• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.38 no.7
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• pp.693-701
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• 2010

In this paper, it is proposed that an attitude and position estimation algorithm based on a stereo camera system for a helmet tracker. Stereo camera system consists of two CCD camera, a helmet, infrared LEDs and a frame grabber. Fifteen infrared LEDs are feature points which are used to determine the attitude and position of the helmet. These features are arranged in triangle pattern with different distance on the helmet. Vision-based the attitude and position algorithm consists of feature segmentation, projective reconstruction, model indexing and attitude estimation. In this paper, the attitude estimation algorithm using UQ (Unit Quaternion) is proposed. The UQ guarantee that the rotation matrix is a unitary matrix. The performance of presented algorithm is verified by simulation and experiment.

• Journal of the Optical Society of Korea
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• v.20 no.1
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• pp.42-54
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• 2016

A hybrid color and grayscale images encryption scheme based on the quaternion Hartley transform (QHT), the two-dimensional (2D) logistic map, the double random phase encoding (DRPE) in gyrator transform (GT) domain and the three-step phase-shifting interferometry (PSI) is presented. First, we propose a new color image processing tool termed as the quaternion Hartley transform, and we develop an efficient method to calculate the QHT of a quaternion matrix. In the presented encryption scheme, the original color and grayscale images are represented by quaternion algebra and processed holistically in a vector manner using QHT. To enhance the security level, a 2D logistic map-based scrambling technique is designed to permute the complex amplitude, which is formed by the components of the QHT-transformed original images. Subsequently, the scrambled data is encoded by the GT-based DRPE system. For the convenience of storage and transmission, the resulting encrypted signal is recorded as the real-valued interferograms using three-step PSI. The parameters of the scrambling method, the GT orders and the two random phase masks form the keys for decryption of the secret images. Simulation results demonstrate that the proposed scheme has high security level and certain robustness against data loss, noise disturbance and some attacks such as chosen plaintext attack.

• Journal of Electrical Engineering and Technology
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• v.12 no.4
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• pp.1675-1682
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• 2017

This paper deals with three dimensional orientation estimation algorithm for an attitude and heading reference system (AHRS) based on nine-axis inertial/magnetic sensor signals. In terms of the orientation estimation based on the use of a Kalman filter (KF), the quaternion is arguably the most popular orientation representation. However, one critical drawback in the quaternion representation is that undesirable magnetic disturbances affect not only yaw estimation but also roll and pitch estimations. In this paper, a sequential direction cosine matrix-based orientation KF for AHRS has been presented. The proposed algorithm uses two linear KFs, consisting of an attitude KF followed by a heading KF. In the latter, the direction of the local magnetic field vector is projected onto the heading axis of the inertial frame by considering the dip angle, which can be determined after the attitude KF. Owing to the sequential KF structure, the effects of even extreme magnetic disturbances are limited to the roll and pitch estimations, without any additional decoupling process. This overcomes an inherent issue in quaternion-based estimation algorithms. Validation test results show that the proposed method outperforms other comparison methods in terms of the yaw estimation accuracy during perturbations and in terms of the recovery speed.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.343-358
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• 2008

The primitive orders in a quaternion algebra play a central role of the theory of Hecke operators. In this paper, we study theta series generated by Brandt matrices and its applications to almost Ramanujan graphs.

• Bulletin of the Korean Chemical Society
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• v.28 no.10
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• pp.1705-1708
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• 2007

Geometric manipulation of molecules is an essential elementary component in computational modeling programs for molecular structure, stability, dynamics, and design. The computational complexity of transformation of internal coordinates to Cartesian coordinates was discussed before.1 The use of rotation matrices was found to be slightly more efficient than that of quaternion although quaternion operators have been widely advertised for rotational operations, especially in molecular dynamics simulations of liquids where the orientation is a dynamical variable.2 The discussion on computational efficiency is extended here to a more general case in which bond angles and sidechain torsion angles are allowed to vary. The algorithm of Thompson3 is derived again in terms of quaternions as well as rotation matrices, and an algorithm with optimal efficiency is described. The algorithm based on rotation matrices is again found to be slightly more efficient than that based on quaternions.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.809-824
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• 1997

With the primitive orders in quaternion algebra, theta series associated with these orders are constructed. Here, we studied the space of modular forms generated by these theta series.

• Honam Mathematical Journal
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• v.44 no.2
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• pp.195-208
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• 2022

In this article, the matrix representation of commutative elliptic octonions and their properties are described. Firstly, definitions and theorems are given for the commutative elliptic octonion matrices using the elliptic quaternion matrices. Then the adjoint matrix, eigenvalue and eigenvector of the commutative elliptic octonions are investigated. Finally, α = -1 for the Gershgorin Theorem is proved using eigenvalue and eigenvector of the commutative elliptic octonion matrix.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.190-196
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• 2008

The dynamical rotor system is investigated through the derivation and formulations of the dynamic equation of the rotating system in terms of both inertial and fixed frame of the system as well as quaternion. The investigation is aimed at analyzing the dynamical rotating system precession speed. The resulting equations of motion consist of the consistent mass matrix and gyroscopic matrix. The formulation shows its features and difference between its linearity and nonlinearity.

• Honam Mathematical Journal
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• v.37 no.4
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• pp.569-575
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• 2015

In this paper, we research some properties of quaternionic regular functions in Clifford analysis. We investigate the corresponding Cauchy-Riemann system and find regularities of some hypercomplex valued functions.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.167.5-167
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• 2001

Single point attitude determination method provides an optimal attitude minimizing the Wahba loss function. However, for the insufficient number of measurement vectors, the conventional single point methods has no unique solution. Thus, we introduce the sequential method to and an optimal attitude minimizing the windowed loss function. In this paper, this function is de ned as the sum of square errors for all measurement vectors within the axed sliding window. For simple implementation, the proposed algorithm is rewritten as a recursive form. Moreover, the covariance matrix is derived and expressed as a recursive form. Finally, we apply this algorithm to the attitude determination system with three LOS measurement sensors.