# A Mathematical Framework for IMU Error Propagation with Applications to Preintegration

arXiv: https://arxiv.org/abs/2003.03908 · HTML: https://mlsanity.com/paper/2003.03908/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2020.

## Built on by (most cited first, 1 of 1)

- [Layout Sequence Prediction From Noisy Mobile Modality](https://mlsanity.com/paper/2310.06138/) (2023)

## Abstract (arXiv)

To fuse information from inertial measurement units (IMU) with other sensors one needs an accurate model for IMU error propagation in terms of position, velocity and orientation, a triplet we call extended pose. In this paper we leverage a nontrivial result, namely log-linearity of inertial navigation equations based on the recently introduced Lie group SE2(3), to transpose the recent methodology of Barfoot and Furgale for associating uncertainty with poses (position, orientation) of SE(3) when using noisy wheel speeds, to the case of extended poses (position, velocity, orientation) of SE2(3) when using noisy IMUs. Besides, our approach to extended poses combined with log-linearity property allows revisiting the theory of preintegration on manifolds and reaching a further theoretic level in this field. We show exact preintegration formulas that account for rotating Earth, that is, centrifugal force and Coriolis effect, may be derived as a byproduct.