Proceedings ArticleDOI
Left-invariant extended Kalman filter and attitude estimation
Silvere Bonnabel
- pp 1027-1032
TLDR
A left- invariant (i.e, intrinsic and thus symmetry-preserving) extended Kalman filter such that the left-invariant estimation error obeys a stochastic differential equation independent of the system trajectory.Abstract:
We consider a left-invariant dynamics on a Lie group. One way to define driving and observation noises is to make them preserve the symmetries. We propose a left- invariant (i.e, intrinsic and thus symmetry-preserving) extended Kalman filter such that the left-invariant estimation error obeys a stochastic differential equation independent of the system trajectory. The theory is illustrated by an attitude estimation example.read more
Citations
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Journal ArticleDOI
Stochastic Processes in Physics and Chemistry
TL;DR: Van Kampen as mentioned in this paper provides an extensive graduate-level introduction which is clear, cautious, interesting and readable, and could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes.
Journal ArticleDOI
The Invariant Extended Kalman Filter as a Stable Observer
Axel Barrau,Silvere Bonnabel +1 more
TL;DR: In this article, the authors analyzed the convergence aspects of the invariant extended Kalman filter (IEKF) when the latter is used as a deterministic nonlinear observer on Lie groups, for continuous-time systems with discrete observations.
Posted Content
The invariant extended Kalman filter as a stable observer
Axel Barrau,Silvere Bonnabel +1 more
TL;DR: This paper analyzes the convergence aspects of the invariant extended Kalman filter (IEKF), when the latter is used as a deterministic nonlinear observer on Lie groups, for continuous-time systems with discrete observations.
Proceedings ArticleDOI
Invariant Extended Kalman Filter: theory and application to a velocity-aided attitude estimation problem
TL;DR: A new version of the extended Kalman filter (EKF) is proposed for nonlinear systems possessing symmetries, which uses a geometrically adapted correction term based on an invariant output error to result in a better convergence of the estimation.
Journal ArticleDOI
Attitude estimation for accelerated vehicles using GPS/INS measurements
Minh-Duc Hua,Minh-Duc Hua +1 more
TL;DR: In this paper, an advanced attitude observer for rigid bodies evolving in 3D-space using GPS-velocity and INS measurements has been proposed without specifying its domain of convergence and stability.
References
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Book
Stochastic processes in physics and chemistry
TL;DR: In this article, the authors introduce the Fokker-planck equation, the Langevin approach, and the diffusion type of the master equation, as well as the statistics of jump events.
Stochastic Processes in Physics and Chemistry
Abstract: Preface to the first edition. Preface to the second edition. Abbreviated references. I. Stochastic variables. II. Random events. III. Stochastic processes. IV. Markov processes. V. The master equation. VI. One-step processes. VII. Chemical reactions. VIII. The Fokker-Planck equation. IX. The Langevin approach. X. The expansion of the master equation. XI. The diffusion type. XII. First-passage problems. XIII. Unstable systems. XIV. Fluctuations in continuous systems. XV. The statistics of jump events. XVI. Stochastic differential equations. XVII. Stochastic behavior of quantum systems.
Journal ArticleDOI
Stochastic Processes in Physics and Chemistry
TL;DR: Van Kampen as mentioned in this paper provides an extensive graduate-level introduction which is clear, cautious, interesting and readable, and could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes.
Proceedings ArticleDOI
Complementary filter design on the special orthogonal group SO(3)
TL;DR: In this article, two different non-linear complementary filters are proposed: Direct complementary filter and Passive nonlinear complementary filter, which evolve explicity on the special orthogonal group SO(3) and can be expressed in quaternion form for easy implementation.
Journal ArticleDOI
Symmetry-Preserving Observers
TL;DR: Using the theory of invariant observers, i.e, symmetry-preserving observers, three non-linear observers are built for three examples of engineering interest: a non-holonomic car, a chemical reactor, and an inertial navigation system.