Near-optimal deterministic attitude filtering

A deterministic attitude filter is derived based on the principles of minimum-energy filtering. The proposed filter is applied to the attitude kinematics of a rigid body in 3D space and is posed directly on the rotation group SO(3). The proposed filter generalizes recently published work by Coote et al. on deterministic filtering on the unit circle. The filter is near-optimal in the sense that it achieves a cost that is close to the cost incurred by a minimum-energy filter. We provide an explicit bound on the difference in cost occurred by the proposed filter vs. an optimal filter and show that this bound is small by means of simulations. We compare the performance of the proposed filter with a quaternion implementation of an Extended Kalman Filter (EKF). While achieving comparable results to an EKF, the proposed filter shows more robustness against a range of deterministic disturbance levels and initialization errors.