• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.641-644
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• 2005

Let L/F be a Galois quadratic extension such that F contains a primitive n-th root of 1. Let N = L(${\alpha}^{{\frac{1}{n}}$) where ${\alpha}{\in}L{\ast}$. We show that if $N_{L/F}({\alpha})\;{\in}L^n{\cap}F$, and [N : L] = m, then $G(N/ F) {\simeq}D_m$ or generalized quaternion group whether $N_{L/F}({\alpha})\;{\in}\;F^n\;or\;{\notin}F^n$, respectively.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.809-817
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• 2013

We research properties of a corresponding Cauchy theorem of hyperholomorphic functions in an open set of product complex spaces, in the sense of complex Clifford analysis.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.44-48
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• 1994

A new method of quaternion feedback control for the attitude acquisition of spacecraft is suggested to limit the angular rates of rigid body which are not desirable and make a control algorithm complicate. New attitude acquisition control algorithm is evaluated and compared with the existing quaternion feedback control method for the large slewing maneuvers through simulations. The simulation results reveal that a new method is effective on limiting the angular rates of spacecraft.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.672-675
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• 1996

This paper presents algorithm including Kalman filter for transfer alignment of velocity and quaternion matching method, when master inertial navigation system is a gimbled type and slave inertial navigation system is a strapdown type on a cruising ship which is naturally in motion of horizontal axis attitude. And relative attitudes are considered on a measurement equation for quaternion matching between master INS and slave INS.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.331-339
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• 2012

In this paper, let Q be the real quaternion algebra which consists of all quaternionic numbers, and let G be the Lie group of all automorphisms of the algebra Q. Assume that g is an arbitrary given left invariant Riemannian metric on the Lie group G. Then, we obtain a necessary and sufficient condition for an automorphism of the group G to be harmonic.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.8
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• pp.717-725
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• 2005

The adaptive filter is proposed for the INS/GPS. The proposed filter can estimate the variance of the process noise using the residual of the filter. To verify the efficiency of the adaptive filter, it is applied to the loosely-coupled INS/CPS that employs the additive quaternion error model. Simulation results demonstrate that the proposed filter is more effective in estimating the attitude error than EKF.

• The Pure and Applied Mathematics
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• v.14 no.2 s.36
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• pp.91-98
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• 2007

We give definitions of hyperholomorphic functions of quaternionic functions of two quaternionic variables. We investigate properties of hyperholomorphic functions on quaternion analysis, and obtain equivalence relations for domains of hyperholomorphy and hyper Stein domains in a domain of $C^2{\times}C^2$.

• The Pure and Applied Mathematics
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• v.20 no.4
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• pp.251-258
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• 2013

We define an ${\varepsilon}$-regular function in dual quaternions. From the properties of ${\varepsilon}$-regular functions, we represent the Taylor series of ${\varepsilon}$-regular functions with values in dual quaternions.

• Bulletin of the Korean Mathematical Society
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• v.10 no.1
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• pp.31-32
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• 1973

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.37 no.6
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• pp.465-472
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• 2019

The SPR (Single Photo Resection) is widely used as a method of estimating the EOPs (Exterior Orientation parameters) at the time of taking a photograph, but it requires an initial value and has a disadvantage of being sensitive to the initial value. In this study, we introduce quaternion-based single photo resection and PnP (Perspective-n-Point) algorithm that do not require initial values and compare the results. Photos were taken using a general smartphone, and the ground control point acquisition was based on the hybrid MMS (Mobile Mapping System) point cloud data possessed by the researchers. As a result, when the collinear condition based SPR is true value, quaternion-based SPR has higher attitude angle estimation accuracy than PnP algorithm. In case of camera position estimation, both algorithms showed accuracy within 0.8m when compared with ground control points.