Deterministic Global Attitude Estimation

A deterministic attitude estimation problem for a rigid body in an attitude dependent potential field with bounded measurement errors is studied. An attitude estimation scheme that does not use generalized coordinate representations of the attitude is presented here. Assuming that the initial attitude, 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 its size gives 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 estimation scheme is optimal in the sense that the attitude estimation error and the size of the uncertainty ellipsoid is minimized at each measurement instant, and it is global since the attitude is represented by a rotation matrix

[1]  J. Norton,et al.  State bounding with ellipsoidal set description of the uncertainty , 1996 .

[2]  M. Psiaki.  Attitude-Determination Filtering via Extended Quaternion Estimation , 2000 .

[3]  I. Bar-Itzhack,et al.  Attitude Determination from Vector Observations: Quaternion Estimation , 1985, IEEE Transactions on Aerospace and Electronic Systems.

[4]  J. Stuelpnagel,et al.  A Least Squares Estimate of Satellite Attitude (Grace Wahba) , 1966 .

[5]  Taeyoung Lee,et al.  Attitude maneuvers of a rigid spacecraft in a circular orbit , 2006, 2006 American Control Conference.

[6]  N. McClamroch,et al.  A lie group variational integrator for the attitude dynamics of a rigid body with applications to the 3D pendulum , 2005, Proceedings of 2005 IEEE Conference on Control Applications, 2005. CCA 2005..

[7]  G. Wahba.  A Least Squares Estimate of Satellite Attitude , 1965 .

[8]  Uri Shaked,et al.  A game theory approach to robust discrete-time H∞-estimation , 1994, IEEE Trans. Signal Process..

[9]  Boris Polyak,et al.  Multi-Input Multi-Output Ellipsoidal State Bounding , 2001 .

[10]  A. Sanyal.  Optimal Attitude Estimation and Filtering Without Using Local Coordinates Part I: Uncontrolled and Deterministic Attitude Dynamics , 2005, 2006 American Control Conference.

[11]  M. Shuster,et al.  Three-axis attitude determination from vector observations , 1981 .

[12]  Xiaoming Hu,et al.  Drift-free attitude estimation for accelerated rigid bodies , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[13]  F. Schweppe.  Recursive state estimation: Unknown but bounded errors and system inputs , 1967 .