• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2005년도 ICCAS
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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.

• Advances in aircraft and spacecraft science
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• 제1권4호
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• pp.427-441
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• 2014

Orbit-raising is an important step to place spacecraft from parking orbits into working orbits. Attitude control system design is crucial in the success of orbit-raising. Several text books have discussed this design and focused mainly on the traditional methods based on single-input single-output (SISO) transfer function models. These models are not good representations for many orbit-raising control systems which have multiple thrusters and each thruster has impact on the attitude defined by all outputs. Only one published article is known to use a more suitable multi-input multi-output (MIMO) Euler angle model in spacecraft orbit-raising attitude control system design. In this paper, a quaternion based MIMO model for the orbit-raising attitude control system design is proposed. The advantages of using quaternion based model for orbit-raising control system designs are (a) there is no need for mathematical transformations because the attitude measurements are normally given by quaternion, (b) quaternion based model does not depend on rotational sequences, which reduces the chance of human errors, and (c) the singular point of reduced quaternion model is the farthest from the operational point where linearization is performed. We will show that performance of quaternion model based design will be as good as the performance of Euler angle model based design for orbit-raising problem.

• 제어로봇시스템학회논문지
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• 제14권9호
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• pp.865-872
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• 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.

• International Journal of Aeronautical and Space Sciences
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• 제12권1호
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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.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2001년도 하계학술대회 논문집 D
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• pp.2092-2095
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• 2001

In this paper, the performance of a new alternative form of three-axis attitude estimation algorithm for a rigid body is evaluated via simulation for the situation where the observed vectors are the estimated baselines of a GPS antenna array. This method is derived based on a simple iterative nonlinear least-squares with four elements of quaternion parameter. The representation of quaternion parameters for three-axis attitude of a rigid body is free from singularity problem. The performance of the proposed algorithm is compared with other eight existing methods, such as, Transformation Method (TM), Vector Observation Method (VOM), TRIAD algorithm, two versions of QUaternion ESTimator (QUEST), Singular Value Decomposition (SVD) method, Fast Optimal Attitude Matrix (FOAM), Slower Optimal Matrix Algorithm (SOMA).

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2006년도 추계학술대회 논문집
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• pp.85-86
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• 2006

• Journal of Mechanical Science and Technology
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• 제20권3호
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• pp.376-381
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• 2006

In this paper, the quaternion, the dual Euler, and the direction cosine methods are numerically compared using a non-aerodynamic 6 degree-of-freedom rigid model at all-attitude angles of an aircraft. The dual Euler method turns out to be superior to the others in the applications because it shows better numerical accuracy, stability, and robustness in integration step sizes. The dual Euler method is affordably less efficient than the quaternion method in terms of computational cost. Numerical accuracy and stability, which allow larger integration step sizes, are more critical in modern real-time applications than computational efficiency because of today's increased computational power. If the quaternion method is required because of constraints in computation time, then a suppression mechanism should be provided for algebraic constraint errors which will eventually add computational burden.

• 한국항공우주학회지
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• 제47권11호
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• pp.795-802
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• 2019

본 논문에서는 인공위성의 근접운용에서 발생할 수 있는 위치-자세 결합운동을 정의하고, 이를 듀얼 쿼터니언 기반의 운동방정식을 통해 접근한다. 인공위성의 위치-자세 결합운동은 두 위성의 상대운동에서 목표 지점이 무게 중심이 아닌 위성체 위의 임의의 점에 위치할 때 발생하며, 특히 근거리 운용에서 명확히 보여진다. 듀얼 쿼터니언 기반의 운동방정식은 각속도 상태를 직접 반영하여, 자세의 변화가 위치에 영향을 미치는 위치-자세 결합운동을 간결하게 정의할 수 있다. 여기에서는 위치-자세 결합운동의 해결을 위해 기존의 접근방법과 함께 듀얼 쿼터니언 기반의 운동방정식을 새롭게 제시한다. 수치 시뮬레이션에서는 두 위성의 상대운동에서 위치-자세 결합운동으로 목표 지점에 대한 위치 오차가 발생함을 보이고, 듀얼 쿼터니언 기반의 운동방정식이 이를 해결할 수 있음을 검증한다.

• Advances in aircraft and spacecraft science
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• 제4권3호
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• pp.335-351
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• 2017

Kalman filter based spacecraft attitude estimation has been used in many space missions and has been widely discussed in literature. While some models in spacecraft attitude estimation include spacecraft dynamics, most do not. To our best knowledge, there is no comparison on which model is a better choice. In this paper, we discuss the reasons why spacecraft dynamics should be considered in the Kalman filter based spacecraft attitude estimation problem. We also propose a reduced quaternion spacecraft dynamics model which admits additive noise. Geometry of the reduced quaternion model and the additive noise are discussed. This treatment is easier in computation than the one with full quaternion. Simulations are conducted to verify our claims.

• 한국항공우주학회지
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• 제38권7호
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• pp.693-701
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• 2010

본 논문에서는 스테레오 카메라 시스템을 이용하여 헬멧의 자세 및 위치를 추정하는 알고리즘을 제안한다. 본 논문에서 구축한 시스템은 두 대의 CCD카메라와 헬멧 그리고 적외선 LED, 영상편집 보드로 구성된다. 이 중 15개의 적외선 LED는 헬멧에 서로 다른 길이로 삼각형 패턴으로 고정되어, 헬멧의 자세 및 위치를 결정하기 위한 특징점이 된다. 본 논문에서 제안한 알고리즘은 특징점 추출, 투영 재구성, 모델 인덱싱 과정으로 구성되며, 단위 쿼터니언(UQ, Unit Quaternion)을 이용하여 자세 및 위치를 추정한다. UQ를 이용하여 회전행렬를 구하면, 회전 행렬이 유니터리 행렬(Unitary Matrix)이 되는 것을 보장할 수 있다. 제안된 알고리즘은 시뮬레이션과 실제 실험 데이터를 이용하여 그 성능을 검증하였다.