• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.894-900
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• 2005

A new approach to the straightforward implementation of the unscented filter in a unit quaternion space is proposed for spacecraft attitude estimation. Since the unscented filter is formulated in a vector space and the unit quaternions do not belong to a vector space but lie on a nonlinear manifold, the weighted sum of quaternion samples does not produce a unit quaternion estimate. To overcome this difficulty, a method of weighted mean computation for quaternions is derived in rotational space, leading to a quaternion with unit norm. A quaternion multiplication is used for predicted covariance computation and quaternion update, which makes a quaternion in a filter lie in the unit quaternion space. Since the quaternion process noise increases the uncertainty in attitude orientation, modeling it either as the vector part of a quaternion or as a rotation vector is considered. Simulation results illustrate that the proposed approach successfully estimates spacecraft attitude for large initial errors and high tip-off rates, and modeling the quaternion process noise as a rotation vector is more optimal than handling it as the vector part of a quaternion.

• 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.

• International Journal of Aeronautical and Space Sciences
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• v.12 no.1
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• pp.24-36
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• 2011

A new approach for spacecraft absolute attitude estimation based on the unscented Kalman filter (UKF) is extended to relative attitude estimation and navigation. This approach for nonlinear systems has faster convergence than the approach based on the standard extended Kalman filter (EKF) even with inaccurate initial conditions in attitude estimation and navigation problems. The filter formulation employs measurements obtained from a vision sensor to provide multiple line(-) of(-) sight vectors from the spacecraft to another spacecraft. The line-of-sight measurements are coupled with gyro measurements and dynamic models in an UKF to determine relative attitude, position and gyro biases. A vector of generalized Rodrigues parameters is used to represent the local error-quaternion between two spacecraft. A multiplicative quaternion-error approach is derived from the local error-quaternion, which guarantees the maintenance of quaternion unit constraint in the filter. The scenario for bounded relative motion is selected to verify this extended application of the UKF. Simulation results show that the UKF is more robust than the EKF under realistic initial attitude and navigation error conditions.

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

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1313-1327
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• 2007

We review the algebraic structure of $\mathbb{H}{\sharp}$ and show that $\mathbb{H}{\sharp}$ has a scalar product that allows as to identify it with semi Euclidean ${\mathbb{E}}^4_2$. We show that a pair q and p of unit split quaternions in $\mathbb{H}{\sharp}$ determines a rotation $R_{qp}:\mathbb{H}{\sharp}{\rightarrow}\mathbb{H}{\sharp}$. Moreover, we prove that $R_{qp}$ is a product of rotations in a pair of orthogonal planes in ${\mathbb{E}}^4_2$. To do that we call upon one tool from the theory of second ordinary differential equations.

• 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.