359 citations · 1.4k across the 40 of their papers we have counts for
11 papers · 1 filter
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…
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 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…
Invariant EKF Design for Scan Matching-aided Localization
Martin Barczyk, Silvère Bonnabel, Jean-Emmanuel Deschaud +1
Localization in indoor environments is a technique which estimates the robot's pose by fusing data from onboard motion sensors with readings of the environment, in our case obtaine…
The invariant extended Kalman filter as a stable observer
Axel Barrau, Silvère Bonnabel
We analyze the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic non-linear observer on Lie groups, for continuous-time…
Experimental Implementation of an Invariant Extended Kalman Filter-based Scan Matching SLAM
Martin Barczyk, Silvère Bonnabel, Jean-Emmanuel Deschaud +1
We describe an application of the Invariant Extended Kalman Filter (IEKF) design methodology to the scan matching SLAM problem. We review the theoretical foundations of the IEKF an…
Optimal cooperative motion planning for vehicles at intersections
Jean Gregoire, Silvère Bonnabel, Arnaud de La Fortelle
We consider the problem of cooperative intersection management. It arises in automated transportation systems for people or goods but also in multi-robots environment. Therefore ma…
Intrinsic filtering on Lie groups with applications to attitude estimation
Axel Barrau, Silvere Bonnabel
This paper proposes a probabilistic approach to the problem of intrinsic filtering of a system on a matrix Lie group with invariance properties. The problem of an invariant continu…
A contraction theory-based analysis of the stability of the Extended Kalman Filter
Silvere Bonnabel, Jean-Jacques Slotine
The contraction properties of the Extended Kalman Filter, viewed as a deterministic observer for nonlinear systems, are analyzed. This yields new conditions under which exponential…