Full-Order Solution to the Attitude Reset Problem for Kalman Filtering of Attitudes

Abstract

Kalman filtering of states including attitudes poses a challenge due to the constraints of the rotation manifold. One of the standard approaches is to consider a deviation attitude, in the form of a reduced three-vector parametrization, to some nominal reference attitude that the Kalman filter tracks. After an update to the statistics of this deviation, a reset step is performed that adjusts the reference attitude. This reset step adjusts the statistics of the deviation, which has commonly been ignored in the literature. This paper presents an algorithm for the case when the deviation is represented as a rotation vector. The adjustment to the mean and covariance after the reset operation is presented, assessed using Monte Carlo sampling, and compared to other approaches used in the literature. The final result may be easily implemented and is computationally inexpensive. Connections and comparisons to the multiplicative extended Kalman filter, the unscented quaternion estimator, and Lie-group Kalman filters are made, with simulations performed on a rigid-body example.