A Least Squares Estimate of Satellite Attitude

Wahba, Grace

doi:10.1137/1007077

Cited by 966 publications

(545 citation statements)

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“…As a single-frame method, SVD aims to solve the problem formulated by Grace Wahba [21]. In every single time frame SVD can estimate the coarse attitude only by using the measurement results and the model vectors.…”

Section: Svd Methodsmentioning

confidence: 99%

Nanosatellite Attitude Estimation from Vector Measurements Using SVD-Aided UKF Algorithm

Çilden

Söken

Hajiyev

2017

Metrology and Measurement Systems

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The integrated Singular Value Decomposition (SVD) and Unscented Kalman Filter (UKF) method can recursively estimate the attitude and attitude rates of a nanosatellite. At first, Wahba's loss function is minimized using the SVD and the optimal attitude angles are determined on the basis of the magnetometer and Sun sensor measurements. Then, the UKF makes use of the SVD's attitude estimates as measurement results and provides more accurate attitude information as well as the attitude rate estimates. The elements of "Rotation angle error covariance matrix" calculated for the SVD estimations are used in the UKF as the measurement noise covariance values. The algorithm is compared with the SVD and UKF only methods for estimating the attitude from vector measurements. Possible algorithm switching ideas are discussed especially for the eclipse period, when the Sun sensor measurements are not available.

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Section: Svd Methodsmentioning

confidence: 99%

Nanosatellite Attitude Estimation from Vector Measurements Using SVD-Aided UKF Algorithm

Çilden

Söken

Hajiyev

2017

Metrology and Measurement Systems

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“…Wahba defined a problem which aims to minimize the loss between chosen reference and measured unit vectors in 1965 [1]. In equation (8), b i (set of unit vectors in body frame) and r i (set of unit vectors in reference frame) with their a i (non-negative weight) are the loss function variables obtained for instant time intervals.…”

Section: Attitude Matrixmentioning

confidence: 99%

“…Single-frame method is one of the common methods used for small satellite attitude determination system. In this method, vectors coming from the selected sensor data and developed models can be placed in Wahba's problem [1][2][3]. Coordinate systems used as reference frame and body frame can be transformed to each other with necessary input parameters.…”

Section: Introductionmentioning

confidence: 99%

Singular value decomposition based satellite attitude determination using different sensor configurations

Cilden–Guler

Hajiyev

2017

Int. J. Metrol. Qual. Eng.

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Abstract. Satellite's attitude can be determined by using several different ways. In order to use a recursive filter to determine the attitude especially after crucial intervals for the satellite including detumbling, eclipse, etc., single-frame methods can be used, and singular value decomposition (SVD) method has been selected because of its robustness for this paper. They can be placed for the initial values, or continuous input to the filter in addition to covariance matrix at each step. Also, sensor configurations depending on the position of the Sun are considered and used in the SVD method. Wahba's loss function is minimized with separating the basic matrix including the reference and model vectors into singular values because many researches show the SVD as the most robust algorithm after error analyses between several single-frame methods. Sun sensor, magnetometer, and horizon sensor are the selected common attitude sensors for small satellites in order to compare their attitude determination performances. For this purpose, absolute errors for different sensor configurations in the simulation environment in addition to the RMS errors are presented. The purpose of the paper is to present an attitude determination concept for a nanosatellite. Also, different sensor configurations are considered in the single-frame method with switching logic depending on the vector data. Horizon sensor and sun sensor are the optimum pair for the light side of the Earth on the other hand, during the eclipse; horizon sensor and magnetometer give the most accurate results. Study shows that the proposed algorithm can be performed for initial values to the Kalman filter, and in the transient phase before the filter tuned in practical satellite usage. In the eclipse period, sun-independent sensors are used and changing configurations provide better attitude estimation results to filtering techniques.

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“…The problem (1) is known as Wahba's problem [3]. The original solution of Wahba's problem is given in [15], and a solution expressed in terms of quaternions, known as the QUEST algorithm, is presented in [7].…”

Section: Attitude Determination Proceduresmentioning

confidence: 99%

Global optimal attitude estimation using uncertainty ellipsoids

Sanyal

Lee

Leok

et al. 2008

Systems & Control Letters

102

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A deterministic attitude estimation problem for a rigid body in a potential field, with bounded attitude and angular velocity measurement errors is considered. An attitude estimation algorithm that globally minimizes the attitude estimation error is obtained. Assuming that the initial attitude, the initial 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 the size of the uncertainty ellipsoid measures 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 attitude and angular velocity estimates are optimal in the sense that the sizes of the uncertainty ellipsoids are minimized.

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A Least Squares Estimate of Satellite Attitude

Cited by 966 publications

References 0 publications

Nanosatellite Attitude Estimation from Vector Measurements Using SVD-Aided UKF Algorithm

Nanosatellite Attitude Estimation from Vector Measurements Using SVD-Aided UKF Algorithm

Singular value decomposition based satellite attitude determination using different sensor configurations

Global optimal attitude estimation using uncertainty ellipsoids

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