Invariant Sliding Window Filtering for Attitude and Bias Estimation

Abstract

This paper considers sliding window filtering in an invariant framework for estimation of attitude and rate gyro bias in a matrix Lie group formulation. The multiplicative extended Kalman filter (MEKF) and invariant extended Kalman filter (IEKF), variants of the extended Kalman filter well suited to estimation on matrix Lie groups, are discussed. The sliding window formulation of both the MEKF and IEKF is presented, leading to the sliding window filter (SWF), the invariant SWF (ISWF), and the imperfect ISWF for systems that are not group affine. Simulation results for an attitude and heading reference system with bias are presented, comparing the ISWF to the traditional $\mathbf{SWF,}$ MEKF, and IEKF.