• Journal of Elementary Mathematics Education in Korea
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• v.17 no.1
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• pp.129-142
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• 2013

The purpose of this study was to investigate the typical characteristics of mathematics education of Japan. In order to achieve this goal, we focused the journal 'Arithmetic Education' from 2007 to 2011. This journal has published by the Japan Society of Mathematical Education and 6 issues each year. A total of 133 articles related with mathematics education were analyzed. The typical characteristics of Japan's research for mathematics education were as follows: The number of single author of article were 98 cases (74%), and those of two co-authors were 21 cases (16%). There are some unusual research topic for mathematics education such as 'combined class'. 'cultural pluralism' and 'mathematics learning disabled children'. The articles 'statistical methods related to educational evaluation', 'statistical analysis for educational evaluation' and 'the relationship between number and quantity on the quaternion number' are very interesting results to the readers who know the basics of statistics and algebra. We may find many researcher who majored pure mathematics in the University of Educations in Korea. So we hope that they may write the paper which combine the pure mathematics and mathematics education. The education survey conducted by the policy is actually very meaningful. If the researcher can connect these surveys to the field of education, then the readers can see a nice paper in the journal of elementary mathematics education in Korea. Finally, it is very difficult to find that counterstatement paper for the results of the other's.

• Journal of Astronomy and Space Sciences
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• v.26 no.1
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• pp.31-46
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• 2009

An Unscented Kalman Filter (UKF) for estimation of the attitude and rate of a spacecraft using only magnetometer vector measurement is developed. The attitude dynamics used in the estimation is the nonlinear Euler's rotational equation which is augmented with the quaternion kinematics to construct a process model. The filter is designed for small satellite in low Earth orbit, so the disturbance torques include gravity-gradient torque, magnetic disturbance torque, and aerodynamic drag torque. The magnetometer measurements are simulated based on time-varying position of the spacecraft. The filter has been tested not only in the standby mode but also in the detumbling mode. Two types of actuators have been modeled and applied in the simulation. The PD controller is used for the two types of actuators (reaction wheels and thrusters) to detumble the spacecraft. The estimation error converged to within 5 deg for attitude and 0.1 deg/s for rate respectively when the two types of actuators were used. A joint state parameter estimation has been tested and the effect of the process noise covariance on the parameter estimation has been indicated. Also, Monte-Carlo simulations have been performed to test the capability of the filter to converge with the initial conditions sampled from a uniform distribution. Finally, the UKF performance has been compared to that of the EKF and it demonstrates that UKF slightly outperforms EKF. The developed algorithm can be applied to any type of small satellites that are actuated by magnetic torquers, reaction wheels or thrusters with a capability of magnetometer vector measurements for attitude and rate estimation.

• Korean Journal of Computational Design and Engineering
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• v.22 no.1
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• pp.89-99
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• 2017

In order to make a virtual endoscopy system effective for exploring the interior of the 3D model of a human organ, it is necessary to generate an accurate navigation path located inside the 3D model and to obtain consistent camera position and pose estimation along the path. In this paper, we propose an approach to virtual navigation of blood vessels, which makes proper use of orthogonal contours and skeleton curves. The approach generates the orthogonal contours and the skeleton curves from the 3D mesh model and its voxel model, all of which represent the blood vessels. For a navigation zone specified by two nodes on the skeleton curves, it computes the shortest path between the two nodes, estimates the positions and poses of a virtual camera at the nodes in the navigation zone, and interpolates the positions and poses to make the camera move smoothly along the path. In addition to keyboard and mouse input, intuitive hand gestures determined by the Leap Motion SDK are used as user interface for virtual navigation of the blood vessels. The proposed approach provides easy and accurate means for the user to examine the interior of 3D blood vessels without any collisions between the camera and their surface. With a simple user study, we present illustrative examples of applying the approach to 3D mesh models of various blood vessels in order to show its quality and usefulness.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.1197-1199
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• 2003

ROCSAT-2 mission is to daily image over Taiwan and the surrounding area for disaster monitoring, land use, and ocean surveillance during the 5-year mission lifetime. The satellite will be launched in December 2003 into its mission orbit, which is selected as a 14 rev/day repetitive Sun-synchronous orbit descending over (120 deg E, 24 deg N) and 9:45 a.m. over the equator with the minimum eccentricity. National Space Program Office (NSPO) is developing a ROCSAT-2 Image Processing System (IPS), which aims to provide real-time high quality image data for ROCSAT-2 mission. A simulated ROCSAT-2 image, based on Level 1B QuickBird Data, is generated for IPS verification. The test image is comprised of one panchromatic data and four multispectral data. The qualification process consists of four procedures: (a) QuickBird image processing, (b) generation of simulated ROCSAT-2 image in Generic Raw Level Data (GERALD) format, (c) ROCSAT-2 image processing, and (d) geometric error analysis. QuickBird standard photogrammetric parameters of a camera that models the imaging and optical system is used to calculate the latitude and longitude of each line and sample. The backward (inverse model) approach is applied to find the relationship between geodetic coordinate system (latitude, longitude) and image coordinate system (line, sample). The bilinear resampling method is used to generate the test image. Ground control points are used to evaluate the error for data processing. The data processing contains various coordinate system transformations using attitude quaternion and orbit elements. Through the qualification test process, it is verified that the IPS is capable of handling high-resolution image data with the accuracy of Level 2 processing within 500 m.

