Equivariant Filter (EqF)

The kinematics of many systems encountered in robotics, mechatronics, and avionics are naturally posed on homogeneous spaces; i.e., their state lies in a smooth manifold equipped with a transitive Lie group symmetry. This article proposes a novel filter, the equivariant filter (EqF), by posing the observer state on the symmetry group, linearizing global error dynamics derived from the equivariance of the system, and applying EKF design principles. We show that equivariance of the system output can be exploited to reduce linearization error and improve filter performance. Simulation experiments of an example application show that the EqF significantly outperforms the EKF and that the reduced linearization error leads to a clear improvement in performance.