A Least Squares Estimate of Satellite Attitude (Grace Wahba)

In general, precise attitude information is required to control a ground simulator, which is designed to simulate attitude control of spacecraft. Two algorithms are well-known to determine the attitude through two or more observation vectors. One is the deterministic method, such as the TRI-axis Attitude Determination (TRIAD) algorithm, and the other is the optimal method, such as the QUaternion ESTimator (QUEST) algorithm. This paper suggests a new efficient attitude determination algorithm, which the authors name an algorithm "Averaging TRIAD." First, it is transformed from the attitude matrix to the attitude angle vectors to maintain orthogonal constraints during calculation. Second, the covariance matrix is used instead of the variance and then it is applied to an unbiased minimum variance formula for more accurate solutions. Finally, the authors suggest a methodology to determine the attitude when more than three measurements are given. The performance of the Averaging TRIAD algorithm upon the combination of different sensors, which are fixed to the ground simulator, is investigated by numerical simulation in terms of standard deviations and computational time.

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“…The equation above can be expressed as the following regarding the constraints of the quaternions [9][10][11].…”

Section: Quest Algorithmmentioning

confidence: 99%

Application of a new efficient attitude determination algorithm on a ground simulator

Kim

Lee

et al. 2011

Int. J. Control Autom. Syst.

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“…The unit quaternion representing elevation can now be computed using (12) and (13), and values for the half-angle trigonometric functions are as follows:…”

Section: B Elevation Quaternionmentioning

confidence: 99%

“…The minimum number of measurement and reference vector pairs is two. Early solutions to Wahba's problem directly computed the orientation matrix A [12]. Davenport [13] introduced a method of parameterizing the orientation matrix by a unit quaternion q and proved that the loss function (9) can be transformed into a quadratic gain function of the unit quaternion in the form of…”

Section: Introductionmentioning

confidence: 99%

A Simplified Quaternion-Based Algorithm for Orientation Estimation From Earth Gravity and Magnetic Field Measurements

Yun

Bachmann

McGhee

2008

IEEE Trans. Instrum. Meas.

266

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Abstract-Orientation of a static or slow-moving rigid body can be determined from the measured gravity and local magnetic field vectors. Some formulation of the QUaternion ESTimator (QUEST) algorithm is commonly used to solve this problem. Triads of accelerometers and magnetometers are used to measure gravity and local magnetic field vectors in sensor coordinates. In the QUEST algorithm, local magnetic field measurements affect not only the estimation of yaw but also that of roll and pitch. Due to the deviations in the direction of the magnetic field vector between locations, it is not desirable to use magnetic data in calculations that are related to the determination of roll and pitch. This paper presents a geometrically intuitive 3-degree-of-freedom (3-DOF) orientation estimation algorithm with physical meaning [which is called the factored quaternion algorithm (FQA)], which restricts the use of magnetic data to the determination of the rotation about the vertical axis. The algorithm produces a quaternion output to represent the orientation. Through a derivation based on half-angle formulas and due to the use of quaternions, the computational cost of evaluating trigonometric functions is avoided. Experimental results demonstrate that the proposed algorithm has an overall accuracy that is essentially identical to that of the QUEST algorithm and is computationally more efficient. Additionally, magnetic variations cause only azimuth errors in FQA attitude estimation. A singularity avoidance method is introduced, which allows the algorithm to track through all orientations.

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“…This problem is known as Wahba's problem [1]. The original solution of Wahba's problem is given in [10], and a solution expressed in terms of quaternions (QUEST) is presented in [11]. We use the solution expressed in terms of a rotation matrix without using generalized coordinates [12].…”

Section: Observationsmentioning

confidence: 99%

Deterministic Global Attitude Estimation

Lee¹,

Sanyal²,

Leok³

et al. 2006

Proceedings of the 45th IEEE Conference on Decision and Control

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Abstract-A deterministic attitude estimation problem for a rigid body in an attitude dependent potential field with bounded measurement errors is studied. An attitude estimation scheme that does not use generalized coordinate representations of the attitude is presented here. Assuming that the initial attitude, angular velocity and measurement noise lie within given ellipsoidal bounds, an uncertainty ellipsoid that bounds the attitude and the angular velocity of the rigid body is obtained. The center of the uncertainty ellipsoid provides point estimates, and its size gives the accuracy of the estimates. The point estimates and the uncertainty ellipsoids are propagated using a Lie group variational integrator and its linearization, respectively. The estimation scheme is optimal in the sense that the attitude estimation error and the size of the uncertainty ellipsoid is minimized at each measurement instant, and it is global since the attitude is represented by a rotation matrix.

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A Least Squares Estimate of Satellite Attitude (Grace Wahba)

Cited by 169 publications

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Application of a new efficient attitude determination algorithm on a ground simulator

Application of a new efficient attitude determination algorithm on a ground simulator

A Simplified Quaternion-Based Algorithm for Orientation Estimation From Earth Gravity and Magnetic Field Measurements

Deterministic Global Attitude Estimation

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