Dot Product Equality Constrained Attitude Determination from Two Vector Observations: Theory and Astronautical Applications

Wu, Jin; Shan, Shangqiu

doi:10.3390/aerospace6090102

Cited by 8 publications

(5 citation statements)

References 46 publications

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“…Gaussian white and mutually independent observation noises with N c denoting the Gaussian distribution. Note that the vector observation based attitude determination is a common application scenario because the Sun sensor, magnetometer, horizon sensor, and the gravitational accelerometer are usually equipped by most spacecrafts in astronautical engineering [1]. A graphical presentation of target application scenario is given in Figure 1.…”

Section: Primaries and Problem Definitionmentioning

confidence: 99%

“…The navigation and control operations in aerospace engineering usually require adequate accurate knowledge of spacecraft orientation in space, and attitude determination from vector observations is usually employed in astronautically applications [1][2][3][4]. The widely used Kalman type filters can infer the state in Euclidean vector space by fusing attitude dynamic and observation sensor according to their probabilities [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

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An Improved Invariant Kalman Filter for Lie Groups Attitude Dynamics with Heavy-Tailed Process Noise

Wang

Zhang

et al. 2021

Machines

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Attitude estimation is a basic task for most spacecraft missions in aerospace engineering and many Kalman type attitude estimators have been applied to the guidance and navigation of spacecraft systems. By building the attitude dynamics on matrix Lie groups, the invariant Kalman filter (IKF) was developed according to the invariance properties of symmetry groups. However, the Gaussian noise assumption of Kalman theory may be violated when a spacecraft maneuvers severely and the process noise might be heavy-tailed, which is prone to degrade IKF’s performance for attitude estimation. To address the attitude estimation problem with heavy-tailed process noise, this paper proposes a hierarchical Gaussian state-space model for invariant Kalman filtering: The probability density function of state prediction is defined based on student’s t distribution, while the conjugate prior distributions of the scale matrix and degrees of freedom (dofs) parameter are respectively formulated as the inverse Wishart and Gamma distribution. For the constructed hierarchical Gaussian attitude estimation state-space model, the Lie groups rotation matrix of spacecraft attitude is inferred together with the scale matrix and dof parameter using the variational Bayesian iteration. Numerical simulation results illustrate that the proposed approach can significantly improve the filtering robustness of invariant Kalman filter for Lie groups spacecraft attitude estimation problems with heavy-tailed process uncertainty.

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Section: Primaries and Problem Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Improved Invariant Kalman Filter for Lie Groups Attitude Dynamics with Heavy-Tailed Process Noise

Wang

Zhang

et al. 2021

Machines

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“…Consider the discrete attitude dynamics on SO (3) associated to observations as follows: where the Gaussian white process noise wk∼ℕtrue(0d×1,Qwtrue) ∈ℝ3 denotes the small process noise injected through the Lie exponential term Exp G ( w k ); Yk∈ℝ6 is a composition of the discrete noisy observations yk′∈ℝ3 and yk′′∈ℝ3 with known vector b′∈ℝ3 and b′′∈ℝ3(A common application of the vector observation–based attitude estimation problem is to determine the attitude of satellites from the vector observations of sun sensor and the magnetic field sensors as shown in Figure 1 Wu and Shan (2019); vk′,vk′′∈ℝ3 are the independent isotropic white noises and their covariance are diagonal matrices and respectively represented by Q v’ and Q v” .…”

Section: Application To Model Conversion Of Attitude Estimation Syste...mentioning

confidence: 99%

On the state independency and log-linearity of error propagation for discrete group affine systems with application to attitude estimation

Wang

Zhang

2021

AEAT

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Purpose This paper aims to propose a general and rigorous study on the propagation property of invariant errors for the model conversion of state estimation problems with discrete group affine systems. Design/methodology/approach The evolution and operation properties of error propagation model of discrete group affine physical systems are investigated in detail. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis which provide a deeper insight and are beneficial to the control and estimation of discrete group affine systems. Findings The investigation on the state independency and log-linearity of invariant errors for discrete group affine systems are presented in this work, and it is pivotal for the convergence and stability of estimation and control of physical systems in engineering practice. The general expressions of the propagation properties are proposed together with the rigorous proof and analysis. Practical implications An example application to the attitude dynamics of a rigid body together with the attitude estimation problem is used to illustrate the theoretical results. Originality/value The mathematical proof and analysis of the state independency and log-linearity property are the unique and original contributions of this work.

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“…As a result, it became and still is a popular attitude determination method, especially for real-time applications. Other quaternion-based methods include the Estimator of the Optimal Quaternion (ESOQ) [ 20 ], the Second Estimator of the Optimal Quaternion (ESOQ2) [ 21 ], the fast linear quaternion attitude estimator (FLAE) [ 22 ], and others such as [ 23 ], where the dot product equality constraint results in simplified covariance expressions for the quaternion solution. The matrix-based solution which applies the SVD is robust but computationally expensive [ 24 ], and its covariance makes some assumptions on the weights of the Wabha loss function.…”

Section: Introductionmentioning

confidence: 99%

Attitude Uncertainty Analysis of a Three-Vehicle Constrained Formation

Cruz

Batista

2022

Sensors

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The uncertainty analysis of attitude estimates enables the comparison between different methods, and, thus, it is important for practical applications. This work studies the uncertainty for the attitude determination of a three-vehicle constrained formation. Moreover, the existing solution is improved by including the uncertainty results in a weighted orthogonal Procrustes problem. In the formation considered herein, the vehicles measure inertial references and relative line-of-sight vectors. Nonetheless, the line of sight between two elements of the formation is restricted. The uncertainty analysis uses perturbation theory and, consequently, considers a small first-order perturbation in the measurements. The covariance matrices are obtained for all relative and inertial attitude candidates from the linearization of the solution using a first-order Taylor expansion. Then, the uncertainty is completed by considering the covariance for the weighted orthogonal Procrustes problem, from the literature, and the definition of covariance for the remaining attitudes. The uncertainty characterization is valid for configurations with a unique solution. Finally, the theoretical results are validated by applying Monte Carlo simulations, which show that the predicted errors are statistically consistent with the numerical implementation of the solution with noise. Furthermore, the theoretical uncertainty predicts the accuracy changes near special configurations where there is loss of information.

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Dot Product Equality Constrained Attitude Determination from Two Vector Observations: Theory and Astronautical Applications

Cited by 8 publications

References 46 publications

An Improved Invariant Kalman Filter for Lie Groups Attitude Dynamics with Heavy-Tailed Process Noise

An Improved Invariant Kalman Filter for Lie Groups Attitude Dynamics with Heavy-Tailed Process Noise

On the state independency and log-linearity of error propagation for discrete group affine systems with application to attitude estimation

Attitude Uncertainty Analysis of a Three-Vehicle Constrained Formation

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