• Bulletin of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.1401-1409
• /
• 2016

In complex analysis, the Bergman kernels for two biholomorphically equivalent complex domains satisfy the transformation formula. Recently new Bergman theory of slice regular functions of the quaternion variables has been investigated. In this paper we construct the transformation formula of the slice Bergman kernels under slice biregular functions in the setting of the quaternion variables.

• East Asian mathematical journal
• /
• v.31 no.1
• /
• pp.119-126
• /
• 2015

The aim of this paper is to research certain properties of conic regular functions of conic quaternion variables in $\mathbb{C}^2$. We generalize the properties of conic regular functions and the Cauchy theorem of conic regular functions in conic quaternion analysis.

• East Asian mathematical journal
• /
• v.33 no.3
• /
• pp.309-315
• /
• 2017

In this paper, we investigate the regularities of the hyper-complex valued functions of the split quaternion variables. We define several differential operators for the split qunaternionic function. We research several left split regular functions for each differential operators. We also investigate split harmonic functions. And we find the corresponding Cauchy-Riemann system and the corresponding Cauchy theorem for each regular functions on the split quaternion field.

• Journal of Institute of Control, Robotics and Systems
• /
• v.14 no.9
• /
• pp.865-872
• /
• 2008

Spacecraft attitude estimation using the nonlinear unscented filter is addressed to fully utilize capabilities of the unscented transformation. To release significant computational load, an efficient technique is proposed by reasonably removing correlation between random variables. This modification introduces considerable reduction of sigma points and computational burden in matrix square-root calculation for most nonlinear systems. Unscented filter technique makes use of a set of sample points to predict mean and covariance. The general QUEST(QUaternion ESTimator) algorithm preserves explicitly the quaternion normalization, whereas extended Kalman filter(EKF) implicitly obeys the constraint. For spacecraft attitude estimation based on quaternion, an approach to computing quaternion means from sampled quaternions with guarantee of the quaternion norm constraint is introduced applying a constrained optimization technique. Finally, the performance of the new approach is demonstrated using a star tracker and rate-gyro measurements.

• East Asian mathematical journal
• /
• v.31 no.1
• /
• pp.127-134
• /
• 2015

We give a rth conic regular functions with conic quaternion variables in $\mathbb{C}^2$ and obtain a hyper-conjugate harmonic function of conic regular function in conic quaternions in the sense of Clifford analysis.

• East Asian mathematical journal
• /
• v.29 no.5
• /
• pp.521-527
• /
• 2013

The aim of this paper is to define hyperholomorphic function with sedenion variables in $\mathbb{C}^8$ and research the properties of hyperholomorphic functions of sedenion variables. We generalize the properties of hyperholomorphic functions in sedenionic analysis.

• The Pure and Applied Mathematics
• /
• v.23 no.1
• /
• pp.97-104
• /
• 2016

We give representations of differential operators and rules for addition and multiplication of dual quaternions. Also, we research the notions and properties of a regular function and a corresponding harmonic function with values in dual quaternions of Clifford analysis.

• The Pure and Applied Mathematics
• /
• v.14 no.2 s.36
• /
• pp.91-98
• /
• 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 $C^2{\times}C^2$.

• East Asian mathematical journal
• /
• v.31 no.5
• /
• pp.667-675
• /
• 2015

In this paper, we provide some properties of several left regular functions in Clifford analysis. We find the corresponding Cauchy-Riemann system and conjugate harmonic functions of the harmonic functions, for each left regular function in the sense of several complex variables. And we investigate certain properties of generalized quaternions in Clifford analysis.

• Journal of Institute of Control, Robotics and Systems
• /
• v.19 no.10
• /
• pp.941-946
• /
• 2013

In this paper, an enhanced method for attitude determination is proposed for systems using an IMU (Inertial Measurement Unit). In attitude determination with IMU, it is generally assumed that the IMU can be located in the center of gravity on the vehicle. If the IMU is not located in the center of gravity, the accelerometers of the IMU are disturbed from additive accelerations such as centripetal acceleration and tangential acceleration. Additive accelerations are derived from the lever arm which is the distance between the center of gravity and the position of the IMU. The performance of estimation errors can be maintained in system with a non-zero lever arm, if the lever arm is estimated to remove the additive accelerations from the accelerometer's measurements. In this paper, an estimation using Kalman filter is proposed to include the lever arm in the state variables of the state space equation. For the Kalman filter, the process model and the measurement model for attitude determination are made up by using quaternion. In order to evaluate the proposed algorithm, both of the simulations and the experiments are performed for the simplified scenario of motion.