Extended information filter on matrix Lie groups

Abstract

In this paper we propose a new state estimation algorithm called the extended information filter on Lie groups. The proposed filter is inspired by the extended Kalman filter on Lie groups and exhibits the advantages of the information filter with regard to multisensor update and decentralization, while keeping the accuracy of stochastic inference on Lie groups. We present the theoretical development and demonstrate its performance on multisensor rigid body attitude tracking by forming the state space on the SO(3) × R 3 group, where the first and second component represent the orientation and angular rates, respectively. The performance of the filter is compared with respect to the accuracy of attitude tracking with parametrization based on Euler angles and with respect to execution time of the extended Kalman filter formulation on Lie groups. The results show that the filter achieves higher performance consistency and smaller error by tracking the state directly on the Lie group and that it keeps smaller computational complexity of the information form with respect to high number of measurements.

An EKF for Lie Groups with Application to Crane Load Dynamics

“…The derivation of the error dynamics relied on the Baker-Campbell-Hausdorff (BCH) formula, and involved time differentiation of the Lie group elements, and was quite involved. This was also investigated in (Cesic et al, 2017), where details of the development of the error dynamics of the D-EKF-LG filter were further investigated. The matrix Lie groups that were used in Bourmaud et al (2013Bourmaud et al ( , 2015 and Cesic et al (2017) included both configuration and velocity components.…”

“…This was also investigated in (Cesic et al, 2017), where details of the development of the error dynamics of the D-EKF-LG filter were further investigated. The matrix Lie groups that were used in Bourmaud et al (2013Bourmaud et al ( , 2015 and Cesic et al (2017) included both configuration and velocity components. In the case of SO(3) the resulting matrix Lie group was SO(3)×R 3 , where also the angular velocity was included in the group.…”

“…The main contribution of this paper is the formulation of an EKF for matrix Lie groups where the error dynamics is simplified compared to Bourmaud et al (2013Bourmaud et al ( , 2015 and Cesic et al (2017). We do this by using the kinematic differential equation of the logarithm directly in the error dynamics.…”

Exactly sparse delayed state filter on Lie groups for long-term pose graph SLAM

“…Fundamentally, we require the information form of the LG-EKF of Bourmaud et al (2015), and we need to be able to compute the augmentation and marginalization of a CGD. In Ćesić et al (2017) we solved the problem of the information form and proposed the LG-EIF. The augmentation and marginalization of the CGD were presented in Bourmaud et al (2016) in the context of iterated LG-EKF, where authors solved the prediction step by approximating the Chapman–Kolmogorov equation with a joint distribution and then marginalizing the posterior state.…”

“…However, following the idea of the information filter approach to LG-EIF of Ćesić et al (2017), rather than keeping the trajectory in the form of the matrix T n , we store the states in the form of concatenated Lie algebra frakturse ( 0.25em 3 ) elements…”