• Korean Journal of Remote Sensing
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• v.19 no.4
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• pp.285-290
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• 2003

In this paper, a camera modeling method that utilizes ephemeris data and imaging geometry is presented. The proposed method constructs a mathematical model only with parameters that are contained in auxiliary files and does not require any ground control points for model construction. Control points are only needed to eliminate geolocation error of the model that is originated from errors embedded in the parameters that are used in model construction. By using a few (one or two) control points, RMS error of around pixel size can be obtained and control points are not necessarily uniformly distributed in line direction of the scene. This advantage is crucial in large-scale projects and will enable to reduce project cost dramatically.

• Korean Journal of Optics and Photonics
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• v.31 no.1
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• pp.26-30
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• 2020

First, if we want to design and construct a robotic camera, we need to understand the parallax errors between adjacent images, caused by rotation and movement of the robotic camera system. In this paper, we try to derive the mathematical formulation of parallax error and connect it to a conventional lens system, to obtain a useful, generalized, analytic algebraic expression for the parallax error. Utilizing this expression, we can structurally design a robotic camera, and study the Google ART camera as an example of a robotic camera.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.47 no.7
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• pp.499-507
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• 2019

Despite the well-known mathematical model of fixed-wing aircraft, there are various studies to meet desired performances by considering the modeling errors in the extended flight envelope. This paper proposes a new adaptation mechanism of model-reference adaptive control, which applies the Levenberg-Marquardt algorithm to the pitch attitude control of fixed-wing UAV. In addition, reference model in the adaptation law is set by referring to the dynamic properties of the plant model. The performance of the proposed adaptive control law is verified through simulations and flight tests.

• Journal of Sensor Science and Technology
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• v.28 no.2
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• pp.81-87
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• 2019

One of the major issues in inertial and magnetic measurement unit (IMMU)-based 3D orientation estimation is compensation for magnetic disturbances in magnetometer signals, as the magnetic disturbance is a major cause of inaccurate yaw estimation. In the proposed approach, a kinematic constraint is used to provide a measurement equation in addition to the accelerometer and magnetometer signals to mitigate the disturbance effect on the orientation estimation. Although a Kalman filter (KF) is the most popular framework for IMMU-based orientation estimation, a complementary filter (CF) has its own advantages over KF in terms of mathematical simplicity and ease of implementation. Accordingly, this paper introduces a quaternion-based CF with a constraint-combined correction equation. Furthermore, the weight of the constraint relative to the magnetometer signal is adjusted to adapt to magnetic environments to optimally deal with the magnetic disturbance. In the results of our validation experiments, the average and maximum of yaw errors were $1.17^{\circ}$ and $1.65^{\circ}$ from the proposed CF, respectively, and $8.88^{\circ}$ and $14.73^{\circ}$ from the conventional CF, respectively, showing the superiority of the proposed approach.

• Tribology and Lubricants
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• v.38 no.4
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• pp.152-161
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• 2022

Chemical mechanical planarization (CMP) is a technology that planarizes the surfaces of semiconductor devices using chemical reaction and mechanical material removal, and it is an essential process in manufacturing highly integrated semiconductors. In the CMP process, a conditioning process using a diamond conditioner is applied to remove by-products generated during processing and ensure the surface roughness of the CMP pad. In previous studies, prediction of pad wear by CMP conditioning has depended on numerical analysis studies based on mathematical simulation. In this study, using an artificial neural network, the ratio of conditioner coverage to the distance between centers in the conditioning system is input, and the average conditioning density, standard deviation, nonuniformity (NU), and conditioning density distribution are trained as targets. The result of training seems to predict the target data well, although the average conditioning density, standard deviation, and NU in the contact area of wafer and pad and all areas of the pad have some errors. In addition, in the case of NU, the prediction calculated from the training results of the average conditioning density and standard deviation can reduce the error of training compared with the results predicted through training. The results of training on the conditioning density profile generally follow the target data well, confirming that the shape of the conditioning density profile can be predicted.

• Journal of Sensor Science and Technology
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• v.32 no.5
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• pp.267-274
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• 2023

LiDAR, one of the most important sensing methods used in mobile robots and cars with assistive/autonomous driving functions, is used to locate surrounding obstacles or to build maps. For real-time path generation, the detection of potholes or puddles on the driving surface is crucial. To achieve this, we used the coordinates of the reflection points provided by LiDAR as well as the intensity information to classify water areas, which was achieved by applying a linear regression method to the intensity distribution. The rationale for using the LiDAR index as an input variable for linear regression is presented, and we demonstrated that it is not affected by errors in the distance measurement value. Because of LiDAR vertical scanning, if the reflective surface is not uniform, it is divided into different groups according to the intensity distribution, and a mathematical basis for this is presented. Through experiments in an outdoor driving area, we could distinguish between flat ground, potholes, and puddles, and kinematic analysis was performed to calculate the maximum width that could be crossed for a given vehicle body size and wheel radius.

