Covariance regulation based invariant Kalman filtering for attitude estimation on matrix Lie groups

For matrix Lie groups attitude estimation problems with the trouble of unknown/inaccurate process noise covariance, by elaborating the proportion based covariance regulation scheme, this work proposes a novel version of adaptive invariant Kalman filter (AIKF). Invariant Kalman filter (IKF) takes into account the group geometry and can give better results than Euclidean Kalman filters, but it still heavily depends on the accuracy of noise statistics parameters. To ease this constraint, IKF's covariance propagation step is removed and a proportional regulation scheme is elaborated for the proposed AIKF: the feedback of posterior sequence is introduced to construct a closed-loop structure of covariance propagation, and then a proportional regulator is employed to amplify the feedback and accelerate the convergence of covariance calibration. As the main benefit, implementation of new AIKF does not require the accurate knowledge of noise statistics, which is also the main advantage over IKF. The mathematical derivation of proposed covariance regulation scheme is presented and the numerical simulations of the Lie groups attitude estimation problem are used to certify the filtering performance of the new approach.