Attitude estimation with feedback particle filter

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 matrix 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). 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, including the multiplicative EKF, the unscented quaternion estimator, the invariant EKF, and the invariant ensemble Kalman filter. Simulation results are presented that help illustrate the comparisons.