  This paper presents theory, application, and comparisons of the feedback
particle filter (FPF) algorithm for the problem of attitude estimation. The
paper builds upon our recent work on the exact FPF solution of the
continuous-time nonlinear filtering problem on compact Lie groups. In this
paper, the details of the FPF algorithm are presented for the problem of
attitude estimation - a nonlinear filtering problem on SO(3). The quaternions
are employed for computational purposes. The algorithm requires a numerical
solution of the filter gain function, and two methods are applied for this
purpose. Comparisons are also provided between the FPF and some popular
algorithms for attitude estimation on SO(3), including the invariant EKF, the
multiplicative EKF, and the unscented Kalman filter. Simulation results are
presented that help illustrate the comparisons.
