Invariant extended Kalman filter on matrix Lie groups Abstract   We derive symmetry preserving invariant extended Kalman filters (IEKF) on matrix Lie groups. These Kalman filters have an advantage over conventional extended Kalman filters as the error dynamics for such filters are independent of the group configuration which, in turn, provides a uniform estimate of the region of convergence. The proposed IEKF differs from existing techniques in literature on the account that it is derived using minimal tools from differential geometry that simplifies its representation and derivation to a large extent. The filter error dynamics is defined on the Lie algebra directly instead of identifying the Lie algebra with an Euclidean space or defining the error dynamics in local coordinates using exponential map, and the associated differential Riccati equations are described on the corresponding space of linear operators using tensor algebra. The proposed filter is implemented for the attitude dynamics of the rigid body, which is a benchmark problem in control, and its performance is compared against a conventional extended Kalman filter (EKF). Numerical experiments support that the IEKF is computationally less intensive and gives better performance than the EKF.

A Novel FuzzyAdaptive Extended Kalman Filter for RealTime Attitude Estimation of Mobile Robots This paper proposes a novel fuzzyadaptive extended Kalman filter (FAEKF) for the realtime attitude estimation of agile mobile platforms equipped with magnetic, angular rate, and gravity (MARG) sensor arrays. The filter structure employs both a quaternionbased EKF and an adaptive extension, in which novel measurement methods are used to calculate the magnitudes of system vibrations, external accelerations, and magnetic distortions. These magnitudes, as external disturbances, are incorporated into a sophisticated fuzzy inference machine, which executes fuzzy IFTHEN rulesbased adaption laws to consistently modify the noise covariance matrices of the filter, thereby providing accurate and robust attitude results. A sixdegrees of freedom (6 DOF) test bench is designed for filter performance evaluation, which executes various dynamic behaviors and enables measurement of the true attitude angles (ground truth) along with the raw MARG sensor data. The tuning of filter parameters is performed with numerical optimization based on the collected measurements from the test environment. A comprehensive analysis highlights that the proposed adaptive strategy significantly improves the attitude estimation quality. Moreover, the filter structure successfully rejects the effects of both slow and fast external perturbations. The FAEKF can be applied to any mobile system in which attitude estimation is necessary for localization and external disturbances greatly influence the filter accuracy.