Attitude Determination from Vector Observations: Quaternion Estimation

Bar-Itzhack, Itzhack Y.; Oshman, Yaakov

doi:10.1109/taes.1985.310546

Cited by 214 publications

(115 citation statements)

References 11 publications

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“…[ 46 ]: (27) The particular problem that we will address is the assessment of noise properties in the gyroscope from measurements. In this context, the motions of the platform will be taken to be zero, i.e., x i = 0.…”

Section: Model Formulationmentioning

confidence: 99%

Kinematic state estimation and motion planning for stochastic nonholonomic systems using the exponential map

Park¹,

Liu²,

et al. 2008

Robotica

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SUMMARYA nonholonomic system subjected to external noise from the environment, or internal noise in its own actuators, will evolve in a stochastic manner described by an ensemble of trajectories. This ensemble of trajectories is equivalent to the solution of a Fokker-Planck equation that typically evolves on a Lie group. If the most likely state of such a system is to be estimated, and plans for subsequent motions from the current state are to be made so as to move the system to a desired state with high probability, then modeling how the probability density of the system evolves is critical. Methods for solving Fokker-Planck equations that evolve on Lie groups then become important. Such equations can be solved using the operational properties of group Fourier transforms in which irreducible unitary representation (IUR) matrices play a critical role. Therefore, we develop a simple approach for the numerical approximation of all the IUR matrices for two of the groups of most interest in robotics: the rotation group in three-dimensional space, SO(3), and the Euclidean motion group of the plane, SE(2). This approach uses the exponential mapping from the Lie algebras of these groups, and takes advantage of the sparse nature of the Lie algebra representation matrices. Other techniques for density estimation on groups are also explored. The computed densities are applied in the context of probabilistic path planning for kinematic cart in the plane and flexible needle steering in three-dimensional space. In these examples the injection of artificial noise into the computational models (rather than noise in the actual physical systems) serves as a tool to search the configuration spaces and plan paths. Finally, we illustrate how density estimation problems arise in the characterization of physical noise in orientational sensors such as gyroscopes.

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Section: Model Formulationmentioning

confidence: 99%

Kinematic state estimation and motion planning for stochastic nonholonomic systems using the exponential map

Park¹,

Liu²,

et al. 2008

Robotica

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“…The solution to the Wahba problem provides single point attitude estimates and requires all the measurements to be synchronized. The EKF and its attitude-specific extensions (most notably additive EKF [9] and multiplicative EKF [10]) in contrast are recursive estimators.…”

Section: Introductionmentioning

confidence: 99%

Q-Method Extended Kalman Filter

Ainscough

Zanetti

Christian

et al. 2015

Journal of Guidance, Control, and Dynamics

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“…A sample of the literature in spacecraft attitude estimation can be found in [4][5][6][7][8]. Applications of attitude estimation to unmanned vehicles and robots can be found in [2,[9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Global optimal attitude estimation using uncertainty ellipsoids

Sanyal

Lee

Leok

et al. 2008

Systems & Control Letters

103

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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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Attitude Determination from Vector Observations: Quaternion Estimation

Cited by 214 publications

References 11 publications

Kinematic state estimation and motion planning for stochastic nonholonomic systems using the exponential map

Kinematic state estimation and motion planning for stochastic nonholonomic systems using the exponential map

Q-Method Extended Kalman Filter

Global optimal attitude estimation using uncertainty ellipsoids

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