152 citations · 493 across the 22 of their papers we have counts for
9 papers · 1 filter
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…
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 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…
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…
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…