A Mathematical Framework for IMU Error Propagation with Applications to Preintegration

Abstract

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 SE 2 (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 SE 2 (3) when using noisy IMUs. Besides, our approach to extended poses combined with loglinearity 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.

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

“…This work improves the Euler integration scheme of [6] to limit discretization errors, whose integration schemes remain compatible with our approach based on exact discretization. This paper is an extension of our preliminary conference paper [8], see also early ideas in [45], that contains in-depth discussions, comprehensive technical derivations, numerical and real experiments, and publicly available implementation.…”

“…In this work, which is an extension of preliminary results [8], we define 5×5 matrices to model extended poses, and show how our approach allows transposing the framework dealing with the Lie group approach to pose uncertainty to the context of IMUs. Our contributions are as follows:…”

Calib-Net: Calibrating the Low-Cost IMU via Deep Convolutional Neural Network

“…They Rehder and Siegwart (2017) then further improved the calibration method by introducing the displacement of individual accelerometer axes into the mathematical noise model. Barrau and Bonnabel (2020) recently adopted Lie group for IMU error propagation. These calibration methods usually adopt different inertial model variants and estimate the parameters of these sensor error models.…”

The Turmell-Meter: In Vivo Ankle Kinematics by Using Draw-Wire and Inertial Sensors

“…Screw theory has been employed in biomechanics for human jaw characterization [28], [29] and characterization of instantaneous screws in a human knee [30]- [32]. Additionally, inertial measurement units have been applied in tracking limbs by referencing multiple sensors in [33]- [39]. There are different 3D ankle models in the literature; in our work, we focus on the two-axis approach, which is included in the International Biomechanics Society recommendations [40], anatomy and biomechanics books [41]- [45], and simulation software [46].…”