Invariant Extended Kalman Filtering for Underwater Navigation

Easton Potokar, Kalin Norman, Joshua G Mangelson

Abstract:

Recent advances in the utilization of Lie Groups for
robotic localization have led to dramatic increases in the accuracy
of estimation and uncertainty characterization. One of the novel
methods, the Invariant Extended Kalman Filter (InEKF) extends
the Extended Kalman Filter (EKF) by leveraging the fact that some
error dynamics defined on matrix Lie Groups satisfy a log-linear
differential equation. Utilization of these observations result in
linearization with minimal approximation error, no dependence
on current state estimates, and excellent convergence and accuracy
properties. In this letter we show that the primary sensors used for
underwater localization, inertial measurement units (IMUs) and
doppler velocity logs (DVLs) meet the requirements of the InEKF.
Furthermore, we show that singleton measurements, such as depth,
can also be used in the InEKF update with minor modifications,
thus expanding the set of measurements usable in an InEKF. We
compare convergence, accuracy and timing results of the InEKF
to a quaternion-based EKF using a Monte Carlo simulation and
show notable improvements in long-term localization and much
faster convergence with negligible difference in computation time.

Index Terms—Unmanned underwater vehicles, filtering
algorithms, state estimation, computational geometry.