Invariant EKF Design for Scan Matching-Aided Localization

Barczyk, Martin; Bonnabel, Silvère; Deschaud, Jean-Emmanuel; Goulette, François

doi:10.1109/tcst.2015.2413933

Cited by 42 publications

(35 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…bias, strictly limits the confidence we may have in the ICP estimate. To our best knowledge this is often omitted with a few exceptions: e.g., [14] removes bias on point measurements due to sensor beam angle, and preliminary ideas may be found in [10,11]. 4) Intern ICP Algorithm: ICP is generally configured with random processes [1], e.g.…”

Section: A Sources Of Icp Uncertaintymentioning

confidence: 99%

A New Approach to 3D ICP Covariance Estimation

Brossard

Bonnabel

Barrau

2020

IEEE Robot. Autom. Lett.

Self Cite

View full text Add to dashboard Cite

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 uncertainty about the obtained rigid transformation, especially for sensor fusion purposes. In this paper we propose a novel approach to 3D ICP covariance computation that accounts for all the sources of errors as listed in Censi's pioneering work, namely wrong convergence, underconstrained situations, and sensor noise. Our approach builds on two facts. First, ICP is not a standard sensor: owing to wrong convergence the concept of ICP covariance per se is actually meaningless, as the dispersion in the ICP outputs may largely depend on the accuracy of the initialization, and is thus inherently related to the prior uncertainty on the displacement. We capture this using the unscented transform, which also reflects correlations between initial and final uncertainties. Then, assuming white sensor noise leads to overoptimism: ICP is biased, owing to e.g. calibration biases, which we account for. Our solution is tested on publicly available real data ranging from structured to unstructured environments, where our algorithm predicts consistent results with actual uncertainty, and compares very favorably to previous methods. We finally demonstrate the benefits of our method for pose-graph localization, where our approach improves accuracy and robustness of the estimates.

show abstract

Section: A Sources Of Icp Uncertaintymentioning

confidence: 99%

A New Approach to 3D ICP Covariance Estimation

Brossard

Bonnabel

Barrau

2020

IEEE Robot. Autom. Lett.

Self Cite

View full text Add to dashboard Cite

show abstract

“…where K(x) ∈ G with coordinates E 1 · φ (x), ..., E d · φ (x) and according to (4), (E n · φ )(x) := d dτ τ=0 φ x exp(τ E n ) for n = 1, ..., d. The vector-field acts on a function f as,…”

Section: A Geometry Of Matrix Lie Groupsmentioning

confidence: 99%

“…In many cases, the constraints are described by smooth Riemannian manifolds, in particular the matrix Lie groups. Engineering applications of filtering on matrix Lie groups include: i) attitude estimation of aircrafts [29], [6]; ii) visual tracking of humans and objects [33], [17]; and iii) localization of mobile robots [4], [27]. In these applications, the matrix Lie groups of interest include the special orthogonal group SO(3) and the special Euclidean group SE(3).…”

Section: Introductionmentioning

confidence: 99%

Feedback particle filter on matrix lie groups

Zhang

Taghvaei

Mehta

2016

2016 American Control Conference (ACC)

View full text Add to dashboard Cite

This paper is concerned with the problem of continuous-time nonlinear filtering for stochastic processes on a connected matrix Lie group. The main contribution of this paper is to derive the feedback particle filter (FPF) algorithm for this problem. In its general form, the FPF is shown to provide a coordinate-free description of the filter that automatically satisfies the geometric constraints of the manifold. The particle dynamics are encapsulated in a Stratonovich stochastic differential equation that retains the feedback structure of the original (Euclidean) FPF. The implementation of the filter requires a solution of a Poisson equation on the Lie group, and two numerical algorithms are described for this purpose. As an example, the FPF is applied to the problem of attitude estimation -a nonlinear filtering problem on the Lie group SO(3). The formulae of the filter are described using both the rotation matrix and the quaternion coordinates. Comparisons are also provided between the FPF and some popular algorithms for attitude estimation, namely the multiplicative EKF, the unscented quaternion estimator, the left invariant EKF, and the invariant ensemble Kalman filter. Numerical simulations are presented to illustrate the comparisons.

show abstract

“…Although dynamical systems possessing symmetries have been studied in control theory, few results taking benefit of system invariances for observers design exist today. Invariant nonlinear estimation theory appears so as a young research area in which the first main contributions can be dated from the beginning of 2000s ( [1], [3], [2], [5], [4], [6], [8], [9], [15], [10], [11], [17], [18] This optimality must be considered here w.r.t. an invariant state estimation error which will be defined precisely further.…”

Section: Introductionmentioning

confidence: 99%