Unscented Filtering for Spacecraft Attitude Estimation

Abstract

A new spacecraft attitude estimation approach based on the Unscented Filter is derived. For nonlinear systems the Unscented Filter uses a carefully selected set of sample points to more accurately map the probability distribution than the linearization of the standard Extended Kalman Filter, leading to faster convergence from inaccurate initial conditions in attitude estimation problems. The filter formulation is based on standard attitude-vector measurements using a gyro-based model for attitude propagation. The global attitude parameterization is given by a quaternion, while a generalized three-dimensional attitude representation is used to define the local attitude error. A multiplicative quaternion-error approach is derived from the local attitude error, which guarantees that quaternion normalization is maintained in the filter. Simulation results indicate that the Unscented Filter is more robust than the Extended Kalman Filter under realistic initial attitude-error conditions.

Global optimal attitude estimation using uncertainty ellipsoids

“…by the definition of the uncertainty ellipsoid given in (12). Then we can show that A f k x k lies in the following uncertainty ellipsoid.…”

“…Most existing attitude estimation schemes use generalized coordinate representations of the attitude. As is well known, minimal coordinate representations of the rotation group, like Euler angles, Rodrigues parameters, and modified Rodrigues parameters (see [12]), usually lead to geometric or kinematic singularities. Non-minimal coordinate representations, like the unit quaternions used in the quaternion estimation (QUEST) algorithm [7] and its several variants [4,8,13], have their own associated problems.…”

Nanosatellite Attitude Estimation from Vector Measurements Using SVD-Aided UKF Algorithm

“…In the reference [24], the authors overcome this problem by using an unconstrained threecomponent vector to represent an attitude-error quaternion instead of using all four components of the quaternion vector. They represent the local error-quaternion by the vector of Generalized Rodrigues Parameters (GRP).…”

“…The essence is the fact that the approximation of a nonlinear distribution is easier than the approximation of a nonlinear function or transformation. The conventional algorithm for the UKF is not presented here for brevity and the reader may refer to [24], specifically for attitude estimation using the UKF.…”

“…When 0 a = and 1 f = then (21) gives the Gibbs vector, whereas when 1 a = and 1 f = then (21) gives the standard vector of modified Rodrigues parameters. In the paper [24] − as well as in this paper − f is chosen as 2( 1) f a = + . The inverse transformation from δ p to δ q is given by:…”