Associating Uncertainty to Extended Poses for on Lie Group IMU Preintegration with Rotating Earth

TL;DR

This paper develops a theory to associate uncertainty with extended poses in 3D space using the SE2(3) matrix group, improving IMU preintegration accuracy by accounting for Earth's rotation in long-term navigation.

Contribution

It introduces a novel method to propagate uncertainty on the SE2(3) group for IMU states, including exact formulas considering Earth's rotation, enhancing long-term navigation accuracy.

Findings

Uncertainty propagation on SE2(3) improves IMU state estimation.

Exact preintegration formulas with Earth's rotation increase accuracy.

Sensor fusion experiments demonstrate benefits for long-term navigation.

Abstract

The recently introduced matrix group SE2(3) provides a 5x5 matrix representation for the orientation, velocity and position of an object in the 3-D space, a triplet we call "extended pose". In this paper we build on this group to develop a theory to associate uncertainty with extended poses represented by 5x5 matrices. Our approach is particularly suited to describe how uncertainty propagates when the extended pose represents the state of an Inertial Measurement Unit (IMU). In particular it allows revisiting the theory of IMU preintegration on manifold and reaching a further theoretic level in this field. Exact preintegration formulas that account for rotating Earth, that is, centrifugal force and Coriolis force, are derived as a byproduct, and the factors are shown to be more accurate. The approach is validated through extensive simulations and applied to sensor-fusion where a loosely-coupled fixed-lag smoother fuses IMU and LiDAR on one hour long experiments using our experimental car. It shows how handling rotating Earth may be beneficial for long-term navigation within incremental smoothing algorithms.