An Invariant Extended H∞ Filter

Abstract

This paper presents an invariant extended ${\\mathcal{H}_\\infty }$ filter for position and attitude estimation on the matrix Lie group SE (2). Extended ${\\mathcal{H}_\\infty }$ 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 ${\\mathcal{H}_\\infty }$ filter over the extended ${\\mathcal{H}_\\infty }$ 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 ${\\mathcal{H}_\\infty }$ filter realizes a substantially lower minimum performance bound γ than the standard extended ${\\mathcal{H}_\\infty }$ filter.