• Asia-pacific Journal of Multimedia Services Convergent with Art, Humanities, and Sociology
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• v.7 no.1
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• pp.177-186
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• 2017

Recently, Autonomous vehicles are getting hot attention. Amazon, the biggest online shopping service provider is developing a delivery system that uses drones. This kinds of platforms are need accurate attitude information for navigation. In this paper, a structure design of AHRS using low-cost inertia sensor is proposed. To estimate attitudes a Kalman filter which uses a quaternion based dynamic model, bias-removed measurements from MEMS Gyro, raw measurements from MEMS accelerometer and magnetometer, is designed. To remove bias from MEMS Gyro, an additional Kalman filter which uses raw Gyro measurements and attitude estimates, is designed. The performance of implemented AHRS is compared with high price off-the-shelf 3DM-GX3-25 AHRS from Microstrain. The Gyro bias was estimated within 0.0001[deg/s]. And from the estimated attitude, roll and pitch angle error is smaller than 0.2 and 0.3 degree. Yaw angle error is smaller than 6 degree.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.38 no.3
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• pp.175-185
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• 2020

Three-dimensional registration is a process of matching data with or without a coordinate system to a reference coordinate system, which is used in various fields such as the absolute orientation of photogrammetry and data combining for producing precise road maps. Three-dimensional registration is divided into a method using points and a method using linear features. In the case of using points, it is difficult to find the same conjugate point when having different spatial resolutions. On the other hand, the use of linear feature has the advantage that the three-dimensional registration is possible by using not only the case where the spatial resolution is different but also the conjugate linear feature that is not the same starting point and ending point in point cloud type data. In this study, we proposed a method to determine the scale and the three-dimensional translation after determining the three-dimensional rotation angle between two data using quaternion to perform three-dimensional registration using linear features. For the verification of the proposed method, three-dimensional registration was performed using the linear features constructed an indoor and the linear features acquired through the terrestrial mobile mapping system in an outdoor environment. The experimental results showed that the mean square root error was 0.001054m and 0.000936m, respectively, when the scale was fixed and if not fixed, using indoor data. The results of the three-dimensional transformation in the 500m section using outdoor data showed that the mean square root error was 0.09412m when the six linear features were used, and the accuracy for producing precision maps was satisfied. In addition, in the experiment where the number of linear features was changed, it was found that nine linear features were sufficient for high-precision 3D transformation through almost no change in the root mean square error even when nine linear features or more linear features were used.

• International Journal of Aeronautical and Space Sciences
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• v.8 no.1
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• pp.10-20
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• 2007

For spacecraft attitude control, reaction wheel (RW) steering laws with more than three wheels for three-axis attitude control can be derived by using a control allocation (CA) approach.1-2 The CA technique deals with a problem of distributing a given control demand to available sets of actuators.3-4 There are many references for CA with applications to aerospace systems. For spacecraft, the control torque command for three body-fixed reference frames can be constructed by a combination of multiple wheels, usually four-wheel pyramid sets. Multi-wheel configurations can be exploited to satisfy a body-axis control torque requirement while satisfying objectives such as minimum control energy.1-2 In general, the reaction wheel steering laws determine required torque command for each wheel in the form of matrix pseudo-inverse. In general, the attitude control command is generated in the form of a feedback control. The spacecraft body angular rate measured by gyros is used to estimate angular displacement also.⁵ Combination of the body angular rate and attitude parameters such as quaternion and MRPs(Modified Rodrigues Parameters) is typically used in synthesizing the control command which should be produced by RWs.¹ The attitude sensor signals are usually corrupted by noise; gyros tend to contain errors such as drift and random noise. The attitude determination system can estimate such errors, and provide best true signals for feedback control.⁶ Even if the attitude determination system, for instance, sophisticated algorithm such as the EKF(Extended Kalman Filter) algorithm⁶, can eliminate the errors efficiently, it is quite probable that the control command still contains noise sources. The noise and/or other high frequency components in the control command would cause the wheel speed to change in an undesirable manner. The closed-loop system, governed by the feedback control law, is also directly affected by the noise due to imperfect sensor characteristics. The noise components in the sensor signal should be mitigated so that the control command is isolated from the noise effect. This can be done by adding a filter to the sensor output or preventing rapid change in the control command. Dynamic control allocation(DCA), recently studied by Härkegård, is to distribute the control command in the sense of dynamics⁴: the allocation is made over a certain time interval, not a fixed time instant. The dynamic behavior of the control command is taken into account in the course of distributing the control command. Not only the control command requirement, but also variation of the control command over a sampling interval is included in the performance criterion to be optimized. The result is a control command in the form of a finite difference equation over the given time interval.⁴ It results in a filter dynamics by taking the previous control command into account for the synthesis of current control command. Stability of the proposed dynamic control allocation (CA) approach was proved to ensure the control command is bounded at the steady-state. In this study, we extended the results presented in Ref. 4 by adding a two-step dynamic CA term in deriving the control allocation law. Also, the strict equality constraint, between the virtual and actual control inputs, is relaxed in order to construct control command with a smooth profile. The proposed DCA technique is applied to a spacecraft attitude control problem. The sensor noise and/or irregular signals, which are existent in most of spacecraft attitude sensors, can be handled effectively by the proposed approach.