Uncorrelated unscented filtering for spacecraft attitude determination

Leeghim, Henzeh; Choi, Youngjun; Jaroux, Belgacem

doi:10.1016/j.actaastro.2009.12.017

Cited by 17 publications

(36 citation statements)

References 15 publications

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“…We call Re

false(bold-italicq false) : = q_{1} \in double-struckR

the real part or the scalar part of the quaternion and Im( q ): = q the imaginary part of the quaternion. The reader should be aware that some authors define a quaternion with different orders for the real and imaginary parts such that

bold-italicq : = \overset{ι}{true} q_{1} + \overset{ȷ}{true} q_{2} + \overset{k}{true} q_{3} + q_{4}

(cf the works of Crassidis and Markley and Leeghim et al).…”

Section: Quaternions and Their Vector Parameterizationsmentioning

confidence: 99%

“…Within the literature, more than one solution has been given to the problem of creating UFs for quaternionic systems (see, eg, other works). Some works use the same algorithms of the UKFs for Euclidean systems to estimate the state of quaternionic systems (these works are not studied in this work), that is, they do not take unit quaternions norm constraint into account (see, eg, the works of Enayati et al and Vaccarella et al); others do take this constraint into account and can be divided into three groups: a first treats unit quaternion norms but does not preserve them in any problematic item (first row of Table ); a second preserves unit quaternion norms only in some (but not all) problematic items (second row of Table ); and a third preserves unit quaternion norms in all problematic items (third row of Table ). …”

Section: Unscented Kalman Filters For Quaternionic Systemsmentioning

confidence: 99%

“…The sigma points

{\overset{χ}{true}}_{i}^{v, k - 1 false| k - 1}

are supposed to be deviation vector parameterizations sigma points; the deviation quaternion sigma points

{\overset{χ}{true}}_{i}^{k - 1 false| k - 1}

are calculated by

{\tilde{bold-italicχ}}_{i}^{k - 1 | k - 1} = VtoQ ({\tilde{χ}}_{i}^{v, k - 1 | k - 1}), i = 1, ⋯, N,

where VtoQ = RoVtoQ; VtoQ = GeRVtoQ; and VtoQ = QtoQuV (in the work of Cheon and Kim, the two possibilities VtoQ = RoVtoQ and VtoQ = QtoQuV are considered but only in this problematic item, whereas in the others, only QuVs are considered). Table summarizes these relations.…”

Section: Unscented Kalman Filters For Quaternionic Systemsmentioning

confidence: 99%

“…In this work, we analyze all diverse additive unscented filters (UFs; meaning UKFs and SRUKFs) for quaternionic systems proposed in the literature; considering essentially distinct algorithms, we can enumerate the following works …”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Unscented and square‐root unscented Kalman filters for quaternionic systems

Menegaz

Ishihara

2018

Intl J Robust & Nonlinear

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Proper construction of an unscented Kalman filter (UKF) for unit quaternionic systems is not straightforward due to the incompatibility between the algebraic properties of the unit quaternions and the common real vector space operations (additions and scalar multiplications) needed in the steps of a filter algorithm. This work studies, in detail, all UKFs and square-root UKFs for quaternionic systems proposed in the literature. First, we classify the algorithms according to the preservation of the unity norm of the quaternion variables. Second, we propose two new algorithms: the quaternionic additive unscented Kalman filter (QuAdUKF) and a square-root variant of it. The QuAdUKF encompasses all known UKFs for quaternionic systems of the literature preserving, in all steps, the norm of the unit quaternion variables. Besides, it can also yield new UKFs with this norm preservation property. The QuAdUKF's square-root variant has better properties in comparison with all the square-root UKFs for quaternionic systems of the literature. Numerical experiments for a spacecraft attitude estimation problem illustrate the theoretical results. KEYWORDS attitude estimation, square-root unscented Kalman filter (SRUKF), unit quaternion, unscented Kalman filter (UKF)In the control literature, the most common state space models are those where the underlying state, input, and output variables are real vectors, that is, elements that lie in a Euclidean vector space ℝ n . For bodies under two-dimensional or three-dimensional (3D) motions, these Euclidean models fit for dimensionless material points, that is, linear displacements and velocities. However, for large rigid bodies, besides these linear displacement characteristics, the body pointing direction and angular (rotational) movements become important. [1][2][3] It is well known that rotations of rigid bodies in a 3D space are mathematically represented by state trajectories, restricted to a compact manifold called the special orthogonal group, SO(3). The high nonlinearity of this manifold, due to the restriction of variables in specific regions, leads to difficulties in dealing with these variables. In estimation algorithms, performing calculations with variables in SO(3) is often computationally expensive, and more computationally-efficient rotation parameterizations were proposed in the literature. Among the alternative rotation parameterizations, such as Euler angles, rotation vectors (RoVs), and unit quaternions, the unit quaternions are often chosen because, unlike other 4500

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“…We call Re

false(bold-italicq false) : = q_{1} \in double-struckR

bold-italicq : = \overset{ι}{true} q_{1} + \overset{ȷ}{true} q_{2} + \overset{k}{true} q_{3} + q_{4}

(cf the works of Crassidis and Markley and Leeghim et al).…”

Section: Quaternions and Their Vector Parameterizationsmentioning

confidence: 99%

Section: Unscented Kalman Filters For Quaternionic Systemsmentioning

confidence: 99%

“…The sigma points

{\overset{χ}{true}}_{i}^{v, k - 1 false| k - 1}

are supposed to be deviation vector parameterizations sigma points; the deviation quaternion sigma points

{\overset{χ}{true}}_{i}^{k - 1 false| k - 1}

are calculated by

{\tilde{bold-italicχ}}_{i}^{k - 1 | k - 1} = VtoQ ({\tilde{χ}}_{i}^{v, k - 1 | k - 1}), i = 1, ⋯, N,

Section: Unscented Kalman Filters For Quaternionic Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Unscented and square‐root unscented Kalman filters for quaternionic systems

Menegaz

Ishihara

2018

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…Generally, the information about angular rate is obtained from gyros [2]. However, the rate gyros have a tendency to degrade or fail in orbit.…”

Section: Introductionmentioning

confidence: 99%

Angular velocity estimation from measurement vectors of star tracker

Liu

Yang

et al. 2012

Appl. Opt.

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In most spacecraft, there is a need to know the craft's angular rate. Approaches with least squares and an adaptive Kalman filter are proposed for estimating the angular rate directly from the star tracker measurements. In these approaches, only knowledge of the vector measurements and sampling interval is required. The designed adaptive Kalman filter can filter out noise without information of the dynamic model and inertia dyadic. To verify the proposed estimation approaches, simulations based on the orbit data of the challenging minisatellite payload (CHAMP) satellite and experimental tests with night-sky observation are performed. Both the simulations and experimental testing results have demonstrated that the proposed approach performs well in terms of accuracy, robustness, and performance.

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