also, comparisons with real sea experiment data are made to prove applicability of the algorithm in real environment. The results show that the proposed algorithm successfully estimates the source position within an error bound of 10%.

• Korean Journal of Computational Design and Engineering
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• v.6 no.1
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• pp.31-39
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• 2001

Presented in this paper are algorithms to compute the positions of vertices and equations of edges of the Voronoi diagram of a circle set. The circles are located in a Euclidean plane, the radii of the circles are not necessarily equal and the circles are not necessarily disjoint. The algorithms correctly and efficiently work when the correct topology of the Voronoi diagram was given. Given three circle generators, the position of the Voronoi vertex is computed by treating the plane as a complex plane, the Z-plane, and transforming it into another complex plane, the W-plane, via the Mobius transformation. Then, the problem is formulated as a simple point location problem in regions defined by two lines and two circles in the W-plane. And the center of the inverse-transformed circle in Z-plane from the line in the W-plane becomes the position of the Voronoi vertex. After the correct topology is constructed with the geometry of the vertices, the equations of edge are computed in a rational quadratic Bezier curve farm.

• The Journal of the Acoustical Society of Korea
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• v.28 no.4
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• pp.318-327
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• 2009

In this paper, we propose a 3-D geometric localization method for near-field broadband source in shallow water environments. According to the waveguide invariant theory, slope of the interference pattern which is seen in a sensor spectrogram directly proportional to a range of the source. The relative ratio of the range between source and sensors was estimated by matching of two interference patterns in spectrogram. Then this ratio is applied to the Apollonius's circle which shows the locus of a source whose range ratio from two sensors is constant. Two Apollonius's circles from three sensors make the intersection point that means the horizontal range and the azimuth angle of the source. And this intersection point is constant with source depth. Therefore the source depth can be estimated using 3-D hyperboloid equation whose range difference from two sensors is constant. To evaluate a performance of the proposed localization algorithm, simulation is performed using acoustic propagation program and analysis of localization error is demonstrated. From simulation results, error estimate for range and depth is described within 50 m and 15 m respectively.

• East Asian mathematical journal
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• v.34 no.2
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• pp.219-238
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• 2018

The purpose of this paper is to reinterpret and visualize Pappus' methods for trisecting the angle by utilizing the Nicomedes' conchoid and Apollonius' symptom of a hyperbola. In particular, we reinterpret the Pappus' three results which are the methods of hyperbola and circle, the trisection of the arc and focus and directrix of the hyperbola by 3 steps(analysis, construction, and proof) in the current middle school curriculum of Mathematics. Moreover, we visualize the construction of an hyperbola which is represented by means of an eccentricity.

• The Journal of the Acoustical Society of Korea
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• v.26 no.8
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• pp.375-380
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• 2007

A reverberation chamber should be designed and constructed so as to satisfy its purposes and available space. However, it is somewhat difficult to meet the intended design requirements due to various errors from construction process. So, the post-construction measurement of its volume and surface areas is very essential to check the actual volume and volume uncertainty of a reverberation chamber These values should be carefully calculated and accurately estimated since they are used not only to evaluate the acoustic characteristics of building materials but also to calculate uncertainties for other acoustic characteristics. In this work, the method for the calculation and uncertainty estimation of the volume of a reverberation chamber is presented. To this end, the coordinates of all corners was measured with Total Station after construction. The results showed that the calculated volume of the measured reverberation chamber differs by 5 % from the design specification. The expanded volume uncertainty was also estimated to be about 2 % of the total calculated volume.