• Communications of Mathematical Education
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• v.28 no.1
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• pp.1-17
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• 2014

Recently a student's mathematical thinking and problem-solving skills are emphasized. Nevertheless, the students solved the problem associated with a given type of problem solving using mechanical algorithms. With this algorithm, It's hard to achieve the goal that are recently emphasized. Furthermore It may be formed error or misconception. However, consistent errors have positive aspects to identify of the current cognitive state of the learner and to provide information about the cause of the error. Thus, this study tried to analyze the error happening in the process of solving gearwheel-involved problem and to propose the correct teaching method. The result of student's error analysis, the student tends to solve the gear-wheel problem with proportional expression only. And the student did not check for the proportional expression whether they are right or wrong. This may be occurred by textbook and curriculum which suggests only best possible conditioned problems. This paper close with implications on the discussion and revision of the concepts presented in the curriculum and sequence related to the gearwheel-involved problem as well as methodological suggested of textbook.

• School Mathematics
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• v.9 no.1
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• pp.119-139
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• 2007

The purpose of this study is to analyze students' misconception in the teaming of the conic sections with the cognitive and pedagogical point of view. The conics sections is very important concept in the high school geometry. High school students approach the conic sections only with algebraic perspective or analytic geometry perspective. So they have various misconception in the conic sections. To achieve the purpose of this study, the research on the following questions is conducted: First, what types of misconceptions do the students have in the loaming of conic sections? Second, what types of errors appear in the problem-solving process related to the conic sections? With the preliminary research, the testing worksheet and the student interviews, the cause of error and the misconception of conic sections were analyzed: First, students lacked the experience in the constructing and manipulating of the conic sections. Second, students didn't link the process of constructing and the application of conic sections with the equation of tangent line of the conic sections. The conclusion of this study ls: First, students should have the experience to manipulate and construct the conic sections to understand mathematical formula instead of rote memorization. Second, as the process of mathematising about the conic sections, students should use the dynamic geometry and the process of constructing in learning conic sections. And the process of constructing should be linked with the equation of tangent line of the conic sections. Third, the mathematical misconception is not the conception to be corrected but the basic conception to be developed toward the precise one.

• School Mathematics
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• v.7 no.4
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• pp.391-402
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• 2005

The purpose of this study is to resolve misunderstanding for centroid of a triangle and to clarify several logical problems in finding the centroid of a Polygon. The conclusions are the followings. For a triangle, the misunderstanding that the centroid of a figure is the intersection of two lines that divide the area of the figure into two equal part is more easily accepted caused by the misinterpretation of a median. Concerning the equilibrium of a triangle, the median of it has the meaning that it makes the torques of both regions it divides to be equal, not the areas. The errors in students' strategies aiming for finding the centroid of a polygon fundamentally lie in the lack of their understanding of the mathematical investigation of physical phenomena. To investigate physical phenomena mathematically, we should abstract some mathematical principals from the phenomena which can provide the appropriate explanations for then. This abstraction is crucial because the development of mathematical theories for physical phenomena begins with those principals. However, the students weren't conscious of this process. Generally, we use the law of lever, the reciprocal proportionality of mass and distance, to explain the equilibrium of an object. But some self-evident principles in symmetry may also be logically sufficient to fix the centroid of a polygon. One of the studies by Archimedes, the famous ancient Greek mathematician, gives a solution to this rather awkward situation. He had developed the general theory of a centroid from a few axioms which concerns symmetry. But it should be noticed that these axioms are achieved from the abstraction of physical phenomena as well.

• KSBB Journal
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• v.20 no.2 s.91
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• pp.106-111
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• 2005

The functional relationship between the number of mole of an i-fatty acid (Si) included in fish oil and the hydrolysis time(t) was expressed as a mathematical model, $S_i=-{\alpha_i}1n(t)+\beta_i$. The average errors of calculated values on the basis of the measured values were distributed in the range of less than $5\%$ for all the 15 fatty aids composing of fish oil. The equation of hydrolysis rate of each fatty acid was deduced as $v_i={\gamma_i}exp(\frac{S_i}{\alpha_i})$ from the above-mentioned $S_i=-{\alpha_i}ln(t)+{\beta_i}$. Therefore the hydrolysis yields of fatty acids were analyzed using the equation of $S_i\;Vs.\;t.$. The 15 fatty acids were categorized into 4groups from the view point of hydrolysis yield. The hydrolysis yields of the first group, including C14:0, C16:0, C16:1, C18:0, C18:1 (n-7) and 1l8:1 (n-9), were higher than $70\%$ at 48 hr of hydrolysis. Those of the second group, C20:1, C22:1, C18:3, C20:4 and C20:5, were distributed from $40\%,\;to\;60\%$, and third group were around $30\%$. The final group containing only C22:6 was very hard to be hydrolyzed and the yield was less than $20\%$ at the same time.