  Attitude filtering is a critical technology with applications in diverse
domains such as aerospace engineering, robotics, computer vision, and augmented
reality. Although attitude filtering is a particular case of the state
estimation problem, attitude filtering is uniquely challenging due to the
special geometric structure of the attitude parameterization. This paper
presents a novel data-driven attitude filter, called the retrospective cost
attitude filter (RCAF), for the SO(3) attitude representation. Like the
multiplicative extended Kalman filter, RCAF uses a multiplicative correction
signal, but instead of computing correction gains using Jacobians, RCAF
computes the corrective signal using retrospective cost optimization and
measured data. The RCAF filter is validated numerically in a scenario with
noisy attitude measurements and noisy and biased rate-gyro measurements.
