152 citations · 493 across the 22 of their papers we have counts for
27 papers
Invariant Kalman Filter for Relative Dynamics
Tejaswi K. C., Maneesha Wickramasuriya, Silvere Bonnabel +2
This paper develops a geometric framework for invariant filtering of relative dynamics on Lie groups. We first revisit the notion of state trajectory independence, under which the…
Invariant filtering for wheeled vehicle localization with unknown wheel radius and unknown GNSS lever arm
Paul Chauchat, Silvère Bonnabel, Axel Barrau
We consider the problem of observer design for a nonholonomic car (more generally a wheeled robot) equipped with wheel speeds with unknown wheel radius, and whose position is measu…
Iterated Invariant Extended Kalman Filter (IterIEKF)
Sven Goffin, Axel Barrau, Silvère Bonnabel +2
We study the mathematical properties of the Invariant Extended Kalman Filter (IEKF) when iterating on the measurement update step, following the principles of the well-known Iterat…
Invariant Smoothing for Localization: Including the IMU Biases
Paul Chauchat, Silvère Bonnabel, Axel Barrau
In this article we investigate smoothing (i.e., optimisation-based) estimation techniques for robot localization using an IMU aided by other localization sensors. We more particula…
Differentiable short-time Fourier transform with respect to the hop length
Maxime Leiber, Yosra Marnissi, Axel Barrau +1
In this paper, we propose a differentiable version of the short-time Fourier transform (STFT) that allows for gradient-based optimization of the hop length or the frame temporal po…
Differentiable adaptive short-time Fourier transform with respect to the window length
Maxime Leiber, Yosra Marnissi, Axel Barrau +1
This paper presents a gradient-based method for on-the-fly optimization for both per-frame and per-frequency window length of the short-time Fourier transform (STFT), related to pr…
Speeding up backpropagation of gradients through the Kalman filter via closed-form expressions
Colin Parellier, Axel Barrau, Silvere Bonnabel
In this paper we provide novel closed-form expressions enabling differentiation of any scalar function of the Kalman filter's outputs with respect to all its tuning parameters and…
A differentiable short-time Fourier transform with respect to the window length
Maxime Leiber, Axel Barrau, Yosra Marnissi +1
In this paper, we revisit the use of spectrograms in neural networks, by making the window length a continuous parameter optimizable by gradient descent instead of an empirically t…
Invariant Smoothing with low process noise
Paul Chauchat, Silvere Bonnabel, Axel Barrau
In this paper we address smoothing-that is, optimisation-based-estimation techniques for localisation problems in the case where motion sensors are very accurate. Our mathematical…
The Geometry of Navigation Problems
Axel Barrau, Silvere Bonnabel
While many works exploiting an existing Lie group structure have been proposed for state estimation, in particular the Invariant Extended Kalman Filter (IEKF), few papers address t…
Factor Graph-Based Smoothing Without Matrix Inversion for Highly Precise Localization
Paul Chauchat, Axel Barrau, Silvère Bonnabel
We consider the problem of localizing a manned, semi-autonomous, or autonomous vehicle in the environment using information coming from the vehicle's sensors, a problem known as na…
Associating Uncertainty to Extended Poses for on Lie Group IMU Preintegration with Rotating Earth
Martin Brossard, Axel Barrau, Paul Chauchat +1
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 "extend…
A Code for Unscented Kalman Filtering on Manifolds (UKF-M)
Martin Brossard, Axel Barrau, Silvere Bonnabel
The present paper introduces a novel methodology for Unscented Kalman Filtering (UKF) on manifolds that extends previous work by the authors on UKF on Lie groups. Beyond filtering…
A Mathematical Framework for IMU Error Propagation with Applications to Preintegration
Axel Barrau, Silvere Bonnabel
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…
Denoising IMU Gyroscopes with Deep Learning for Open-Loop Attitude Estimation
Martin Brossard, Silvere Bonnabel, Axel Barrau
This paper proposes a learning method for denoising gyroscopes of Inertial Measurement Units (IMUs) using ground truth data, and estimating in real time the orientation (attitude)…
Generalized mean shift with triangular kernel profile
Sébastien Razakarivony, Axel Barrau
The mean shift algorithm is a popular way to find modes of some probability density functions taking a specific kernel-based shape, used for clustering or visual tracking. Since it…
A New Approach to 3D ICP Covariance Estimation
Martin Brossard, Silvere Bonnabel, Axel Barrau
In mobile robotics, scan matching of point clouds using Iterative Closest Point (ICP) allows estimating sensor displacements. It may prove important to assess the associated uncert…
AI-IMU Dead-Reckoning
Martin Brossard, Axel Barrau, Silvère Bonnabel
In this paper we propose a novel accurate method for dead-reckoning of wheeled vehicles based only on an Inertial Measurement Unit (IMU). In the context of intelligent vehicles, ro…
Exploiting Symmetries to Design EKFs with Consistency Properties for Navigation and SLAM
Martin Brossard, Axel Barrau, Silvère Bonnabel
The Extended Kalman Filter (EKF) is both the historical algorithm for multi-sensor fusion and still state of the art in numerous industrial applications. However, it may prove inco…
RINS-W: Robust Inertial Navigation System on Wheels
Martin Brossard, Axel Barrau, Silvere Bonnabel
This paper proposes a real-time approach for long-term inertial navigation based only on an Inertial Measurement Unit (IMU) for self-localizing wheeled robots. The approach builds…
Invariant Smoothing on Lie Groups
Paul Chauchat, Axel Barrau, Silvère Bonnabel
In this paper we propose a (non-linear) smoothing algorithm for group-affine observation systems, a recently introduced class of estimation problems on Lie groups that bear a parti…
Symmetry reduction for dynamic programming
John Maidens, Axel Barrau, Silvere Bonnabel +1
We present a method of exploiting symmetries of discrete-time optimal control problems to reduce the dimensionality of dynamic programming iterations. The results are derived for s…
An EKF-SLAM algorithm with consistency properties
Axel Barrau, Silvere Bonnabel
In this paper we address the inconsistency of the EKF-based SLAM algorithm that stems from non-observability of the origin and orientation of the global reference frame. We prove o…
An intrinsic Cramér-Rao bound on Lie groups
Silvère Bonnabel, Axel Barrau
In his 2005 paper, S.T. Smith proposed an intrinsic Cramér-Rao bound on the variance of estimators of a parameter defined on a Riemannian manifold. In the present technical note, w…