An Invariant Extended H∞ Filter

Marc-Antoine Lavoie, Jonathan Arsenault, James Richard Forbes

Abstract: This paper presents an invariant extended H∞ filter for position and attitude estimation on the matrix Lie group SE (2). Extended H∞ filtering results are adapted to work directly within a matrix Lie group framework in an analogous way to how the invariant extended Kalman filter (IEKF) adapts the standard extended Kalman filter (EKF) to work within a matrix Lie group framework. The principal advantage of the invariant extended H∞ filter over the extended H∞ filter is that the linearization of the state and measurement models is independent of the current state estimate, leading to state-independent Jacobians at any linearization point. Moreover, for the SE (2) problem considered, the invariant extended H∞ filter realizes a substantially lower minimum performance bound γ than the standard extended H∞ filter.

External IDs:dblp:conf/cdc/LavoieAF19