Attitude Estimation or Quaternion Estimation?
- PDF / 2,646,678 Bytes
- 18 Pages / 496.08 x 722.88 pts Page_size
- 22 Downloads / 270 Views
Attitude Estimation or Quaternion Estimation?1 F. Landis Markley?
Abstract The absence of a globally nonsingular three-parameter representation of the rotation group forces attitude Kalman filters to estimate either a singular or a redundant attitude representation. We compare two filtering strategies using simplified kinematics and measurement models. Our favored strategy estimates a three-parameter representation of attitude deviations from a reference attitude specified by a higher-dimensional nonsingular parameterization. The deviations from the reference are assumed to be small enough to avoid any singularity or discontinuity of the three-dimensional parameterization. We point out some disadvantages of the other strategy, which directly estimates the four-component quatemion representation.
Introduction Real-time spacecraft attitude estimation generally employs an Extended Kalman Filter (EKF) [1, 2]. Although the 3 X 3 orthogonal attitude matrix is the fundamental representation of the spacecraft's attitude, the orthogonality requirement imposes six constraints on its nine elements, reflecting the fact that the special orthogonal group SO(3) of rotation matrices has dimension three. Therefore, employing the nine elements of the attitude matrix as components of a state vector in a Kalman filter leads to some complexity in enforcing the constraints [3, 4]. Most EKFs use lower-dimensional parameterizations of SO(3), and several have used minimal three-dimensional parameterizations [5- 7]. However, it is a well-known fact that all three-parameter representations of SO(3) are singular or discontinuous for certain attitudes [8]. This has led to the use of higher-dimensional nonsingular parameterizations in EKFs, especially the four-component quatemion [9-13]. Reference [12] presents an overview of Kalman filtering for spacecraft attitude estimation, emphasizing the quatemion representation, with a complete list of references through 1981. The quatemion has the lowest dimensionality possible for a globally nonsingular representation of SO(3), but it still has one superfluous degree of freedom. Thus 'Dedicated to John L. Junkins on the occasion of his sixtieth birthday. 2Aerospace Engineer, Guidance, Navigation, and Control Systems Engineering Branch, Code 591, NASA Goddard Space Flight Center, Greenbelt, MD. Email: [email protected].
221
222
Markley
we are faced with the alternatives of using an attitude representation that is either singular or redundant. Various strategies to avoid or evade this dilemma have been proposed and analyzed [14-20], and we will consider two in this paper. The first strategy uses a nonsingular representation for a reference attitude and a threecomponent representation for the deviations from this reference, with the deviations assumed to be small enough to avoid any singularity or discontinuity of the three-dimensional parameterization. This method, known as the Multiplicative EKF (MEKF), has been discussed in detail in references [19] and [20]. The MEKF was first used in the
Data Loading...
