Strapdown inertial navigation system algorithms based on dual quaternions

Wu, Yuanxin; Hu, Xiaoping; Hu, Dewen; Li, Tao; Lian, Junxiang

doi:10.1109/taes.2005.1413751

Cited by 203 publications

(38 citation statements)

References 26 publications

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“…Alternatively, the pose of the body frame with respect to another frame can be represented more compactly by the unit dual quaternion [22] q B∕I q B∕I;r ϵq B∕I;d q B∕I ϵ 1 2 r I B∕I q B∕I q B∕I ϵ…”

Section: Dual Quaternionsmentioning

confidence: 99%

“…Note that, whereas the relation between r B B∕I and r I B∕I is quadratic in q B∕I , q B∕I;d is related linearly in q B∕I with r B B∕I and r I B∕I . A unit dual quaternion is defined as a dual quaternion that belongs to the set [23] H u d fq ∈ H d : q · q qq q q 1g fq ∈ H d : q r · q r 1 and q r · q d 0g (22) From this constraint, assuming that −180 < ϕ < 180 deg, the scalar parts of the real and dual parts of a unit dual quaternion can be computed from their respective vector parts from…”

Section: Dual Quaternionsmentioning

confidence: 99%

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Extended Kalman Filter for Spacecraft Pose Estimation Using Dual Quaternions

Filipe

Kontitsis

Tsiotras

2015

Journal of Guidance, Control, and Dynamics

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Based on the highly successful quaternion multiplicative extended Kalman filter for spacecraft attitude estimation using unit quaternions, this paper proposes a dual quaternion multiplicative extended Kalman filter for spacecraft pose (i.e., attitude and position) and linear and angular velocity estimation using unit dual quaternions. By using the concept of error unit dual quaternion, defined analogously to the concept of error unit quaternion in the quaternion multiplicative extended Kalman filter, this paper proposes, as far as the authors know, the first multiplicative extended Kalman filter for pose estimation. The state estimate of the dual quaternion multiplicative extended Kalman filter can directly be used by recently proposed pose controllers based on dual quaternions, without any additional conversions, thus providing an elegant solution to the output dynamic compensation problem of the full six degree-offreedom motion of a rigid body. Three formulations of the dual quaternion multiplicative extended Kalman filter are presented. The first takes continuous-time linear and angular velocity measurements with noise and bias and discretetime pose measurements with noise. The second takes only discrete-time pose measurements with noise and hence is suitable for satellite proximity operation scenarios where the chaser satellite has only access to measurements of the relative pose, but requires the relative linear and angular velocities for control. The third formulation takes continuous-time angular velocity and linear acceleration measurements with noise and bias and discrete-time pose measurements with noise. The proposed dual quaternion multiplicative extended Kalman filter is compared with two alternative extended Kalman filter formulations on a five degree-of-freedom air-bearing platform and through extensive Monte Carlo simulations.

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Section: Dual Quaternionsmentioning

confidence: 99%

Section: Dual Quaternionsmentioning

confidence: 99%

Extended Kalman Filter for Spacecraft Pose Estimation Using Dual Quaternions

Filipe

Kontitsis

Tsiotras

2015

Journal of Guidance, Control, and Dynamics

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“…According to the Chasles theorem, the rigid body motion can be represented by a rotation about an axis and a translation along that axis, and on this basis a SDINS algorithm based on dual quaternion (DQ) is presented [9]. The rotation vector and the translation vector are combined to construct the screw vector, which is utilized to calculate the DQs representing the vehicle's motions.…”

Section: Introductionmentioning

confidence: 99%

“…The velocity/position updating algorithms in both [8,9] are related to the rotation vector algorithm which has been commonly used in modern SDINS algorithms. However, the attitude updating is combined with the velocity and position updating in [9], which is different from in [8] or other references, where the attitude updating is generally manipulated separately from the velocity and position updating. The benefit of the DQ-based SDINS algorithm is that the structure of the navigation algorithm can be simplified, and the precision can be promoted.…”

Section: Introductionmentioning

confidence: 99%

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Strapdown Navigation Using Geometric Algebra: Screw Blade Algorithm

Wu¹,

Wang²

2012

POS

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The rigid body motion can be represented by a motor in geometric algebra, and the motor can be rewritten as a trinometric function of the screw blade. In this paper, a screw blade strapdown inertial navigation system (SDINS) algorithm is developed. The trigonometric function form of the motor is derived and utilized to deduce the Bortz equation of the screw blade. The screw blade SDINS algorithm is proposed by using the procedure similar to that of the conventional rotation vector attitude updating algorithm. The superiority of the screw blade algorithm over the conventional ones in precision is analyzed. Simulation results reveal that the screw blade algorithm is more suitable for the high-precision SDINS than the conventional ones.

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Distributed estimation for spatial rigid motion based on dual quaternions

Lee

Dai

2018

Optim Control Appl Methods

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Summary This paper proposes 2 distributed optimization algorithms for the estimation of spatial rigid motion using multiple image sensors in a connected network. The objective is to increase the estimation precision of translational and rotational motion based on dual quaternion models and the cooperation between connected sensors. The dual decomposition subgradient method and distributed Newton optimization method are applied to decompose the filtering task into a series of suboptimal problems and then solve them individually to achieve the global optimality. Our approach assumes that each sensor can communicate with its neighboring sensors to update the individual estimates. Discussion on converging speed of both methods are provided. Simulation examples are demonstrated to compare the 2 distributed algorithms with the traditional extended Kalman filter in terms of estimation accuracy and converging rate.

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Strapdown inertial navigation system algorithms based on dual quaternions

Cited by 203 publications

References 26 publications

Extended Kalman Filter for Spacecraft Pose Estimation Using Dual Quaternions

Extended Kalman Filter for Spacecraft Pose Estimation Using Dual Quaternions

Strapdown Navigation Using Geometric Algebra: Screw Blade Algorithm

Distributed estimation for spatial rigid motion based on dual quaternions

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