A comparison study of state estimators for a spherical pendulum

Gregory, Elizabeth Dimmitt
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[Honolulu] : [University of Hawaii at Manoa], [May 2011]
In the field of spacecraft attitude determination and control, the prevailing state estimation method is the Extended Kalman Filter (EKF). Often, with the EKF, a lower dimensional representation is used to describe the attitude of the spacecraft which leads to singularities and ambiguities. The EKF also requires the definition of the uncertainty of the process and sensor noise to be described with a Gaussian distribution. HawaiʻiSat-1 plans to use an alternative, deterministic estimation scheme which uses the global representation of attitude and angular velocity and which only requires the measurement noise and the initial state uncertainty to be bounded by known ellipsoidal bounds. These bounds are referred to as uncertainty ellipsoids. In order to reduce risk associated with using an estimation scheme with no flight history, a comparison of this deterministic estimation scheme with an EKF was conducted for a spherical pendulum as a simplified analogy for the pointing needs of a satellite. This thesis documents the comparison. The deterministic estimation schemes use a reduced attitude vector and the angular velocity vector to represent the state. This state representation is also used to define uncertainty ellipsoids characterizing bounds on the state estimate error and sensor measurement error. The Extended Kalman Filter uses spherical coordinates to represent the state and Gaussian noise to describe uncertainty of both the estimate and sensor readings. The comparison concludes with the deterministic estimator performing comparably or better than the EKF for various initial conditions and noise models.
M.S. University of Hawaii at Manoa 2011.
Includes bibliographical references.
Extended Kalman Filter
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